AQA A-Level Physics: Engineering Physics

The petrol engine in a car operates on a four-stroke cycle. The behaviour of the gas in one cylinder over a complete cycle can be represented on an indicator (p-V) diagram.

Describe and explain the sequence of the four strokes of a petrol engine cycle, making clear reference to the shape of the indicator diagram. Your answer should make clear, for each stroke, what the piston does, how the pressure and volume of the gas change, and where energy enters or leaves the gas. You should also state which stroke does useful work on the piston and identify the feature of the indicator diagram that represents the net work done per cycle.

(6 marks)

A flywheel used for short-term energy storage is mounted on frictionless bearings. The flywheel is initially at rest. Data for the flywheel are given below.

Quantity	Value
Moment of inertia of flywheel	12 kg m²
Constant accelerating torque applied	18 N m
Final angular speed reached	250 rad s⁻¹

(a) Calculate the angular acceleration of the flywheel and hence the time taken to reach its final angular speed from rest. (2 marks)

(b) Calculate the rotational kinetic energy stored in the flywheel when it is rotating at 250 rad s⁻¹. (2 marks)

(c) The accelerating torque is then removed and the flywheel is used to deliver a steady output power of 5.0 kW to a machine. Assuming the stored energy is the only source, calculate the time for which the flywheel can supply this power. (2 marks)

A single-cylinder four-stroke petrol engine is tested using an indicator (p-V) diagram. The closed loop on the diagram is drawn on a grid in which each small square represents 20 J of work. The area enclosed by the loop is found, by counting squares, to be approximately 23 squares. Further test data are listed below.

Quantity	Value
Energy represented by one grid square	20 J
Number of squares enclosed by the loop	23
Engine speed	3000 revolutions per minute
Rate at which fuel supplies chemical energy	36 kW

(a) Use the grid to estimate the net work done by the gas per cycle (the indicated work per cycle). (1 mark)

(b) Calculate the indicated power of the engine. Remember that a four-stroke engine completes one cycle every two revolutions of the crankshaft. (2 marks)

(c) Hence calculate the thermal (overall) efficiency of the engine, expressing your answer as a percentage. (2 marks)

A heat engine in a small power unit takes in energy from a hot source and rejects energy to a cold sink. The operating data, measured per second, are shown below.

Quantity	Value
Temperature of hot source, $T_H$TH​	800 K
Temperature of cold sink, $T_C$TC​	320 K
Energy input from the hot source each second, $Q_{in}$Qin​	60 kW
Useful work output each second, $W$W	18 kW

(a) Calculate the actual thermal efficiency of this engine. (2 marks)

(b) Calculate the maximum theoretical efficiency of an engine operating between these two temperatures, and briefly state one reason the actual efficiency is lower than this maximum. (2 marks)

(c) Calculate the energy rejected to the cold sink each second. (1 mark)

A horizontal disc A is rotating freely on a frictionless vertical axle. A second disc B, initially stationary, is dropped gently onto disc A so that the two rotate together about the same axis. There is no external torque about the axle. The data are:

Quantity	Value
Moment of inertia of disc A, $I_A$IA​	0.40 kg m²
Initial angular speed of disc A, $\omega_1$ω1​	24 rad s⁻¹
Moment of inertia of disc B, $I_B$IB​	0.20 kg m²

(a) Calculate the common angular speed of the two discs after disc B has been dropped on. (2 marks)

(b) By calculating the rotational kinetic energy before and after, show that rotational kinetic energy is not conserved in this process, and state where the "lost" energy goes. (2 marks)

The first law of thermodynamics for a fixed mass of gas can be written as

$Q = \Delta U + W$Q=ΔU+W

State what each of the three terms $Q$Q, $\Delta U$ΔU and $W$W represents, and make clear the sign convention (the direction of energy transfer) that applies to $Q$Q and to $W$W in this form of the equation. (3 marks)