DP Physics Questionbank

Calculate the Carnot efficiency of the nuclear power plant.

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

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.

Water flows through a constricted pipe. Vertical tubes A and B, open to the air, are located along the pipe.

Describe why tube B has a lower water level than tube A.

Explain, with reference to energy in the system, the amplitude of oscillation between

(i) t = 0 and t_A.

(ii) t_A and t_B.

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

A solid cube of side 0.15 m has an average density of 210 kg m^–3.

(i) Calculate the weight of the cube.

(ii) The cube is placed in gasoline of density 720 kg m^–3. Calculate the proportion of the volume of the cube that is above the surface of the gasoline.

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.

Calculate the Q factor for the system.

Estimate the magnitude of the force on the ball, ignoring gravity.

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.

Explain the origin of the buoyancy force on the air bubble.

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.

The Q factor of the system increases. State and explain the change to the graph.

With reference to the ratio of weight to buoyancy force, show that the weight of the air bubble can be neglected in this situation.

On the diagram, draw an arrow to indicate the direction of this force.

State and explain the displacement of the sine wave vibrator at t = 8.0 s.

The vibrator is switched off and the spring continues to oscillate. The Q factor is 25.

Calculate the ratio $\frac{\text{energy stored}}{\text{power loss}}$ for the oscillations of the spring–mass system.

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

State what is meant by damping.

On the graph, sketch a curve to show the variation with driving frequency of the amplitude when the damping of the system increases.

Calculate the terminal speed.

State one assumption you made in your estimate in (a)(i).

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.

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

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

Determine the terminal velocity of the sphere.

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 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.

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.

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.

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.

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.

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

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.

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.

Describe the motion of the spring-mass system.

calculate the Q at the start of the motion.

Outline whether your answer to (a) is valid.

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

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).

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.

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.

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

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.

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

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.

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

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.

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

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.

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.

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.