Option B: Engineering physics (Core topics)

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.

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.

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.

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 $\sqrt{\frac{10gh}{7}}$.

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 $\sqrt{\frac{10gh}{7}}$.

Explain the direction in which the person-turntable system starts to rotate.

Explain the direction in which the person-turntable system starts to rotate.

Explain the direction in which the person-turntable system starts to rotate.

Calculate the work done during the compression.

Calculate the work done during the compression.

Calculate the work done during the compression.

Calculate the work done during the increase in pressure.

Calculate the work done during the increase in pressure.

Calculate the work done during the increase in pressure.

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.

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.

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.

Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{g\times \sin q}{2}$

Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{g\times \sin q}{2}$

Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{g\times \sin q}{2}$

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.

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.

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.

State the relationship between the force of friction and the angle of the incline.

State the relationship between the force of friction and the angle of the incline.

State the relationship between the force of friction and the angle of the incline.

Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.

Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.

Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.

Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.

Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.

Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.

The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.

The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.

The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.

Outline the change in entropy of the gas during the cooling at constant volume.

Outline the change in entropy of the gas during the cooling at constant volume.

Outline the change in entropy of the gas during the cooling at constant volume.

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.

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.

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.

Describe the effect of F on the angular speed of the wheel.

Describe the effect of F on the angular speed of the wheel.

Describe the effect of F on the angular speed of the wheel.

Calculate, in J, the work done by the gas during this expansion.

Calculate, in J, the work done by the gas during this expansion.

Calculate, in J, the work done by the gas during this expansion.

There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.

There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.

There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.

The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.

The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.

The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.

Determine the angular velocity of the wheel at B.

Determine the angular velocity of the wheel at B.

Determine the angular velocity of the wheel at B.

Show that the final volume of the gas is about 53 m³.

Show that the final volume of the gas is about 53 m³.

Show that the final volume of the gas is about 53 m³.

Determine the thermal energy which enters the gas during this expansion.

Determine the thermal energy which enters the gas during this expansion.

Determine the thermal energy which enters the gas during this expansion.

Calculate, for the merry-go-round after one revolution, the angular speed. 

Calculate, for the merry-go-round after one revolution, the angular speed. 

Calculate, for the merry-go-round after one revolution, the angular speed. 

Calculate, for the merry-go-round after one revolution, the angular momentum.

Calculate, for the merry-go-round after one revolution, the angular momentum.

Calculate, for the merry-go-round after one revolution, the angular momentum.

Calculate the new angular speed of the rotating system.

Calculate the new angular speed of the rotating system.

Calculate the new angular speed of the rotating system.

Explain why the angular speed will increase.

Explain why the angular speed will increase.

Explain why the angular speed will increase.

Calculate the work done by the child in moving from the edge to the centre.

Calculate the work done by the child in moving from the edge to the centre.

Calculate the work done by the child in moving from the edge to the centre.

Show that the pressure at B is about 5 × 10⁵ Pa.

Show that the pressure at B is about 5 × 10⁵ Pa.

Show that the pressure at B is about 5 × 10⁵ Pa.

For the process BC, calculate, in J, the work done by the gas.

For the process BC, calculate, in J, the work done by the gas.

For the process BC, calculate, in J, the work done by the gas.

For the process BC, calculate, in J, the change in the internal energy of the gas.

For the process BC, calculate, in J, the change in the internal energy of the gas.

For the process BC, calculate, in J, the change in the internal energy of the gas.

For the process BC, calculate, in J, the thermal energy transferred to the gas.

For the process BC, calculate, in J, the thermal energy transferred to the gas.

For the process BC, calculate, in J, the thermal energy transferred to the gas.

Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.

Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.

Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.

Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.

Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.

Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.

Outline why an efficiency calculation is important for an engineer designing a heat engine.

Outline why an efficiency calculation is important for an engineer designing a heat engine.

Outline why an efficiency calculation is important for an engineer designing a heat engine.

At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.

At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.

At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.

Show that the thermal energy transferred from the gas during the change B → C is 238 J.

Show that the thermal energy transferred from the gas during the change B → C is 238 J.

Show that the thermal energy transferred from the gas during the change B → C is 238 J.

The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.

The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.

The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.

Show that at C the temperature is 254 K.

Show that at C the temperature is 254 K.

Show that at C the temperature is 254 K.

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).

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).

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).

Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.

Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.

Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.

Show that at C the pressure is 1.00 × 10⁶Pa.

Show that at C the pressure is 1.00 × 10⁶Pa.

Show that at C the pressure is 1.00 × 10⁶Pa.

State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.

State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.

State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.

Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is $E_{\text{K}}=\frac{7}{10}m{v}^2$.

Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is $E_{\text{K}}=\frac{7}{10}m{v}^2$.

Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is $E_{\text{K}}=\frac{7}{10}m{v}^2$.

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.

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.

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.

Show that the work done on the gas for the isothermal process C→A is approximately 440 J.

Show that the work done on the gas for the isothermal process C→A is approximately 440 J.

Show that the work done on the gas for the isothermal process C→A is approximately 440 J.

Calculate the change in internal energy of the gas for the process A→B.

Calculate the change in internal energy of the gas for the process A→B.

Calculate the change in internal energy of the gas for the process A→B.

determine the thermal energy removed from the system.

determine the thermal energy removed from the system.

determine the thermal energy removed from the system.

Calculate the ratio $\frac{V_{\mathrm{A}}}{V_{\mathrm{C}}}$.

Calculate the ratio $\frac{V_{\mathrm{A}}}{V_{\mathrm{C}}}$.

Calculate the ratio $\frac{V_{\mathrm{A}}}{V_{\mathrm{C}}}$.

Calculate the maximum tension in the string.

Calculate the maximum tension in the string.

Calculate the maximum tension in the string.

explain why the entropy of the gas decreases.

explain why the entropy of the gas decreases.

explain why the entropy of the gas decreases.

Show that the pressure at B is about 130 kPa.

Show that the pressure at B is about 130 kPa.

Show that the pressure at B is about 130 kPa.

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.

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.

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.

Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.

Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.

Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.

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.

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.

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.

Calculate F.

Calculate F.

Calculate F.

Show that the final angular velocity of the bar is about $3 \mathrm{rad} {\mathrm{s}}^{-1}$.

Show that the final angular velocity of the bar is about $3 \mathrm{rad} {\mathrm{s}}^{-1}$.

Show that the final angular velocity of the bar is about $3 \mathrm{rad} {\mathrm{s}}^{-1}$.

Draw the variation with time $t$ of the angular displacement $\theta$ of the bar during the acceleration.

Draw the variation with time $t$ of the angular displacement $\theta$ of the bar during the acceleration.

Draw the variation with time $t$ of the angular displacement $\theta$ of the bar during the acceleration.

Calculate the torque acting on the bar while it is accelerating.

Calculate the torque acting on the bar while it is accelerating.

Calculate the torque acting on the bar while it is accelerating.

Calculate the pressure following this process.

Calculate the pressure following this process.

Calculate the pressure following this process.

Show that the net torque on the system about the central axis is approximately 30 N m.

Show that the net torque on the system about the central axis is approximately 30 N m.

Show that the net torque on the system about the central axis is approximately 30 N m.

Show that the net torque on the system about the central axis is approximately 30 N m.

Show that the net torque on the system about the central axis is approximately 30 N m.

Show that the net torque on the system about the central axis is approximately 30 N m.

Calculate the pressure of the gas at B.

Calculate the pressure of the gas at B.

Calculate the pressure of the gas at B.

Calculate the pressure of the gas at B.

Calculate the pressure of the gas at B.

Calculate the pressure of the gas at B.