AQA A Level Physics Paper 3 Section B: Engineering physics June 2023 question paper 7408/3BC

One equation used in translational dynamics is:

force = mass × acceleration

State in words the equivalent equation used in rotational dynamics.

Figure 1 shows two identical uniform plates A and B. The axis of rotation of each plate is shown.

State and explain which plate has the greater moment of inertia about its axis of rotation.

An electric motor drives a machine that punches out plates from a long strip of sheet metal. The motor runs continuously and is fitted with a flywheel. Figure 2 shows how the angular velocity ω of the flywheel varies with time t.

Table 1 describes the sequence for the machine after it has been brought up to

A new flywheel with a greater moment of inertia is fitted in place of the original flywheel. The motor torque is constant and the same as before.

Sketch on Figure 2 a graph showing how the angular velocity varies with time for the machine fitted with the new flywheel.

Assume that:

• the punching operation starts at the same angular speed ω_A

• the same quantity of energy is transferred when punching the metal sheet.

Explain one difference between your graph and the original graph.

Figure 3 shows a heavy stone grinding wheel used for sharpening tools.

The pedal is connected to the axle of the wheel by a connecting link and crank. The operator pushes the pedal downwards to accelerate the wheel from rest. The wheel begins to rotate in the direction shown.

Explain why the torque applied to the axle varies as the operator pushes downwards on the pedal.

The wheel is rotating at a high angular speed. The operator is told not to use the pedal to stop the rotation of the wheel suddenly.

Explain, with reference to angular impulse, why a sudden stop is likely to damage the mechanism.

The connecting link breaks. At this instant the angular speed of the wheel

speeds.

Calculate the moment of inertia of the wheel.

The arrangement is modified as shown in Figure 4. The pedal, connecting link and crank are removed and the grinding wheel is driven by an electric motor.

Figure 4 also shows a tool being sharpened by pressing it on the edge of the rotating wheel. The tool applies a tangential force F on the wheel. A torque of 3.10 N m is needed at the axle to drive the wheel at constant angular speed while the tool is being sharpened.

frictional torque at the axle bearings = 0.77 N m radius of wheel = 0.24 m

Calculate F.

Three motors E, F and G were available to drive the wheel in Figure 4. Figure 5 shows how the torque T varies with angular speed ω for each motor.

The no-load speed ω₀ is the angular speed of a motor when the torque applied is zero. The maximum power of each motor is developed at about 0.5ω₀. The required output power of the motor when a tool is being sharpened is 52 W. The required output power of the chosen motor should be about of its maximum power.

Deduce which motor E, F or G was chosen for this application.

The first law of thermodynamics can be written as:

Q = Δ U + W

State what Q represents in this equation.

Air in the brake pipe of a bicycle hydraulic brake system can be dangerous. Figure 6 shows a bubble of air in a brake pipe.

Assume that the hydraulic fluid is incompressible. During a sudden application of the brake, the air is compressed adiabatically to a high pressure.

The work done on the air when it is compressed is 10.8 mJ.

Which row is correct for this adiabatic compression?

The initial conditions for the air are:

During sudden braking, the air in the bubble is compressed adiabatically to a volume

Calculate the pressure and the temperature of the air immediately after the compression.

γ for air = 1.4

To produce the adiabatic change, the brake lever is pulled very quickly. The cyclist thinks that by applying the brake slowly, the work done to compress the bubble to a volume of 3.19 × 10⁻⁹ m³ will be greater than 10.8 mJ.

Deduce without calculation whether the cyclist is correct.

Figure 7 shows the p – V diagram for a theoretical diesel engine cycle. Figure 8 shows the indicator diagram for a real four-stroke diesel engine working between the same maximum and minimum volumes.

Compare the indicator diagram with the theoretical diesel cycle. In your answer, explain:

• the differences between region A on Figure 7 and region A on Figure 8

• the differences between region B on Figure 7 and region B on Figure 8

• why the features shown in region C appear only on the indicator diagram

• why the efficiency of the real engine will always be less than the efficiency predicted by an analysis of the theoretical cycle.

Figure 9 shows an ideal heat engine.

The engine operates between a source at a temperature of 730 K and a sink at a temperature of 290 K. The input power is 16.0 kW and the power rejected to the sink is 6.4 kW.

Calculate the efficiency of this engine.

Figure 10 shows another system operating between the same overall temperatures and with the same input power as the engine in Figure 9. This system consists of two ideal engines.

The sink for engine 1 forms the source for engine 2. The temperature of the intermediate reservoir is 510 K. All the energy rejected by heat transfer in engine 1 provides the input energy to engine 2. A student suggests that the system in Figure 10 can provide more output power and be more efficient than the engine in Figure 9.

Deduce whether the student’s suggestions are correct. You may annotate Figures 9 and 10.