Engineering - Exam Questions

Question 1

State the law of conservation of angular momentum (1)

Answer 1

The angular momentum of a system remains constant provided no external torque acts on the system

Question 2

The satellite is initially rotating slowly about its axis with the arms fully extended. The arms
are slowly retracted so that the instrument pods move closer to the body of the satellite.
State and explain the change in the angular speed of the satellite as the arms are
retracted. (3)

Answer 2

M of I decreases
Because more mass closer to axis
Iω is conserved so ω must increase

Question 3

A turntable is spinning at ω1, when a mass is added to the turntable, it’s speed decreases. Explain this (3)

Answer 3

Law of conservation of angular momentum applies and I1ω1=I2ω2
Adding plasticine increases I
So ω must decrease to conserve angular momentum

Question 4

As mass is added to a spinning turntable, the angular speed decreases and overall rotational kinetic energy decreases. Why? (1)

Answer 4

Work done against friction

Question 5

A diver starts with feet first. He brings his legs to his chest after rotating 90° (c shape). Explain how this movement of the legs causes the moment of inertia about the axis of rotation to decrease (2)

Answer 5

I = Σmr^2

With legs close to chest, more mass at smaller r, so I smaller

Question 6

Explain what is meant by a reversed heat engine (2)

Answer 6

A device in which an input of work, causes heat to transfer from a cold space to a hot space

Question 7

Explain why the coefficient of performance of a reversed heat engine when operating as a heat pump is always greater than the coefficient of performance of the same reversed heat engine when operating as a refrigerator (2)

Answer 7

Heat transfer to hot space equals work done plus heat transfer from cold space so always: Qin > Qout
So COP(heat pump) >COP(fridge)

Question 8

Explain what is meant by the coefficient of performance of a heat pump (1)

Answer 8

Ratio of energy given to hot space over work input

Question 9

Conversion of electrical energy to heat is nearly 100% efficient. Explain why it was proposed to install a heat pump rather than an electrical heater to provide an additional heat (2)

Answer 9

Heat pump delivers more heat energy than the electrical energy input
Because it adds energy from external source to electrical energy input

Question 10

How would you show a process is isothermal?

Answer 10

p1V1=p2V2 for two points on the line

Question 11

A theoretical engine cycle has an isothermal compression, expansion at constant p then adiabatic expansion to return to initial p and V.
Describe two problems that would be encountered designing a real engine for this cycle (2)

Answer 11

Isothermal process would requires engine to be highly conductive
Adiabatic process requires perfectly insulating container

Question 12

How is net work done on the air during a cycle obtained from a p-V graph?

Answer 12

Counting squares in enclosed loop

Squares x change in p and V for one square

Question 13

State two reasons why the actual efficiency of a turbine power station is much less than the maximum theorertical efficiency (2)

Answer 13

Friction in bearings of all machinery

Turbine cycle will not give max theoretical efficiency

Question 14

Explain the basic differences in operation between a petrol engine and a diesel engine (2)

Answer 14

Diesel: air only is drawn into cylinder, Petrol: air and fuel is drawn into cylinder
Diesel: ignition by temperature rise in compression, Petrol: ignition by means of spark

Question 15

A person is standing on a roundabout ride at constant r due to a centripetal force. State the origin of the force and suggest why they have to lean towards the centre of the ride to not fall over (2)

Answer 15

Force produced by friction between feet and roundabout

Centripetal force has to act through the centre of mass of the operator

Question 16

A pocket of air is at constant V at the base of a mountain, upon rising to the top it expands adiabatically. Explain, with reference to first law of thermodynamics, why T of air decreases as it rises (3)

Answer 16

Q = ΔU + W and in adiabatic expansion, Q=0
W is positive so W=-ΔU meaning internal energy decreases
Internal energy related to T therefore T falls

Question 17

A designer wishes to store more energy in a flywheel, without increasing the radius due to limitations of model. Describe and explain other changes that can be made.
Consider: flywheel’s shape, material it is made of and changes to the mechanism (6)

Answer 17

Shape:
I depends on mass and distribution of mass around axis
I = Σmr^2 so increase thickness of flywheel to increase m and thus I
Material:
Higher density material
Gives greater mass for given size
Mechanism:
Increase ω by reducing friction at bearings so use lubrication
A small increase in ω gives large increase in Ek (because ω^2)

Question 18

State one function of a flywheel (1)

Answer 18

To store rotational kinetic energy

Question 19

A water jet produces a reaction force on the arms, causing the spinner to rotate. Explain why the spinner initially accelerates but then reaches a constant angular speed (2)

Answer 19

Initially friction torque < applied torque so spinner accelerates
Eventually applied torque = friction torque and angular speed remains constant

Question 20

First law of thermodynamics can be written as Q = ∆U + W

State the meaning of these terms (3)

Answer 20

Q: Energy supplied to gas by heat transfer
∆U: Increase in internal energy
W: Work done by gas

Question 21

State what is meant by moment of inertia and explain why extending mass from axis of rotation increases by a large factor (3)

Answer 21

I is the sum of the mr^2 products for point masses m at radius r
More of the mass is at greater radius
Small change in r gives large change in r^2, hence large change in I

Question 22

Explain the term QH with reference to a heat pump used to provide heating in a building (1)

Answer 22

QH is energy into the hot space

Question 23

Explain why the rapid compression of the gas can be assumed to be an adiabatic process (2)

Answer 23

In adiabatic compression there is no heat transfer

If compression is quick there is no time for heat transfer

Question 24

The terms force and mass are used in translational dynamics, what are the respective terms for rotational dynamics? (2)

Answer 24

Force -> Torque

Mass -> Moment of inertia

Question 25

Why might there be a difference between indicated power and brake power? (1)

Answer 25

Power expended in overcoming friction

Question 26

Explain why, for an isothermal expansion, the first law can be written as ΔW = ΔQ (3)

Answer 26

Temperature is constant in isothermal expansion
Absolute temperature depends upon internal energy
Hence ΔU = 0

Question 27

Explain why a compression of air can be considered to be adiabatic (2)

Answer 27

Rapid compression of air in cylinder

Gives little time for heat transfer

Question 28

A torque against time graph is shown. Explain how the graph can be used to estimate the average torque acting on the system (3)

Answer 28

Area under curve = angular impulse = T(average) x t
Area found by counting squares
T(average) = angular impulse/t

Question 29

Explain why a low moment of inertia is desirable when the speed and direction of rotation must be changed quickly (2)

Answer 29

Ek = 1/2 Iω^2 so small stored energy if I is small

Question 30

A rocket propels using adiabatic expansion of air inside it. State and explain whether the rocket would have reached the same height if the air had expanded isothermally (3)

Answer 30

Isothermal line would have been less steep
So greater area under line and more work done
So rocket would rise higher

Question 31

With reference to a refrigerator, explain Q(in) and Q(out) (2)

Answer 31

Q(out) is energy removed from the fridge contents

Q(in) is the energy given to the surroundings

Question 32

A student claims: “A heat pump delivers more energy than is supplied to it”. Discuss this
statement and explain why a heat pump does not contradict the law of conservation of
energy or the second law of thermodynamics (3)

Answer 32

Heat pump does deliver more energy than is input as work on the system, but there must also be energy input from cold space
Obeys conservation of energy because work done plus energy from cold space equals energy by heat transfer to hot space
Obeys second law because operates between hot and cold spaces