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

Determine the force exerted by the spring on the sphere when the sphere is at rest.

Determine the force exerted by the spring on the sphere when the sphere is at rest.

Determine the force exerted by the spring on the sphere when the sphere is at rest.

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 $\mathrm{Q}$ factor for this system.

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 $\mathrm{Q}$ factor for this system.

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 $\mathrm{Q}$ factor for this system.

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.

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.

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.

Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.

Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.

Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.

Show that the distance to Vega from Earth is about 25 ly.

Show that the distance to Vega from Earth is about 25 ly.

Show that the distance to Vega from Earth is about 25 ly.

Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.

Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.

Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.

Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.

Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.

Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s^–1.

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.

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.

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.

Outline whether it is reasonable to assume that flow is laminar in this situation.

Outline whether it is reasonable to assume that flow is laminar in this situation.

Outline whether it is reasonable to assume that flow is laminar in this situation.

State the difference in terms of the velocity of the water between laminar and turbulent flow.

State the difference in terms of the velocity of the water between laminar and turbulent flow.

State the difference in terms of the velocity of the water between laminar and turbulent flow.

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 = $\sqrt{2gH}$.

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 = $\sqrt{2gH}$.

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 = $\sqrt{2gH}$.

Calculate the Reynolds number for the water flow.

Calculate the Reynolds number for the water flow.

Calculate the Reynolds number for the water flow.

Describe the motion of the spring-mass system.

Describe the motion of the spring-mass system.

Describe the motion of the spring-mass system.

calculate the Q at the start of the motion.

calculate the Q at the start of the motion.

calculate the Q at the start of the motion.

Outline whether your answer to (a) is valid.

Outline whether your answer to (a) is valid.

Outline whether your answer to (a) is valid.

Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.

Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.

Show that the velocity of the fluid at X is about 2 ms^–1, assuming that the flow is laminar.

Estimate the Reynolds number for the fluid in your answer to (a).

Estimate the Reynolds number for the fluid in your answer to (a).

Estimate the Reynolds number for the fluid in your answer to (a).

Draw a graph to show the variation of amplitude of oscillation of the system with frequency.

Draw a graph to show the variation of amplitude of oscillation of the system with frequency.

Draw a graph to show the variation of amplitude of oscillation of the system with frequency.

The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.

The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.

The Q factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.

State and explain the direction of motion of the mass at this instant.

State and explain the direction of motion of the mass at this instant.

State and explain the direction of motion of the mass at this instant.

The density of water is 1000 kg m^–3. Calculate u.

The density of water is 1000 kg m^–3. Calculate u.

The density of water is 1000 kg m^–3. Calculate u.

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.

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.

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.

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.

Draw and label the forces acting on the sphere at the instant when it is released.

Draw and label the forces acting on the sphere at the instant when it is released.

Draw and label the forces acting on the sphere at the instant when it is released.

State one condition that must be satisfied for the Bernoulli equation

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

to apply

State one condition that must be satisfied for the Bernoulli equation

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

to apply

State one condition that must be satisfied for the Bernoulli equation

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

to apply

Calculate the difference in pressure between X and Y.

Calculate the difference in pressure between X and Y.

Calculate the difference in pressure between X and Y.

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.

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.

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.

The Q factor for the system is 25. Determine the period of oscillation for this system.

The Q factor for the system is 25. Determine the period of oscillation for this system.

The Q factor for the system is 25. Determine the period of oscillation for this system.

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.

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.

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.

After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.

After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.

After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.

Explain why the levels of the liquid are at different heights.

Explain why the levels of the liquid are at different heights.

Explain why the levels of the liquid are at different heights.

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.

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.

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.

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.

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.

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.

Determine the terminal velocity of the sphere.

Determine the terminal velocity of the sphere.

Determine the terminal velocity of the sphere.

Outline the effect on $\mathrm{Q}$ of changing the oil to one with greater viscosity.

Outline the effect on $\mathrm{Q}$ of changing the oil to one with greater viscosity.

Outline the effect on $\mathrm{Q}$ of changing the oil to one with greater viscosity.

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.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

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.  $\frac{(2n-1)V}{2L}$

B.  $\frac{(2n-1)V}{4L}$

C.  $\frac{nV}{2L}$

D.  $\frac{nV}{4L}$

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

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