AQA A Level Physics Paper 3 Section B: Engineering physics June 2017 question paper 7408/3BC

There is an analogy between quantities in rotational and translational dynamics.

Complete Table 1, stating in words the quantities in rotational dynamics that are analogous to force and mass in translational dynamics.

Figure 1 shows a side view of the jib of a tower crane. The load is supported by a trolley which can move along the jib. The jib consists of all the parts of the crane above the bearing, but excluding the trolley and load.

The moment of inertia of the jib about the axis of rotation = 2.6 × 10⁷ kg m²

Mass of trolley and load = 2.2 × 10³ kg

The load is at a distance of 35 m from the axis of rotation.

Show that the total moment of inertia of the jib, and the trolley and load, about the axis of rotation is about 3 × 10⁷ kg m².

Figure 2 shows the variation of angular speed of the jib as it turns through an angle of 4.7 rad (270°) in a total time of 95 s. The trolley and load remain at a distance of 35 m from the axis.

Calculate the maximum angular speed ω_max of the jib.

At time X in Figure 2 the motor that is driving the jib is disengaged. A constant braking torque is then applied to bring the jib to a standstill from its maximum angular speed.

The crane driver repeats the movement of the jib with the same load at 35 m from the axis of rotation. Up to time X the motion is the same as before. From time X the trolley is driven at a steady speed away from the axis as the jib continues to rotate until the jib comes to a standstill.

Assume the braking torque remains the same as before.

Discuss how the motion of the trolley affects the time taken for the jib to come to a standstill.

Figure 3

The salad is placed in the basket and the lid is attached.

When handle A is turned the basket and its contents spin rapidly. Water on the salad is driven through holes in the basket into the stationary water collecting bowl. The pivot for gear B is fixed to the lid. This pivot and the lid do not move. When gear B rotates, gear C also rotates but at a greater angular speed. Gear C is fixed to the basket and rotates it.

A force of 6.0 N is applied to handle A as shown. Handle A is at a radius of 36 mm from its centre of rotation.

Calculate the input torque.

Gear C rotates four times for every one revolution of gear B.

Deduce whether it is possible for the torque on gear C to be greater than one quarter of the input torque.

It takes 2.1 s for the empty basket to reach an angular speed of 76 rad s^–1. The torque on gear C is a constant 0.054 N m during this time. Frictional losses are negligible.

Calculate the moment of inertia of the basket about its axis of rotation.

The gears are made from polymer (plastic). An early version of this salad spinner suffered from damaged gear teeth.

Explain with reference to angular impulse why a great force is put on the gear teeth if the user tries to stop the loaded basket too quickly using the handle.

A fixed mass of nitrogen gas is sealed into the cylinder of the strut.

The gas is initially at a pressure of 1.2 × 10⁶ Pa, a volume of 9.0 × 10^–5 m³ and a temperature of 290 K.

When the lid is closed quickly the gas is compressed rapidly to a final volume of

Calculate the pressure and temperature of the gas at the end of the compression assuming the compression to be an adiabatic process.

adiabatic index γ for nitrogen = 1.4

Explain why the rapid compression of the gas can be assumed to be an adiabatic process.

When the lid is closed slowly, the compression can be assumed to be isothermal.

The gas can be compressed either isothermally or adiabatically from the same initial conditions to the same final volume.

Compare without calculation the work done in each process.

maximum and minimum volumes.

Compare the theoretical and real engine cycles. In your answer you should:

state and explain the differences between the cycles

explain why the work output per cycle of the real engine is less than that predicted by an analysis of the theoretical cycle.

An ideal heat pump and an ideal refrigerator operate between the same hot and cold spaces.

Which statement relating to the coefficient of performance (COP) is correct? Tick (✓) the correct answer.

An ideal refrigerator operates between a cold space at a temperature of ̶ 1 °C and a hot space at a temperature of 70 °C.

Calculate the input power to the refrigerator if the rate of transfer of energy to the hot space is 100 W.