DP Physics Questionbank

Calculate the Carnot efficiency of the nuclear power plant.

The velocity of the falling object is 1.89 m s^–1 at 3.98 s. Calculate the average angular acceleration of the flywheel.

(i) Calculate the tension in the string.

(ii) Determine the mass m of the falling object.

The nuclear power plant works at 71.0% of the Carnot efficiency. The power produced is 1.33 GW. Calculate how much waste thermal energy is released per hour.

Show that the torque acting on the flywheel is about 0.3 Nm.

Explain, with a reason, why a real nuclear power plant operating between the stated temperatures cannot reach the efficiency calculated in (a).

Hence, show that $\omega =\frac{v}{4R}$.

State what is meant by an adiabatic process.

Determine the temperature of the gas at A.

The volume at B is 2.30 × 10^–3$$m³. Determine the pressure at B.

Calculate the number of revolutions made by the system before it comes to rest.

Write down an expression, in terms of M, v and R, for the angular momentum of the system about the vertical axis just before the collision.

The volume at C is 2.90 × 10^–3$$m³. Calculate the temperature at C.

State a reason why a Carnot cycle is of little use for a practical heat engine.

Just after the collision the system begins to rotate about the vertical axis with angular velocity ω. Show that the angular momentum of the system is equal to $\frac{4}{3}M{R}^2\omega$.

Show that $P_B{V}_B^{\frac{5}{3}}=nR{T}_C{V}_C^{\frac{2}{3}}$

Determine in terms of M and v the energy lost during the collision.

Show that the angular deceleration of the system is 0.043 rad$$s^–2.

Identify the two isothermal processes.

Determine the final angular speed of the probe–satellite system.

State and explain at which point in the cycle ABCA the entropy of the gas is the largest.

Deduce the linear acceleration of the centre of mass of the probe.

Calculate the resultant torque about the axis of the probe.

The forces act for 2.00 s. Show that the final angular speed of the probe is about 16 rad$$s^–1.

Calculate the loss of rotational kinetic energy due to the linking of the probe with the satellite.

Show that the temperature of the gas at C is 386 K.

Show that the thermal energy removed from the gas for the change BC is approximately 330 J.

Determine the efficiency of the heat engine.

Justify why the thermal energy supplied during the expansion AB is 416 J.

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

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.

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

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 $\sqrt{\frac{10gh}{7}}$.

Calculate the pressure following this process.

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

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 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.

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.

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.

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.

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.

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

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.

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.

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

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

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.

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

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 the new angular speed of the rotating system.

Explain why the angular speed will increase.

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.

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 thermal energy transferred to the gas.

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.

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.

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.

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).

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

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.

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.

Calculate F.

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.

determine the thermal energy removed from the system.

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

Calculate the maximum tension in the string.

explain why the entropy of the gas decreases.

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.