DP Physics (last assessment 2024)

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Option B: Engineering physics

Option B: Engineering physics

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20N.3.SL.TZ0.6d:
The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
20N.3.SL.TZ0.6d:
The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
20N.3.SL.TZ0.d:
The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
20N.3.SL.TZ0.7b: Explain the changes to the rotational kinetic energy in the person-turntable system.
20N.3.SL.TZ0.7b: Explain the changes to the rotational kinetic energy in the person-turntable system.
20N.3.SL.TZ0.b: Explain the changes to the rotational kinetic energy in the person-turntable system.
20N.3.SL.TZ0.8:
A solid sphere of radius $r$ and mass $m$ is released from rest and rolls down a slope, without slipping. The vertical height of the slope is $h$ . The moment of inertia $I$ of this sphere about an axis through its centre is $\frac{2}{5} m r^{2}$ .

Show that the linear velocity $v$ of the sphere as it leaves the slope is $\sqrt{\frac{10 g h}{7}}$ .
20N.3.SL.TZ0.8:
A solid sphere of radius $r$ and mass $m$ is released from rest and rolls down a slope, without slipping. The vertical height of the slope is $h$ . The moment of inertia $I$ of this sphere about an axis through its centre is $\frac{2}{5} m r^{2}$ .

Show that the linear velocity $v$ of the sphere as it leaves the slope is $\sqrt{\frac{10 g h}{7}}$ .
20N.3.SL.TZ0.7a:
Explain the direction in which the person-turntable system starts to rotate.
20N.3.SL.TZ0.7a:
Explain the direction in which the person-turntable system starts to rotate.
20N.3.SL.TZ0.a:
Explain the direction in which the person-turntable system starts to rotate.
20N.3.SL.TZ0.9a(i):
Calculate the work done during the compression.
20N.3.SL.TZ0.9a(i):
Calculate the work done during the compression.
20N.3.SL.TZ0.a(i):
Calculate the work done during the compression.
20N.3.SL.TZ0.9a(ii):
Calculate the work done during the increase in pressure.
20N.3.SL.TZ0.9a(ii):
Calculate the work done during the increase in pressure.
20N.3.SL.TZ0.a(ii):
Calculate the work done during the increase in pressure.
20N.3.HL.TZ0.12a: State two properties of an ideal fluid.
20N.3.HL.TZ0.12a: State two properties of an ideal fluid.
20N.3.HL.TZ0.a: State two properties of an ideal fluid.
20N.3.HL.TZ0.12c(i):
Determine the force exerted by the spring on the sphere when the sphere is at rest.
20N.3.HL.TZ0.12c(i):
Determine the force exerted by the spring on the sphere when the sphere is at rest.
20N.3.HL.TZ0.c(i):
Determine the force exerted by the spring on the sphere when the sphere is at rest.
20N.3.HL.TZ0.12c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by $10 %$ . Calculate the $Q$ factor for this system.
20N.3.HL.TZ0.12c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by $10 %$ . Calculate the $Q$ factor for this system.
20N.3.HL.TZ0.c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by $10 %$ . Calculate the $Q$ factor for this system.
17N.3.HL.TZ0.12b: Outline what change would be required to the value of Q for the mass–spring system in order for...
17N.3.HL.TZ0.12b: Outline what change would be required to the value of Q for the mass–spring system in order for...
17N.3.HL.TZ0.b: Outline what change would be required to the value of Q for the mass–spring system in order for...
17N.3.HL.TZ0.11b:
The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m^–3 to 785.16 kg m^–3. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.
17N.3.HL.TZ0.11b:
The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m^–3 to 785.16 kg m^–3. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.
17N.3.HL.TZ0.b:
The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m^–3 to 785.16 kg m^–3. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.
17N.3.SL.TZ0.10c:
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
17N.3.SL.TZ0.10c:
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
17N.3.SL.TZ0.c:
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
17N.3.SL.TZ0.11a.i: Identify the mechanism leading stars to produce the light they emit.
17N.3.SL.TZ0.11a.i: Identify the mechanism leading stars to produce the light they emit.
17N.3.SL.TZ0.a.i: Identify the mechanism leading stars to produce the light they emit.
17N.3.SL.TZ0.11a.ii:
Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.
17N.3.SL.TZ0.11a.ii:
Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.
17N.3.SL.TZ0.a.ii:
Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.
17N.3.SL.TZ0.11b.i: Outline what is meant by a constellation.
17N.3.SL.TZ0.11b.i: Outline what is meant by a constellation.
17N.3.SL.TZ0.b.i: Outline what is meant by a constellation.
17N.3.SL.TZ0.11b.iii:
Show that the distance to Vega from Earth is about 25 ly.
17N.3.SL.TZ0.11b.iii:
Show that the distance to Vega from Earth is about 25 ly.
17N.3.SL.TZ0.b.iii:
Show that the distance to Vega from Earth is about 25 ly.
17N.3.HL.TZ0.11a.i:
Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.
17N.3.HL.TZ0.11a.i:
Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.
17N.3.HL.TZ0.a.i:
Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.
17N.3.HL.TZ0.12a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.
17N.3.HL.TZ0.12a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.
17N.3.HL.TZ0.a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.
17N.3.SL.TZ0.7b:
Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{{g \times \sin q}}{2}$
17N.3.SL.TZ0.7b:
Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{{g \times \sin q}}{2}$
17N.3.SL.TZ0.b:
Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{{g \times \sin q}}{2}$
17N.3.SL.TZ0.7c: Calculate the acceleration of the hoop when θ = 20°. Assume that the hoop continues to roll...
17N.3.SL.TZ0.7c: Calculate the acceleration of the hoop when θ = 20°. Assume that the hoop continues to roll...
17N.3.SL.TZ0.c: Calculate the acceleration of the hoop when θ = 20°. Assume that the hoop continues to roll...
17N.3.SL.TZ0.8b: Using the axes, sketch the three-step cycle.
17N.3.SL.TZ0.8b: Using the axes, sketch the three-step cycle.
17N.3.SL.TZ0.b: Using the axes, sketch the three-step cycle.
17N.3.SL.TZ0.7e:
The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.
17N.3.SL.TZ0.7e:
The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.
17N.3.SL.TZ0.e:
The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.
17N.3.SL.TZ0.7d:
State the relationship between the force of friction and the angle of the incline.
17N.3.SL.TZ0.7d:
State the relationship between the force of friction and the angle of the incline.
17N.3.SL.TZ0.d:
State the relationship between the force of friction and the angle of the incline.
17N.3.SL.TZ0.8a:
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.
17N.3.SL.TZ0.8a:
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.
17N.3.SL.TZ0.a:
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.
17N.3.SL.TZ0.8d:
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
17N.3.SL.TZ0.8d:
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
17N.3.SL.TZ0.d:
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
17N.3.HL.TZ0.11a.ii:
When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m^–3. Calculate the percentage of the sphere volume filled by water.
17N.3.HL.TZ0.11a.ii:
When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m^–3. Calculate the percentage of the sphere volume filled by water.
17N.3.HL.TZ0.a.ii:
When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m^–3. Calculate the percentage of the sphere volume filled by water.
17N.3.SL.TZ0.7a: On the diagram, draw and label the forces acting on the hoop.
17N.3.SL.TZ0.7a: On the diagram, draw and label the forces acting on the hoop.
17N.3.SL.TZ0.a: On the diagram, draw and label the forces acting on the hoop.
17N.3.SL.TZ0.6a: Explain what is meant by proper length.
17N.3.SL.TZ0.6a: Explain what is meant by proper length.
17N.3.SL.TZ0.a: Explain what is meant by proper length.
17N.3.SL.TZ0.8c:
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
17N.3.SL.TZ0.8c:
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
17N.3.SL.TZ0.c:
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
18M.3.HL.TZ1.10c.ii:
Outline whether it is reasonable to assume that flow is laminar in this situation.
18M.3.HL.TZ1.10c.ii:
Outline whether it is reasonable to assume that flow is laminar in this situation.
18M.3.HL.TZ1.c.ii:
Outline whether it is reasonable to assume that flow is laminar in this situation.
18M.3.HL.TZ1.10a:
State the difference in terms of the velocity of the water between laminar and turbulent flow.
18M.3.HL.TZ1.10a:
State the difference in terms of the velocity of the water between laminar and turbulent flow.
18M.3.HL.TZ1.a:
State the difference in terms of the velocity of the water between laminar and turbulent flow.
18M.3.HL.TZ1.10b:
The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.

Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = $\sqrt {2gH}$ .
18M.3.HL.TZ1.10b:
The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.

Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = $\sqrt {2gH}$ .
18M.3.HL.TZ1.b:
The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.

Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = $\sqrt {2gH}$ .
18M.3.HL.TZ1.10c.i:
Calculate the Reynolds number for the water flow.
18M.3.HL.TZ1.10c.i:
Calculate the Reynolds number for the water flow.
18M.3.HL.TZ1.c.i:
Calculate the Reynolds number for the water flow.
18M.3.HL.TZ1.11a:
Describe the motion of the spring-mass system.
18M.3.HL.TZ1.11a:
Describe the motion of the spring-mass system.
18M.3.HL.TZ1.a:
Describe the motion of the spring-mass system.
18M.3.HL.TZ1.11b.ii:
calculate the Q at the start of the motion.
18M.3.HL.TZ1.11b.ii:
calculate the Q at the start of the motion.
18M.3.HL.TZ1.b.ii:
calculate the Q at the start of the motion.
18M.3.SL.TZ2.7d.ii:
Outline the change in entropy of the gas during the cooling at constant volume.
18M.3.SL.TZ2.7d.ii:
Outline the change in entropy of the gas during the cooling at constant volume.
18M.3.SL.TZ2.d.ii:
Outline the change in entropy of the gas during the cooling at constant volume.
18M.3.HL.TZ2.10b.ii:
Outline whether your answer to (a) is valid.
18M.3.HL.TZ2.10b.ii:
Outline whether your answer to (a) is valid.
18M.3.HL.TZ2.b.ii:
Outline whether your answer to (a) is valid.
18M.3.HL.TZ2.10a:
Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.
18M.3.HL.TZ2.10a:
Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.
18M.3.HL.TZ2.a:
Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.
18M.3.HL.TZ2.10b.i:
Estimate the Reynolds number for the fluid in your answer to (a).
18M.3.HL.TZ2.10b.i:
Estimate the Reynolds number for the fluid in your answer to (a).
18M.3.HL.TZ2.b.i:
Estimate the Reynolds number for the fluid in your answer to (a).
18M.3.HL.TZ2.11a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
18M.3.HL.TZ2.11a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
18M.3.HL.TZ2.a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
18M.3.HL.TZ2.11b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
18M.3.HL.TZ2.11b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
18M.3.HL.TZ2.b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
18M.3.SL.TZ2.6a.ii:
In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.
18M.3.SL.TZ2.6a.ii:
In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.
18M.3.SL.TZ2.a.ii:
In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.
18M.3.SL.TZ2.6b.ii:
Describe the effect of F on the angular speed of the wheel.
18M.3.SL.TZ2.6b.ii:
Describe the effect of F on the angular speed of the wheel.
18M.3.SL.TZ2.b.ii:
Describe the effect of F on the angular speed of the wheel.
18M.3.SL.TZ2.7b:
Calculate, in J, the work done by the gas during this expansion.
18M.3.SL.TZ2.7b:
Calculate, in J, the work done by the gas during this expansion.
18M.3.SL.TZ2.b:
Calculate, in J, the work done by the gas during this expansion.
18M.3.SL.TZ2.7e:
There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.
18M.3.SL.TZ2.7e:
There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.
18M.3.SL.TZ2.e:
There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.
18M.3.SL.TZ2.6a.i:
The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.
18M.3.SL.TZ2.6a.i:
The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.
18M.3.SL.TZ2.a.i:
The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.
18M.3.SL.TZ2.6a.iii:
Determine the angular velocity of the wheel at B.
18M.3.SL.TZ2.6a.iii:
Determine the angular velocity of the wheel at B.
18M.3.SL.TZ2.a.iii:
Determine the angular velocity of the wheel at B.
18M.3.SL.TZ2.7a:
Show that the final volume of the gas is about 53 m³.
18M.3.SL.TZ2.7a:
Show that the final volume of the gas is about 53 m³.
18M.3.SL.TZ2.a:
Show that the final volume of the gas is about 53 m³.
18M.3.SL.TZ2.7c:
Determine the thermal energy which enters the gas during this expansion.
18M.3.SL.TZ2.7c:
Determine the thermal energy which enters the gas during this expansion.
18M.3.SL.TZ2.c:
Determine the thermal energy which enters the gas during this expansion.
18M.3.SL.TZ1.6b.i:
Calculate, for the merry-go-round after one revolution, the angular speed.
18M.3.SL.TZ1.6b.i:
Calculate, for the merry-go-round after one revolution, the angular speed.
18M.3.SL.TZ1.b.i:
Calculate, for the merry-go-round after one revolution, the angular speed.
18M.3.SL.TZ1.6b.ii:
Calculate, for the merry-go-round after one revolution, the angular momentum.
18M.3.SL.TZ1.6b.ii:
Calculate, for the merry-go-round after one revolution, the angular momentum.
18M.3.SL.TZ1.b.ii:
Calculate, for the merry-go-round after one revolution, the angular momentum.
18M.3.SL.TZ1.6c:
Calculate the new angular speed of the rotating system.
18M.3.SL.TZ1.6c:
Calculate the new angular speed of the rotating system.
18M.3.SL.TZ1.c:
Calculate the new angular speed of the rotating system.
18M.3.SL.TZ1.6d.i:
Explain why the angular speed will increase.
18M.3.SL.TZ1.6d.i:
Explain why the angular speed will increase.
18M.3.SL.TZ1.d.i:
Explain why the angular speed will increase.
18M.3.SL.TZ1.6d.ii:
Calculate the work done by the child in moving from the edge to the centre.
18M.3.SL.TZ1.6d.ii:
Calculate the work done by the child in moving from the edge to the centre.
18M.3.SL.TZ1.d.ii:
Calculate the work done by the child in moving from the edge to the centre.
18M.3.SL.TZ1.7a:
Show that the pressure at B is about 5 × 10⁵ Pa.
18M.3.SL.TZ1.7a:
Show that the pressure at B is about 5 × 10⁵ Pa.
18M.3.SL.TZ1.a:
Show that the pressure at B is about 5 × 10⁵ Pa.
18M.3.SL.TZ1.7b.i:
For the process BC, calculate, in J, the work done by the gas.
18M.3.SL.TZ1.7b.i:
For the process BC, calculate, in J, the work done by the gas.
18M.3.SL.TZ1.b.i:
For the process BC, calculate, in J, the work done by the gas.
18M.3.SL.TZ1.7b.ii:
For the process BC, calculate, in J, the change in the internal energy of the gas.
18M.3.SL.TZ1.7b.ii:
For the process BC, calculate, in J, the change in the internal energy of the gas.
18M.3.SL.TZ1.b.ii:
For the process BC, calculate, in J, the change in the internal energy of the gas.
18M.3.SL.TZ1.7b.iii:
For the process BC, calculate, in J, the thermal energy transferred to the gas.
18M.3.SL.TZ1.7b.iii:
For the process BC, calculate, in J, the thermal energy transferred to the gas.
18M.3.SL.TZ1.b.iii:
For the process BC, calculate, in J, the thermal energy transferred to the gas.
18M.3.SL.TZ1.7c.i:
Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.
18M.3.SL.TZ1.7c.i:
Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.
18M.3.SL.TZ1.c.i:
Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.
18M.3.SL.TZ1.7c.ii:
Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.
18M.3.SL.TZ1.7c.ii:
Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.
18M.3.SL.TZ1.c.ii:
Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.
18M.3.SL.TZ1.7d:
Outline why an efficiency calculation is important for an engineer designing a heat engine.
18M.3.SL.TZ1.7d:
Outline why an efficiency calculation is important for an engineer designing a heat engine.
18M.3.SL.TZ1.d:
Outline why an efficiency calculation is important for an engineer designing a heat engine.
18N.3.SL.TZ0.6c.i:
At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.
18N.3.SL.TZ0.6c.i:
At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.
18N.3.SL.TZ0.c.i:
At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.
18N.3.SL.TZ0.7b:
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
18N.3.SL.TZ0.7b:
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
18N.3.SL.TZ0.b:
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
18N.3.SL.TZ0.6a: Calculate the force the support exerts on the rod.
18N.3.SL.TZ0.6a: Calculate the force the support exerts on the rod.
18N.3.SL.TZ0.a: Calculate the force the support exerts on the rod.
18N.3.SL.TZ0.6b.i:
Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.
18N.3.SL.TZ0.6b.i:
Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.
18N.3.SL.TZ0.b.i:
Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.
18N.3.SL.TZ0.7a.i:
Show that at C the pressure is 1.00 × 10⁶Pa.
18N.3.SL.TZ0.7a.i:
Show that at C the pressure is 1.00 × 10⁶Pa.
18N.3.SL.TZ0.a.i:
Show that at C the pressure is 1.00 × 10⁶Pa.
18N.3.SL.TZ0.7c.ii:
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.
18N.3.SL.TZ0.7c.ii:
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.
18N.3.SL.TZ0.c.ii:
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.
18N.3.HL.TZ0.11a:
State and explain the direction of motion of the mass at this instant.
18N.3.HL.TZ0.11a:
State and explain the direction of motion of the mass at this instant.
18N.3.HL.TZ0.a:
State and explain the direction of motion of the mass at this instant.
18N.3.HL.TZ0.10b.ii:
The density of water is 1000 kg m^–3. Calculate u.
18N.3.HL.TZ0.10b.ii:
The density of water is 1000 kg m^–3. Calculate u.
18N.3.HL.TZ0.b.ii:
The density of water is 1000 kg m^–3. Calculate u.
18N.3.HL.TZ0.11b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
18N.3.HL.TZ0.11b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
18N.3.HL.TZ0.b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
18N.3.HL.TZ0.10a: An ice cube floats in water that is contained in a tube. The ice cube melts. Suggest what...
18N.3.HL.TZ0.10a: An ice cube floats in water that is contained in a tube. The ice cube melts. Suggest what...
18N.3.HL.TZ0.a: An ice cube floats in water that is contained in a tube. The ice cube melts. Suggest what...
18N.3.HL.TZ0.10b.i: Outline why u = 4v.
18N.3.HL.TZ0.10b.i: Outline why u = 4v.
18N.3.HL.TZ0.b.i: Outline why u = 4v.
19M.3.SL.TZ2.8a: Outline why the normal force acting on the ladder at the point of contact with the wall is equal...
19M.3.SL.TZ2.8a: Outline why the normal force acting on the ladder at the point of contact with the wall is equal...
19M.3.SL.TZ2.a: Outline why the normal force acting on the ladder at the point of contact with the wall is equal...
19M.3.HL.TZ2.14a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
19M.3.HL.TZ2.14a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
19M.3.HL.TZ2.a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
19M.3.SL.TZ2.10d: Suggest why this cycle is not a suitable model for a working heat pump.
19M.3.SL.TZ2.10d: Suggest why this cycle is not a suitable model for a working heat pump.
19M.3.SL.TZ2.d: Suggest why this cycle is not a suitable model for a working heat pump.
19M.3.SL.TZ2.10a:
Show that the work done on the gas for the isothermal process C→A is approximately 440 J.
19M.3.SL.TZ2.10a:
Show that the work done on the gas for the isothermal process C→A is approximately 440 J.
19M.3.SL.TZ2.a:
Show that the work done on the gas for the isothermal process C→A is approximately 440 J.
19M.3.HL.TZ2.13a:
Draw and label the forces acting on the sphere at the instant when it is released.
19M.3.HL.TZ2.13a:
Draw and label the forces acting on the sphere at the instant when it is released.
19M.3.HL.TZ2.a:
Draw and label the forces acting on the sphere at the instant when it is released.
19M.3.HL.TZ1.10a:
State one condition that must be satisfied for the Bernoulli equation

$\frac{1}{2}$ ρv² + ρgz + ρ = constant

to apply
19M.3.HL.TZ1.10a:
State one condition that must be satisfied for the Bernoulli equation

$\frac{1}{2}$ ρv² + ρgz + ρ = constant

to apply
19M.3.HL.TZ1.a:
State one condition that must be satisfied for the Bernoulli equation

$\frac{1}{2}$ ρv² + ρgz + ρ = constant

to apply
19M.3.HL.TZ1.10b.iii: The diameter at Y is made smaller than that at X. Explain why the pressure difference between X...
19M.3.HL.TZ1.10b.iii: The diameter at Y is made smaller than that at X. Explain why the pressure difference between X...
19M.3.HL.TZ1.b.iii: The diameter at Y is made smaller than that at X. Explain why the pressure difference between X...
19M.3.HL.TZ1.11a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
19M.3.HL.TZ1.11a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
19M.3.HL.TZ1.a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
19N.3.SL.TZ0.5b(i): Identify the physical quantity represented by the area under the graph.
19N.3.SL.TZ0.5b(i): Identify the physical quantity represented by the area under the graph.
19N.3.SL.TZ0.b(i): Identify the physical quantity represented by the area under the graph.
19N.3.SL.TZ0.6b(iii): state and explain whether the second law of thermodynamics is violated.
19N.3.SL.TZ0.6b(iii): state and explain whether the second law of thermodynamics is violated.
19N.3.SL.TZ0.b(iii): state and explain whether the second law of thermodynamics is violated.
19N.3.SL.TZ0.6b(i):
determine the thermal energy removed from the system.
19N.3.SL.TZ0.6b(i):
determine the thermal energy removed from the system.
19N.3.SL.TZ0.b(i):
determine the thermal energy removed from the system.
19N.3.SL.TZ0.6a(ii):
Calculate the ratio $\frac{V_{A}}{V_{C}}$ .
19N.3.SL.TZ0.6a(ii):
Calculate the ratio $\frac{V_{A}}{V_{C}}$ .
19N.3.SL.TZ0.a(ii):
Calculate the ratio $\frac{V_{A}}{V_{C}}$ .
19N.3.SL.TZ0.5b(iii):
Calculate the maximum tension in the string.
19N.3.SL.TZ0.5b(iii):
Calculate the maximum tension in the string.
19N.3.SL.TZ0.b(iii):
Calculate the maximum tension in the string.
19N.3.SL.TZ0.5b(ii): Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s–1.
19N.3.SL.TZ0.5b(ii): Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s–1.
19N.3.SL.TZ0.b(ii): Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s–1.
19N.3.SL.TZ0.6b(ii):
explain why the entropy of the gas decreases.
19N.3.SL.TZ0.6b(ii):
explain why the entropy of the gas decreases.
19N.3.SL.TZ0.b(ii):
explain why the entropy of the gas decreases.
19N.3.SL.TZ0.6a(i):
Show that the pressure at B is about 130 kPa.
19N.3.SL.TZ0.6a(i):
Show that the pressure at B is about 130 kPa.
19N.3.SL.TZ0.a(i):
Show that the pressure at B is about 130 kPa.
19N.3.SL.TZ0.5c(ii):
At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.
19N.3.SL.TZ0.5c(ii):
At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.
19N.3.SL.TZ0.c(ii):
At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.
19N.3.SL.TZ0.5a: State the torque provided by the force W about the axis of the flywheel.
19N.3.SL.TZ0.5a: State the torque provided by the force W about the axis of the flywheel.
19N.3.SL.TZ0.a: State the torque provided by the force W about the axis of the flywheel.
19N.3.SL.TZ0.5c(i): The flywheel is in translational equilibrium. Distinguish between translational equilibrium and...
19N.3.SL.TZ0.5c(i): The flywheel is in translational equilibrium. Distinguish between translational equilibrium and...
19N.3.SL.TZ0.c(i): The flywheel is in translational equilibrium. Distinguish between translational equilibrium and...
19N.3.HL.TZ0.10c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.

When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
19N.3.HL.TZ0.10c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.

When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
19N.3.HL.TZ0.c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.

When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
19N.3.HL.TZ0.10b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
19N.3.HL.TZ0.10b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
19N.3.HL.TZ0.b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
19N.3.HL.TZ0.9a:
Explain why the levels of the liquid are at different heights.
19N.3.HL.TZ0.9a:
Explain why the levels of the liquid are at different heights.
19N.3.HL.TZ0.a:
Explain why the levels of the liquid are at different heights.
19N.3.HL.TZ0.9b:
The density of the liquid in the tube is 8.7 × 10²kg m^–3 and the density of air is 1.2 kg m^–3. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.
19N.3.HL.TZ0.9b:
The density of the liquid in the tube is 8.7 × 10²kg m^–3 and the density of air is 1.2 kg m^–3. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.
19N.3.HL.TZ0.b:
The density of the liquid in the tube is 8.7 × 10²kg m^–3 and the density of air is 1.2 kg m^–3. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.
19N.3.HL.TZ0.10a: Describe what is meant by damped motion.
19N.3.HL.TZ0.10a: Describe what is meant by damped motion.
19N.3.HL.TZ0.a: Describe what is meant by damped motion.
17N.3.SL.TZ0.11b.ii: Outline how the stellar parallax angle is measured.
17N.3.SL.TZ0.11b.ii: Outline how the stellar parallax angle is measured.
17N.3.SL.TZ0.b.ii: Outline how the stellar parallax angle is measured.
18M.3.SL.TZ1.6a:
Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.
18M.3.SL.TZ1.6a:
Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.
18M.3.SL.TZ1.a:
Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.
18M.3.SL.TZ2.7d.i:
Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.
18M.3.SL.TZ2.7d.i:
Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.
18M.3.SL.TZ2.d.i:
Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.
18N.3.SL.TZ0.6b.ii:
After time t the rod makes an angle θ with the horizontal. Outline why the equation $\theta = \frac{1}{2}\alpha {t^2}$ cannot be used to find the time it takes θ to become $\frac{\pi }{2}$ (that is for the rod to become vertical for the first time).
18N.3.SL.TZ0.6b.ii:
After time t the rod makes an angle θ with the horizontal. Outline why the equation $\theta = \frac{1}{2}\alpha {t^2}$ cannot be used to find the time it takes θ to become $\frac{\pi }{2}$ (that is for the rod to become vertical for the first time).
18N.3.SL.TZ0.b.ii:
After time t the rod makes an angle θ with the horizontal. Outline why the equation $\theta = \frac{1}{2}\alpha {t^2}$ cannot be used to find the time it takes θ to become $\frac{\pi }{2}$ (that is for the rod to become vertical for the first time).
18N.3.SL.TZ0.6c.ii: At the instant the rod becomes vertical calculate the angular momentum of the rod.
18N.3.SL.TZ0.6c.ii: At the instant the rod becomes vertical calculate the angular momentum of the rod.
18N.3.SL.TZ0.c.ii: At the instant the rod becomes vertical calculate the angular momentum of the rod.
18N.3.SL.TZ0.7a.ii:
Show that at C the temperature is 254 K.
18N.3.SL.TZ0.7a.ii:
Show that at C the temperature is 254 K.
18N.3.SL.TZ0.a.ii:
Show that at C the temperature is 254 K.
18N.3.SL.TZ0.7c.i:
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
18N.3.SL.TZ0.7c.i:
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
18N.3.SL.TZ0.c.i:
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
19M.3.SL.TZ2.8b:
Calculate F.
19M.3.SL.TZ2.8b:
Calculate F.
19M.3.SL.TZ2.b:
Calculate F.
19M.3.SL.TZ2.9a:
Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .
19M.3.SL.TZ2.9a:
Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .
19M.3.SL.TZ2.a:
Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .
19M.3.SL.TZ2.9b:
A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s^-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.
19M.3.SL.TZ2.9b:
A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s^-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.
19M.3.SL.TZ2.b:
A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s^-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.
19M.3.SL.TZ2.10bi:
Calculate the change in internal energy of the gas for the process A→B.
19M.3.SL.TZ2.10bi:
Calculate the change in internal energy of the gas for the process A→B.
19M.3.SL.TZ2.bi:
Calculate the change in internal energy of the gas for the process A→B.
19M.3.SL.TZ2.10bii: Calculate the temperature at A if the temperature at B is −40°C.
19M.3.SL.TZ2.10bii: Calculate the temperature at A if the temperature at B is −40°C.
19M.3.SL.TZ2.bii: Calculate the temperature at A if the temperature at B is −40°C.
19M.3.SL.TZ2.10c: Determine, using the first law of thermodynamics, the total thermal energy transferred to the...
19M.3.SL.TZ2.10c: Determine, using the first law of thermodynamics, the total thermal energy transferred to the...
19M.3.SL.TZ2.c: Determine, using the first law of thermodynamics, the total thermal energy transferred to the...
19M.3.HL.TZ2.13b: Explain why the sphere will reach a terminal speed.
19M.3.HL.TZ2.13b: Explain why the sphere will reach a terminal speed.
19M.3.HL.TZ2.b: Explain why the sphere will reach a terminal speed.
19M.3.HL.TZ2.13c:
The weight of the sphere is 6.16 mN and the radius is 5.00 × 10^-3 m. For a fluid of density 8.50 × 10² kg m^-3, the terminal speed is found to be 0.280 m s^-1. Calculate the viscosity of the fluid.
19M.3.HL.TZ2.13c:
The weight of the sphere is 6.16 mN and the radius is 5.00 × 10^-3 m. For a fluid of density 8.50 × 10² kg m^-3, the terminal speed is found to be 0.280 m s^-1. Calculate the viscosity of the fluid.
19M.3.HL.TZ2.c:
The weight of the sphere is 6.16 mN and the radius is 5.00 × 10^-3 m. For a fluid of density 8.50 × 10² kg m^-3, the terminal speed is found to be 0.280 m s^-1. Calculate the viscosity of the fluid.
19M.3.HL.TZ2.14b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
19M.3.HL.TZ2.14b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
19M.3.HL.TZ2.b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
19M.3.HL.TZ2.14c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
19M.3.HL.TZ2.14c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
19M.3.HL.TZ2.c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
19M.3.HL.TZ1.10b.i: Outline why the speed of the gasoline at X is the same as that at Y.
19M.3.HL.TZ1.10b.i: Outline why the speed of the gasoline at X is the same as that at Y.
19M.3.HL.TZ1.b.i: Outline why the speed of the gasoline at X is the same as that at Y.
19M.3.HL.TZ1.10b.ii:
Calculate the difference in pressure between X and Y.
19M.3.HL.TZ1.10b.ii:
Calculate the difference in pressure between X and Y.
19M.3.HL.TZ1.b.ii:
Calculate the difference in pressure between X and Y.
19M.3.HL.TZ1.11b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
19M.3.HL.TZ1.11b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
19M.3.HL.TZ1.b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
20N.3.SL.TZ0.6a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
20N.3.SL.TZ0.6a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
20N.3.SL.TZ0.a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
20N.3.SL.TZ0.6b:
Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.
20N.3.SL.TZ0.6b:
Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.
20N.3.SL.TZ0.b:
Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.
20N.3.SL.TZ0.6c:
Calculate the torque acting on the bar while it is accelerating.
20N.3.SL.TZ0.6c:
Calculate the torque acting on the bar while it is accelerating.
20N.3.SL.TZ0.c:
Calculate the torque acting on the bar while it is accelerating.
20N.3.SL.TZ0.9b(i):
Calculate the pressure following this process.
20N.3.SL.TZ0.9b(i):
Calculate the pressure following this process.
20N.3.SL.TZ0.b(i):
Calculate the pressure following this process.
20N.3.SL.TZ0.9b(ii): Outline how an approximate adiabatic change can be achieved.
20N.3.SL.TZ0.9b(ii): Outline how an approximate adiabatic change can be achieved.
20N.3.SL.TZ0.b(ii): Outline how an approximate adiabatic change can be achieved.
20N.3.HL.TZ0.12b:
Determine the terminal velocity of the sphere.
20N.3.HL.TZ0.12b:
Determine the terminal velocity of the sphere.
20N.3.HL.TZ0.b:
Determine the terminal velocity of the sphere.
20N.3.HL.TZ0.12c(iii):
Outline the effect on $Q$ of changing the oil to one with greater viscosity.
20N.3.HL.TZ0.c(iii):
Outline the effect on $Q$ of changing the oil to one with greater viscosity.
20N.3.HL.TZ0.12c(iii):
Outline the effect on $Q$ of changing the oil to one with greater viscosity.
23M.1.HL.TZ1.14:
A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A. $\frac{(2 n - 1) V}{2 L}$

B. $\frac{(2 n - 1) V}{4 L}$

C. $\frac{n V}{2 L}$

D. $\frac{n V}{4 L}$
23M.1.HL.TZ1.14:
A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A. $\frac{(2 n - 1) V}{2 L}$

B. $\frac{(2 n - 1) V}{4 L}$

C. $\frac{n V}{2 L}$

D. $\frac{n V}{4 L}$
23M.1.HL.TZ1.37: A gamma ray can split into an electron and a positron when it passes through certain...
23M.1.HL.TZ1.37: A gamma ray can split into an electron and a positron when it passes through certain...
23M.1.HL.TZ1.35: Three changes are made to a transformer. I. increasing the thickness of wire in the coilsII. ...
23M.1.HL.TZ1.35: Three changes are made to a transformer. I. increasing the thickness of wire in the coilsII. ...
23M.1.HL.TZ1.36:
A resistor of resistance R is connected to an alternating current power supply. The peak voltage across the resistor is V₀.

What is the mean power dissipated by the resistor?

A. $\frac{{V_{0}}^{2} \sqrt{2}}{R}$

B. $\frac{{V_{0}}^{2}}{R}$

C. $\frac{{V_{0}}^{2}}{R \sqrt{2}}$

D. $\frac{{V_{0}}^{2}}{2 R}$
23M.1.HL.TZ1.36:
A resistor of resistance R is connected to an alternating current power supply. The peak voltage across the resistor is V₀.

What is the mean power dissipated by the resistor?

A. $\frac{{V_{0}}^{2} \sqrt{2}}{R}$

B. $\frac{{V_{0}}^{2}}{R}$

C. $\frac{{V_{0}}^{2}}{R \sqrt{2}}$

D. $\frac{{V_{0}}^{2}}{2 R}$
23M.3.HL.TZ1.9a: Suggest why AC is the adiabatic part of the cycle.
23M.3.SL.TZ1.7a: Suggest why AC is the adiabatic part of the cycle.
23M.3.HL.TZ1.9a: Suggest why AC is the adiabatic part of the cycle.
23M.3.HL.TZ1.a: Suggest why AC is the adiabatic part of the cycle.
23M.3.SL.TZ1.7a: Suggest why AC is the adiabatic part of the cycle.
23M.3.SL.TZ1.a: Suggest why AC is the adiabatic part of the cycle.
23M.3.HL.TZ1.8a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.SL.TZ1.6a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.HL.TZ1.8a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.HL.TZ1.a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.SL.TZ1.6a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.SL.TZ1.a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.1.SL.TZ2.15: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
23M.1.HL.TZ2.11: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
23M.1.SL.TZ2.15: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
23M.1.HL.TZ2.11: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
23M.1.SL.TZ2.14:
A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$ .

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$ ?

A. 400 Hz

B. 200 Hz

C. 100 Hz

D. 50 Hz
23M.1.SL.TZ2.14:
A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$ .

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$ ?

A. 400 Hz

B. 200 Hz

C. 100 Hz

D. 50 Hz
23M.3.HL.TZ2.8a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.SL.TZ2.6a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.HL.TZ2.8a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.HL.TZ2.a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.SL.TZ2.6a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.SL.TZ2.a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.HL.TZ2.9a:
Calculate the pressure of the gas at B.
23M.3.SL.TZ2.7a:
Calculate the pressure of the gas at B.
23M.3.HL.TZ2.9a:
Calculate the pressure of the gas at B.
23M.3.HL.TZ2.a:
Calculate the pressure of the gas at B.
23M.3.SL.TZ2.7a:
Calculate the pressure of the gas at B.
23M.3.SL.TZ2.a:
Calculate the pressure of the gas at B.

Sub sections and their related questions

Option B: Engineering physics (Core topics)

17N.3.SL.TZ0.6a: Explain what is meant by proper length.
17N.3.SL.TZ0.7a: On the diagram, draw and label the forces acting on the hoop.
17N.3.SL.TZ0.7b:
Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{{g \times \sin q}}{2}$
17N.3.SL.TZ0.7c: Calculate the acceleration of the hoop when θ = 20°. Assume that the hoop continues to roll...
17N.3.SL.TZ0.7d:
State the relationship between the force of friction and the angle of the incline.
17N.3.SL.TZ0.7e:
The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.
17N.3.SL.TZ0.8a:
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.
17N.3.SL.TZ0.8b: Using the axes, sketch the three-step cycle.
17N.3.SL.TZ0.8c:
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
17N.3.SL.TZ0.8d:
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
17N.3.SL.TZ0.10c:
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
18M.3.SL.TZ1.6a:
Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.
18M.3.SL.TZ1.6b.i:
Calculate, for the merry-go-round after one revolution, the angular speed.
18M.3.SL.TZ1.6b.ii:
Calculate, for the merry-go-round after one revolution, the angular momentum.
18M.3.SL.TZ1.6c:
Calculate the new angular speed of the rotating system.
18M.3.SL.TZ1.6d.i:
Explain why the angular speed will increase.
18M.3.SL.TZ1.6d.ii:
Calculate the work done by the child in moving from the edge to the centre.
18M.3.SL.TZ1.7a:
Show that the pressure at B is about 5 × 10⁵ Pa.
18M.3.SL.TZ1.7b.i:
For the process BC, calculate, in J, the work done by the gas.
18M.3.SL.TZ1.7b.ii:
For the process BC, calculate, in J, the change in the internal energy of the gas.
18M.3.SL.TZ1.7b.iii:
For the process BC, calculate, in J, the thermal energy transferred to the gas.
18M.3.SL.TZ1.7c.i:
Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.
18M.3.SL.TZ1.7c.ii:
Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.
18M.3.SL.TZ1.7d:
Outline why an efficiency calculation is important for an engineer designing a heat engine.
18M.3.SL.TZ2.6a.i:
The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.
18M.3.SL.TZ2.6a.ii:
In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.
18M.3.SL.TZ2.6a.iii:
Determine the angular velocity of the wheel at B.
18M.3.SL.TZ2.6b.ii:
Describe the effect of F on the angular speed of the wheel.
18M.3.SL.TZ2.7a:
Show that the final volume of the gas is about 53 m³.
18M.3.SL.TZ2.7b:
Calculate, in J, the work done by the gas during this expansion.
18M.3.SL.TZ2.7c:
Determine the thermal energy which enters the gas during this expansion.
18M.3.SL.TZ2.7d.i:
Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.
18M.3.SL.TZ2.7d.ii:
Outline the change in entropy of the gas during the cooling at constant volume.
18M.3.SL.TZ2.7e:
There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.
18N.3.SL.TZ0.6a: Calculate the force the support exerts on the rod.
18N.3.SL.TZ0.6b.i:
Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.
18N.3.SL.TZ0.6b.ii:
After time t the rod makes an angle θ with the horizontal. Outline why the equation $\theta = \frac{1}{2}\alpha {t^2}$ cannot be used to find the time it takes θ to become $\frac{\pi }{2}$ (that is for the rod to become vertical for the first time).
18N.3.SL.TZ0.6c.i:
At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.
18N.3.SL.TZ0.6c.ii: At the instant the rod becomes vertical calculate the angular momentum of the rod.
18N.3.SL.TZ0.7a.i:
Show that at C the pressure is 1.00 × 10⁶Pa.
18N.3.SL.TZ0.7a.ii:
Show that at C the temperature is 254 K.
18N.3.SL.TZ0.7b:
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
18N.3.SL.TZ0.7c.i:
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
18N.3.SL.TZ0.7c.ii:
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.
19M.3.SL.TZ2.8a: Outline why the normal force acting on the ladder at the point of contact with the wall is equal...
19M.3.SL.TZ2.8b:
Calculate F.
19M.3.SL.TZ2.9a:
Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .
19M.3.SL.TZ2.9b:
A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s^-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.
19M.3.SL.TZ2.10a:
Show that the work done on the gas for the isothermal process C→A is approximately 440 J.
19M.3.SL.TZ2.10bi:
Calculate the change in internal energy of the gas for the process A→B.
19M.3.SL.TZ2.10bii: Calculate the temperature at A if the temperature at B is −40°C.
19M.3.SL.TZ2.10c: Determine, using the first law of thermodynamics, the total thermal energy transferred to the...
19M.3.SL.TZ2.10d: Suggest why this cycle is not a suitable model for a working heat pump.
19N.3.SL.TZ0.5a: State the torque provided by the force W about the axis of the flywheel.
19N.3.SL.TZ0.5b(i): Identify the physical quantity represented by the area under the graph.
19N.3.SL.TZ0.5b(ii): Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s–1.
19N.3.SL.TZ0.5b(iii):
Calculate the maximum tension in the string.
19N.3.SL.TZ0.5c(i): The flywheel is in translational equilibrium. Distinguish between translational equilibrium and...
19N.3.SL.TZ0.5c(ii):
At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.
19N.3.SL.TZ0.6a(i):
Show that the pressure at B is about 130 kPa.
19N.3.SL.TZ0.6a(ii):
Calculate the ratio $\frac{V_{A}}{V_{C}}$ .
19N.3.SL.TZ0.6b(i):
determine the thermal energy removed from the system.
19N.3.SL.TZ0.6b(ii):
explain why the entropy of the gas decreases.
19N.3.SL.TZ0.6b(iii): state and explain whether the second law of thermodynamics is violated.
20N.3.SL.TZ0.6a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
20N.3.SL.TZ0.6b:
Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.
20N.3.SL.TZ0.6c:
Calculate the torque acting on the bar while it is accelerating.
20N.3.SL.TZ0.6d:
The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
20N.3.SL.TZ0.7a:
Explain the direction in which the person-turntable system starts to rotate.
20N.3.SL.TZ0.7b: Explain the changes to the rotational kinetic energy in the person-turntable system.
20N.3.SL.TZ0.8:
A solid sphere of radius $r$ and mass $m$ is released from rest and rolls down a slope, without slipping. The vertical height of the slope is $h$ . The moment of inertia $I$ of this sphere about an axis through its centre is $\frac{2}{5} m r^{2}$ .

Show that the linear velocity $v$ of the sphere as it leaves the slope is $\sqrt{\frac{10 g h}{7}}$ .
20N.3.SL.TZ0.9a(i):
Calculate the work done during the compression.
20N.3.SL.TZ0.9a(ii):
Calculate the work done during the increase in pressure.
20N.3.SL.TZ0.9b(i):
Calculate the pressure following this process.
20N.3.SL.TZ0.9b(ii): Outline how an approximate adiabatic change can be achieved.
23M.3.HL.TZ1.8a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.HL.TZ1.9a: Suggest why AC is the adiabatic part of the cycle.
23M.3.HL.TZ2.8a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.HL.TZ2.9a:
Calculate the pressure of the gas at B.
23M.1.HL.TZ1.35: Three changes are made to a transformer. I. increasing the thickness of wire in the coilsII. ...
23M.3.SL.TZ2.6a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.SL.TZ2.7a:
Calculate the pressure of the gas at B.
23M.3.SL.TZ1.6a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.SL.TZ1.7a: Suggest why AC is the adiabatic part of the cycle.
19M.3.SL.TZ2.8a: Outline why the normal force acting on the ladder at the point of contact with the wall is equal...
19M.3.SL.TZ2.8b:
Calculate F.
19M.3.SL.TZ2.a: Outline why the normal force acting on the ladder at the point of contact with the wall is equal...
19M.3.SL.TZ2.b:
Calculate F.
19M.3.SL.TZ2.9a:
Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .
19M.3.SL.TZ2.9b:
A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s^-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.
19M.3.SL.TZ2.a:
Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .
19M.3.SL.TZ2.b:
A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s^-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.
19M.3.SL.TZ2.10a:
Show that the work done on the gas for the isothermal process C→A is approximately 440 J.
19M.3.SL.TZ2.10bi:
Calculate the change in internal energy of the gas for the process A→B.
19M.3.SL.TZ2.10bii: Calculate the temperature at A if the temperature at B is −40°C.
19M.3.SL.TZ2.10c: Determine, using the first law of thermodynamics, the total thermal energy transferred to the...
19M.3.SL.TZ2.10d: Suggest why this cycle is not a suitable model for a working heat pump.
19M.3.SL.TZ2.a:
Show that the work done on the gas for the isothermal process C→A is approximately 440 J.
19M.3.SL.TZ2.bi:
Calculate the change in internal energy of the gas for the process A→B.
19M.3.SL.TZ2.bii: Calculate the temperature at A if the temperature at B is −40°C.
19M.3.SL.TZ2.c: Determine, using the first law of thermodynamics, the total thermal energy transferred to the...
19M.3.SL.TZ2.d: Suggest why this cycle is not a suitable model for a working heat pump.
19N.3.SL.TZ0.5a: State the torque provided by the force W about the axis of the flywheel.
19N.3.SL.TZ0.5b(i): Identify the physical quantity represented by the area under the graph.
19N.3.SL.TZ0.5b(ii): Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s–1.
19N.3.SL.TZ0.5b(iii):
Calculate the maximum tension in the string.
19N.3.SL.TZ0.5c(i): The flywheel is in translational equilibrium. Distinguish between translational equilibrium and...
19N.3.SL.TZ0.5c(ii):
At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.
19N.3.SL.TZ0.a: State the torque provided by the force W about the axis of the flywheel.
19N.3.SL.TZ0.b(i): Identify the physical quantity represented by the area under the graph.
19N.3.SL.TZ0.b(ii): Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s–1.
19N.3.SL.TZ0.b(iii):
Calculate the maximum tension in the string.
19N.3.SL.TZ0.c(i): The flywheel is in translational equilibrium. Distinguish between translational equilibrium and...
19N.3.SL.TZ0.c(ii):
At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.
19N.3.SL.TZ0.6a(i):
Show that the pressure at B is about 130 kPa.
19N.3.SL.TZ0.6a(ii):
Calculate the ratio $\frac{V_{A}}{V_{C}}$ .
19N.3.SL.TZ0.6b(i):
determine the thermal energy removed from the system.
19N.3.SL.TZ0.6b(ii):
explain why the entropy of the gas decreases.
19N.3.SL.TZ0.6b(iii): state and explain whether the second law of thermodynamics is violated.
19N.3.SL.TZ0.a(i):
Show that the pressure at B is about 130 kPa.
19N.3.SL.TZ0.a(ii):
Calculate the ratio $\frac{V_{A}}{V_{C}}$ .
19N.3.SL.TZ0.b(i):
determine the thermal energy removed from the system.
19N.3.SL.TZ0.b(ii):
explain why the entropy of the gas decreases.
19N.3.SL.TZ0.b(iii): state and explain whether the second law of thermodynamics is violated.
20N.3.SL.TZ0.6a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
20N.3.SL.TZ0.6b:
Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.
20N.3.SL.TZ0.6c:
Calculate the torque acting on the bar while it is accelerating.
20N.3.SL.TZ0.6d:
The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
20N.3.SL.TZ0.a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
20N.3.SL.TZ0.b:
Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.
20N.3.SL.TZ0.c:
Calculate the torque acting on the bar while it is accelerating.
20N.3.SL.TZ0.d:
The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
20N.3.SL.TZ0.7a:
Explain the direction in which the person-turntable system starts to rotate.
20N.3.SL.TZ0.7b: Explain the changes to the rotational kinetic energy in the person-turntable system.
20N.3.SL.TZ0.a:
Explain the direction in which the person-turntable system starts to rotate.
20N.3.SL.TZ0.b: Explain the changes to the rotational kinetic energy in the person-turntable system.
20N.3.SL.TZ0.8:
A solid sphere of radius $r$ and mass $m$ is released from rest and rolls down a slope, without slipping. The vertical height of the slope is $h$ . The moment of inertia $I$ of this sphere about an axis through its centre is $\frac{2}{5} m r^{2}$ .

Show that the linear velocity $v$ of the sphere as it leaves the slope is $\sqrt{\frac{10 g h}{7}}$ .
20N.3.SL.TZ0.9a(i):
Calculate the work done during the compression.
20N.3.SL.TZ0.9a(ii):
Calculate the work done during the increase in pressure.
20N.3.SL.TZ0.9b(i):
Calculate the pressure following this process.
20N.3.SL.TZ0.9b(ii): Outline how an approximate adiabatic change can be achieved.
20N.3.SL.TZ0.a(i):
Calculate the work done during the compression.
20N.3.SL.TZ0.a(ii):
Calculate the work done during the increase in pressure.
20N.3.SL.TZ0.b(i):
Calculate the pressure following this process.
20N.3.SL.TZ0.b(ii): Outline how an approximate adiabatic change can be achieved.
17N.3.SL.TZ0.6a: Explain what is meant by proper length.
17N.3.SL.TZ0.a: Explain what is meant by proper length.
17N.3.SL.TZ0.7a: On the diagram, draw and label the forces acting on the hoop.
17N.3.SL.TZ0.7b:
Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{{g \times \sin q}}{2}$
17N.3.SL.TZ0.7c: Calculate the acceleration of the hoop when θ = 20°. Assume that the hoop continues to roll...
17N.3.SL.TZ0.7d:
State the relationship between the force of friction and the angle of the incline.
17N.3.SL.TZ0.7e:
The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.
17N.3.SL.TZ0.a: On the diagram, draw and label the forces acting on the hoop.
17N.3.SL.TZ0.b:
Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{{g \times \sin q}}{2}$
17N.3.SL.TZ0.c: Calculate the acceleration of the hoop when θ = 20°. Assume that the hoop continues to roll...
17N.3.SL.TZ0.d:
State the relationship between the force of friction and the angle of the incline.
17N.3.SL.TZ0.e:
The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.
17N.3.SL.TZ0.8a:
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.
17N.3.SL.TZ0.8b: Using the axes, sketch the three-step cycle.
17N.3.SL.TZ0.8c:
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
17N.3.SL.TZ0.8d:
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
17N.3.SL.TZ0.a:
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.
17N.3.SL.TZ0.b: Using the axes, sketch the three-step cycle.
17N.3.SL.TZ0.c:
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
17N.3.SL.TZ0.d:
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
17N.3.SL.TZ0.10c:
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
17N.3.SL.TZ0.c:
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
23M.3.HL.TZ1.8a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.HL.TZ1.a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.HL.TZ1.9a: Suggest why AC is the adiabatic part of the cycle.
23M.3.HL.TZ1.a: Suggest why AC is the adiabatic part of the cycle.
23M.3.HL.TZ2.8a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.HL.TZ2.a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.HL.TZ2.9a:
Calculate the pressure of the gas at B.
23M.3.HL.TZ2.a:
Calculate the pressure of the gas at B.
23M.1.HL.TZ1.35: Three changes are made to a transformer. I. increasing the thickness of wire in the coilsII. ...
23M.3.SL.TZ2.6a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.SL.TZ2.a:
Show that the net torque on the system about the central axis is approximately 30 N m.
23M.3.SL.TZ2.7a:
Calculate the pressure of the gas at B.
23M.3.SL.TZ2.a:
Calculate the pressure of the gas at B.
23M.3.SL.TZ1.6a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.SL.TZ1.a: The moment of inertia of the rod about the axis is 0.180 kg m2. Show that the moment of inertia...
23M.3.SL.TZ1.7a: Suggest why AC is the adiabatic part of the cycle.
23M.3.SL.TZ1.a: Suggest why AC is the adiabatic part of the cycle.
18M.3.SL.TZ1.6a:
Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.
18M.3.SL.TZ1.6b.i:
Calculate, for the merry-go-round after one revolution, the angular speed.
18M.3.SL.TZ1.6b.ii:
Calculate, for the merry-go-round after one revolution, the angular momentum.
18M.3.SL.TZ1.6c:
Calculate the new angular speed of the rotating system.
18M.3.SL.TZ1.6d.i:
Explain why the angular speed will increase.
18M.3.SL.TZ1.6d.ii:
Calculate the work done by the child in moving from the edge to the centre.
18M.3.SL.TZ1.a:
Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.
18M.3.SL.TZ1.b.i:
Calculate, for the merry-go-round after one revolution, the angular speed.
18M.3.SL.TZ1.b.ii:
Calculate, for the merry-go-round after one revolution, the angular momentum.
18M.3.SL.TZ1.c:
Calculate the new angular speed of the rotating system.
18M.3.SL.TZ1.d.i:
Explain why the angular speed will increase.
18M.3.SL.TZ1.d.ii:
Calculate the work done by the child in moving from the edge to the centre.
18M.3.SL.TZ1.7a:
Show that the pressure at B is about 5 × 10⁵ Pa.
18M.3.SL.TZ1.7b.i:
For the process BC, calculate, in J, the work done by the gas.
18M.3.SL.TZ1.7b.ii:
For the process BC, calculate, in J, the change in the internal energy of the gas.
18M.3.SL.TZ1.7b.iii:
For the process BC, calculate, in J, the thermal energy transferred to the gas.
18M.3.SL.TZ1.7c.i:
Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.
18M.3.SL.TZ1.7c.ii:
Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.
18M.3.SL.TZ1.7d:
Outline why an efficiency calculation is important for an engineer designing a heat engine.
18M.3.SL.TZ1.a:
Show that the pressure at B is about 5 × 10⁵ Pa.
18M.3.SL.TZ1.b.i:
For the process BC, calculate, in J, the work done by the gas.
18M.3.SL.TZ1.b.ii:
For the process BC, calculate, in J, the change in the internal energy of the gas.
18M.3.SL.TZ1.b.iii:
For the process BC, calculate, in J, the thermal energy transferred to the gas.
18M.3.SL.TZ1.c.i:
Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.
18M.3.SL.TZ1.c.ii:
Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.
18M.3.SL.TZ1.d:
Outline why an efficiency calculation is important for an engineer designing a heat engine.
18M.3.SL.TZ2.6a.i:
The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.
18M.3.SL.TZ2.6a.ii:
In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.
18M.3.SL.TZ2.6a.iii:
Determine the angular velocity of the wheel at B.
18M.3.SL.TZ2.6b.ii:
Describe the effect of F on the angular speed of the wheel.
18M.3.SL.TZ2.a.i:
The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.
18M.3.SL.TZ2.a.ii:
In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.
18M.3.SL.TZ2.a.iii:
Determine the angular velocity of the wheel at B.
18M.3.SL.TZ2.b.ii:
Describe the effect of F on the angular speed of the wheel.
18M.3.SL.TZ2.7a:
Show that the final volume of the gas is about 53 m³.
18M.3.SL.TZ2.7b:
Calculate, in J, the work done by the gas during this expansion.
18M.3.SL.TZ2.7c:
Determine the thermal energy which enters the gas during this expansion.
18M.3.SL.TZ2.7d.i:
Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.
18M.3.SL.TZ2.7d.ii:
Outline the change in entropy of the gas during the cooling at constant volume.
18M.3.SL.TZ2.7e:
There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.
18M.3.SL.TZ2.a:
Show that the final volume of the gas is about 53 m³.
18M.3.SL.TZ2.b:
Calculate, in J, the work done by the gas during this expansion.
18M.3.SL.TZ2.c:
Determine the thermal energy which enters the gas during this expansion.
18M.3.SL.TZ2.d.i:
Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.
18M.3.SL.TZ2.d.ii:
Outline the change in entropy of the gas during the cooling at constant volume.
18M.3.SL.TZ2.e:
There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.
18N.3.SL.TZ0.6a: Calculate the force the support exerts on the rod.
18N.3.SL.TZ0.6b.i:
Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.
18N.3.SL.TZ0.6b.ii:
After time t the rod makes an angle θ with the horizontal. Outline why the equation $\theta = \frac{1}{2}\alpha {t^2}$ cannot be used to find the time it takes θ to become $\frac{\pi }{2}$ (that is for the rod to become vertical for the first time).
18N.3.SL.TZ0.6c.i:
At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.
18N.3.SL.TZ0.6c.ii: At the instant the rod becomes vertical calculate the angular momentum of the rod.
18N.3.SL.TZ0.a: Calculate the force the support exerts on the rod.
18N.3.SL.TZ0.b.i:
Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.
18N.3.SL.TZ0.b.ii:
After time t the rod makes an angle θ with the horizontal. Outline why the equation $\theta = \frac{1}{2}\alpha {t^2}$ cannot be used to find the time it takes θ to become $\frac{\pi }{2}$ (that is for the rod to become vertical for the first time).
18N.3.SL.TZ0.c.i:
At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.
18N.3.SL.TZ0.c.ii: At the instant the rod becomes vertical calculate the angular momentum of the rod.
18N.3.SL.TZ0.7a.i:
Show that at C the pressure is 1.00 × 10⁶Pa.
18N.3.SL.TZ0.7a.ii:
Show that at C the temperature is 254 K.
18N.3.SL.TZ0.7b:
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
18N.3.SL.TZ0.7c.i:
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
18N.3.SL.TZ0.7c.ii:
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.
18N.3.SL.TZ0.a.i:
Show that at C the pressure is 1.00 × 10⁶Pa.
18N.3.SL.TZ0.a.ii:
Show that at C the temperature is 254 K.
18N.3.SL.TZ0.b:
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
18N.3.SL.TZ0.c.i:
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
18N.3.SL.TZ0.c.ii:
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.

Option B: Engineering physics (Additional higher level option topics)

17N.3.SL.TZ0.11a.i: Identify the mechanism leading stars to produce the light they emit.
17N.3.SL.TZ0.11a.ii:
Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.
17N.3.SL.TZ0.11b.i: Outline what is meant by a constellation.
17N.3.SL.TZ0.11b.ii: Outline how the stellar parallax angle is measured.
17N.3.SL.TZ0.11b.iii:
Show that the distance to Vega from Earth is about 25 ly.
17N.3.HL.TZ0.11a.i:
Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.
17N.3.HL.TZ0.11a.ii:
When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m^–3. Calculate the percentage of the sphere volume filled by water.
17N.3.HL.TZ0.11b:
The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m^–3 to 785.16 kg m^–3. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.
17N.3.HL.TZ0.12a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.
17N.3.HL.TZ0.12b: Outline what change would be required to the value of Q for the mass–spring system in order for...
18M.3.HL.TZ1.10a:
State the difference in terms of the velocity of the water between laminar and turbulent flow.
18M.3.HL.TZ1.10b:
The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.

Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = $\sqrt {2gH}$ .
18M.3.HL.TZ1.10c.i:
Calculate the Reynolds number for the water flow.
18M.3.HL.TZ1.10c.ii:
Outline whether it is reasonable to assume that flow is laminar in this situation.
18M.3.HL.TZ1.11a:
Describe the motion of the spring-mass system.
18M.3.HL.TZ1.11b.ii:
calculate the Q at the start of the motion.
18M.3.HL.TZ2.10a:
Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.
18M.3.HL.TZ2.10b.i:
Estimate the Reynolds number for the fluid in your answer to (a).
18M.3.HL.TZ2.10b.ii:
Outline whether your answer to (a) is valid.
18M.3.HL.TZ2.11a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
18M.3.HL.TZ2.11b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
18N.3.HL.TZ0.10a: An ice cube floats in water that is contained in a tube. The ice cube melts. Suggest what...
18N.3.HL.TZ0.10b.i: Outline why u = 4v.
18N.3.HL.TZ0.10b.ii:
The density of water is 1000 kg m^–3. Calculate u.
18N.3.HL.TZ0.11a:
State and explain the direction of motion of the mass at this instant.
18N.3.HL.TZ0.11b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
19M.3.HL.TZ2.13a:
Draw and label the forces acting on the sphere at the instant when it is released.
19M.3.HL.TZ2.13b: Explain why the sphere will reach a terminal speed.
19M.3.HL.TZ2.13c:
The weight of the sphere is 6.16 mN and the radius is 5.00 × 10^-3 m. For a fluid of density 8.50 × 10² kg m^-3, the terminal speed is found to be 0.280 m s^-1. Calculate the viscosity of the fluid.
19M.3.HL.TZ2.14a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
19M.3.HL.TZ2.14b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
19M.3.HL.TZ2.14c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
19M.3.HL.TZ1.10a:
State one condition that must be satisfied for the Bernoulli equation

$\frac{1}{2}$ ρv² + ρgz + ρ = constant

to apply
19M.3.HL.TZ1.10b.i: Outline why the speed of the gasoline at X is the same as that at Y.
19M.3.HL.TZ1.10b.ii:
Calculate the difference in pressure between X and Y.
19M.3.HL.TZ1.10b.iii: The diameter at Y is made smaller than that at X. Explain why the pressure difference between X...
19M.3.HL.TZ1.11a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
19M.3.HL.TZ1.11b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
19N.3.HL.TZ0.9a:
Explain why the levels of the liquid are at different heights.
19N.3.HL.TZ0.9b:
The density of the liquid in the tube is 8.7 × 10²kg m^–3 and the density of air is 1.2 kg m^–3. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.
19N.3.HL.TZ0.10a: Describe what is meant by damped motion.
19N.3.HL.TZ0.10b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
19N.3.HL.TZ0.10c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.

When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
20N.3.HL.TZ0.12a: State two properties of an ideal fluid.
20N.3.HL.TZ0.12b:
Determine the terminal velocity of the sphere.
20N.3.HL.TZ0.12c(i):
Determine the force exerted by the spring on the sphere when the sphere is at rest.
20N.3.HL.TZ0.12c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by $10 %$ . Calculate the $Q$ factor for this system.
20N.3.HL.TZ0.12c(iii):
Outline the effect on $Q$ of changing the oil to one with greater viscosity.
23M.1.SL.TZ2.14:
A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$ .

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$ ?

A. 400 Hz

B. 200 Hz

C. 100 Hz

D. 50 Hz
23M.1.SL.TZ2.15: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
23M.1.HL.TZ1.14:
A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A. $\frac{(2 n - 1) V}{2 L}$

B. $\frac{(2 n - 1) V}{4 L}$

C. $\frac{n V}{2 L}$

D. $\frac{n V}{4 L}$
23M.1.HL.TZ2.11: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
19M.3.HL.TZ2.13a:
Draw and label the forces acting on the sphere at the instant when it is released.
19M.3.HL.TZ2.13b: Explain why the sphere will reach a terminal speed.
19M.3.HL.TZ2.13c:
The weight of the sphere is 6.16 mN and the radius is 5.00 × 10^-3 m. For a fluid of density 8.50 × 10² kg m^-3, the terminal speed is found to be 0.280 m s^-1. Calculate the viscosity of the fluid.
19M.3.HL.TZ2.a:
Draw and label the forces acting on the sphere at the instant when it is released.
19M.3.HL.TZ2.b: Explain why the sphere will reach a terminal speed.
19M.3.HL.TZ2.c:
The weight of the sphere is 6.16 mN and the radius is 5.00 × 10^-3 m. For a fluid of density 8.50 × 10² kg m^-3, the terminal speed is found to be 0.280 m s^-1. Calculate the viscosity of the fluid.
19M.3.HL.TZ2.14a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
19M.3.HL.TZ2.14b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
19M.3.HL.TZ2.14c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
19M.3.HL.TZ2.a:
Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.
19M.3.HL.TZ2.b: Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m...
19M.3.HL.TZ2.c: The damping of the bridge system can be varied. Draw, on the graph, a second curve when the...
19M.3.HL.TZ1.10a:
State one condition that must be satisfied for the Bernoulli equation

$\frac{1}{2}$ ρv² + ρgz + ρ = constant

to apply
19M.3.HL.TZ1.10b.i: Outline why the speed of the gasoline at X is the same as that at Y.
19M.3.HL.TZ1.10b.ii:
Calculate the difference in pressure between X and Y.
19M.3.HL.TZ1.10b.iii: The diameter at Y is made smaller than that at X. Explain why the pressure difference between X...
19M.3.HL.TZ1.a:
State one condition that must be satisfied for the Bernoulli equation

$\frac{1}{2}$ ρv² + ρgz + ρ = constant

to apply
19M.3.HL.TZ1.b.i: Outline why the speed of the gasoline at X is the same as that at Y.
19M.3.HL.TZ1.b.ii:
Calculate the difference in pressure between X and Y.
19M.3.HL.TZ1.b.iii: The diameter at Y is made smaller than that at X. Explain why the pressure difference between X...
19M.3.HL.TZ1.11a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
19M.3.HL.TZ1.11b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
19M.3.HL.TZ1.a:
The Q factor for the system is 25. Determine the period of oscillation for this system.
19M.3.HL.TZ1.b:
Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.
19N.3.HL.TZ0.9a:
Explain why the levels of the liquid are at different heights.
19N.3.HL.TZ0.9b:
The density of the liquid in the tube is 8.7 × 10²kg m^–3 and the density of air is 1.2 kg m^–3. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.
19N.3.HL.TZ0.a:
Explain why the levels of the liquid are at different heights.
19N.3.HL.TZ0.b:
The density of the liquid in the tube is 8.7 × 10²kg m^–3 and the density of air is 1.2 kg m^–3. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.
19N.3.HL.TZ0.10a: Describe what is meant by damped motion.
19N.3.HL.TZ0.10b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
19N.3.HL.TZ0.10c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.

When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
19N.3.HL.TZ0.a: Describe what is meant by damped motion.
19N.3.HL.TZ0.b:
After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.
19N.3.HL.TZ0.c:
The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.

When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.
20N.3.HL.TZ0.12a: State two properties of an ideal fluid.
20N.3.HL.TZ0.12b:
Determine the terminal velocity of the sphere.
20N.3.HL.TZ0.12c(i):
Determine the force exerted by the spring on the sphere when the sphere is at rest.
20N.3.HL.TZ0.12c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by $10 %$ . Calculate the $Q$ factor for this system.
20N.3.HL.TZ0.12c(iii):
Outline the effect on $Q$ of changing the oil to one with greater viscosity.
20N.3.HL.TZ0.a: State two properties of an ideal fluid.
20N.3.HL.TZ0.b:
Determine the terminal velocity of the sphere.
20N.3.HL.TZ0.c(i):
Determine the force exerted by the spring on the sphere when the sphere is at rest.
20N.3.HL.TZ0.c(ii):
The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by $10 %$ . Calculate the $Q$ factor for this system.
20N.3.HL.TZ0.c(iii):
Outline the effect on $Q$ of changing the oil to one with greater viscosity.
17N.3.SL.TZ0.11a.i: Identify the mechanism leading stars to produce the light they emit.
17N.3.SL.TZ0.11a.ii:
Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.
17N.3.SL.TZ0.11b.i: Outline what is meant by a constellation.
17N.3.SL.TZ0.11b.ii: Outline how the stellar parallax angle is measured.
17N.3.SL.TZ0.11b.iii:
Show that the distance to Vega from Earth is about 25 ly.
17N.3.SL.TZ0.a.i: Identify the mechanism leading stars to produce the light they emit.
17N.3.SL.TZ0.a.ii:
Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.
17N.3.SL.TZ0.b.i: Outline what is meant by a constellation.
17N.3.SL.TZ0.b.ii: Outline how the stellar parallax angle is measured.
17N.3.SL.TZ0.b.iii:
Show that the distance to Vega from Earth is about 25 ly.
17N.3.HL.TZ0.11a.i:
Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.
17N.3.HL.TZ0.11a.ii:
When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m^–3. Calculate the percentage of the sphere volume filled by water.
17N.3.HL.TZ0.11b:
The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m^–3 to 785.16 kg m^–3. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.
17N.3.HL.TZ0.a.i:
Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.
17N.3.HL.TZ0.a.ii:
When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m^–3. Calculate the percentage of the sphere volume filled by water.
17N.3.HL.TZ0.b:
The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m^–3 to 785.16 kg m^–3. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.
17N.3.HL.TZ0.12a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.
17N.3.HL.TZ0.12b: Outline what change would be required to the value of Q for the mass–spring system in order for...
17N.3.HL.TZ0.a:
Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.
17N.3.HL.TZ0.b: Outline what change would be required to the value of Q for the mass–spring system in order for...
23M.1.SL.TZ2.14:
A standing wave is formed between two loudspeakers that emit sound waves of frequency $f$ .

A student walking between the two loudspeakers finds that the distance between two consecutive sound maxima is 1.5 m. The speed of sound is 300 m s⁻¹.

What is $f$ ?

A. 400 Hz

B. 200 Hz

C. 100 Hz

D. 50 Hz
23M.1.SL.TZ2.15: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
23M.1.HL.TZ1.14:
A standing wave is formed in a pipe open at one end and closed at the other. The length of the pipe is L and the speed of sound in the pipe is V.

n is a positive integer.

What expression is correct about the frequencies of the harmonics in the pipe?

A. $\frac{(2 n - 1) V}{2 L}$

B. $\frac{(2 n - 1) V}{4 L}$

C. $\frac{n V}{2 L}$

D. $\frac{n V}{4 L}$
23M.1.HL.TZ2.11: A pipe containing air is closed at one end and open at the other. The third harmonic standing...
18M.3.HL.TZ1.10a:
State the difference in terms of the velocity of the water between laminar and turbulent flow.
18M.3.HL.TZ1.10b:
The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.

Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = $\sqrt {2gH}$ .
18M.3.HL.TZ1.10c.i:
Calculate the Reynolds number for the water flow.
18M.3.HL.TZ1.10c.ii:
Outline whether it is reasonable to assume that flow is laminar in this situation.
18M.3.HL.TZ1.a:
State the difference in terms of the velocity of the water between laminar and turbulent flow.
18M.3.HL.TZ1.b:
The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.

Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = $\sqrt {2gH}$ .
18M.3.HL.TZ1.c.i:
Calculate the Reynolds number for the water flow.
18M.3.HL.TZ1.c.ii:
Outline whether it is reasonable to assume that flow is laminar in this situation.
18M.3.HL.TZ1.11a:
Describe the motion of the spring-mass system.
18M.3.HL.TZ1.11b.ii:
calculate the Q at the start of the motion.
18M.3.HL.TZ1.a:
Describe the motion of the spring-mass system.
18M.3.HL.TZ1.b.ii:
calculate the Q at the start of the motion.
18M.3.HL.TZ2.10a:
Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.
18M.3.HL.TZ2.10b.i:
Estimate the Reynolds number for the fluid in your answer to (a).
18M.3.HL.TZ2.10b.ii:
Outline whether your answer to (a) is valid.
18M.3.HL.TZ2.a:
Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.
18M.3.HL.TZ2.b.i:
Estimate the Reynolds number for the fluid in your answer to (a).
18M.3.HL.TZ2.b.ii:
Outline whether your answer to (a) is valid.
18M.3.HL.TZ2.11a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
18M.3.HL.TZ2.11b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
18M.3.HL.TZ2.a:
Draw a graph to show the variation of amplitude of oscillation of the system with frequency.
18M.3.HL.TZ2.b:
The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.
18N.3.HL.TZ0.10a: An ice cube floats in water that is contained in a tube. The ice cube melts. Suggest what...
18N.3.HL.TZ0.10b.i: Outline why u = 4v.
18N.3.HL.TZ0.10b.ii:
The density of water is 1000 kg m^–3. Calculate u.
18N.3.HL.TZ0.a: An ice cube floats in water that is contained in a tube. The ice cube melts. Suggest what...
18N.3.HL.TZ0.b.i: Outline why u = 4v.
18N.3.HL.TZ0.b.ii:
The density of water is 1000 kg m^–3. Calculate u.
18N.3.HL.TZ0.11a:
State and explain the direction of motion of the mass at this instant.
18N.3.HL.TZ0.11b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.
18N.3.HL.TZ0.a:
State and explain the direction of motion of the mass at this instant.
18N.3.HL.TZ0.b:
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm. Determine the amplitude after one complete period of oscillation.