materials exam style questions 54 marks

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Materials

Exam Style Questions

54 Marks

My mark = ____/54

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Q1. (a) Define the density of a material.

......................................................................................................................

...................................................................................................................... (1)

(b) Brass, an alloy of copper and zinc, consists of 70% by volume of copper and 30% by volume of zinc.

density of copper = 8.9 × 103 kg m–3

density of zinc = 7.1 × 103 kg m–3

(i) Determine the mass of copper and the mass of zinc required to make a rod of brass of volume 0.80 × 10–3 m3.

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(ii) Calculate the density of brass.

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............................................................................................................. (4)

(Total 5 marks)


Q2.The diagram below shows a lorry of mass 1.2 × 103 kg parked on a platform used to weigh vehicles. The lorry compresses the spring that supports the platform by 0.030 m.

Calculate the energy stored in the spring.

gravitational field strength g = 9.8 N kg–1

Energy stored = ........................................... (Total 3 marks)

Q3.(a) The Young modulus is defined as the ratio of tensile stress to tensile strain. Explain what is meant by each of the terms in italics.

tensile stress .................................................................................................

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........................................................................................................................

tensile strain ...................................................................................................

........................................................................................................................ (3)

(b) A long wire is suspended vertically and a load of 10 N is attached to its lower end. The extension of the wire is measured accurately. In order to obtain a value for the Young modulus of the material of the wire, two more quantities must be measured. State what these are and in each case indicate how an accurate measurement might be made.

quantity 1 ........................................................................................................

method of measurement ...............................................................................

........................................................................................................................

quantity 2 ........................................................................................................

method of measurement ................................................................................

........................................................................................................................ (4)


(c) Sketch below a graph showing how stress and strain are related for a ductile substance and label important features.

(2)

(Total 9 marks)

Q4. A student investigated how the extension of a rubber cord varied with the force used to extend it. She measured the extension for successive increases of the force and then for successive decreases. The diagram below shows a graph of her results.

(a) (i) Give a reason why the graph shows the rubber cord does not obey Hooke’s law.

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............................................................................................................. (1)

(ii) Give a reason why the graph shows the rubber cord does not exhibit plastic behaviour.

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............................................................................................................. (1)

(iii) What physical quantity is represented by the area shaded on the graph between the loading curve and the extension axis?

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............................................................................................................. (1)

(b) Describe, with the aid of a diagram, the procedure and the measurements you would make to carry out this investigation.

The quality of your written answer will be assessed in this question.

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...................................................................................................................... (6)

(Total 9 marks)


Q4. The table below shows the results of an experiment where a force was applied to a sample of metal.

(a) On the axes below, plot a graph of stress against strain using the data in the table.

Strain / 10–3 0 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Stress /108 Pa

0 0.90 2.15 3.15 3.35 3.20 3.30 3.50 3.60 3.60 3.50

(3)

(b) Use your graph to find the Young modulus of the metal.

answer = ...................................... Pa (2)


(c) A 3.0 m length of steel rod is going to be used in the construction of a bridge. The tension in the rod will be 10 kN and the rod must extend by no more than 1.0mm. Calculate the minimum cross-sectional area required for the rod.

Young modulus of steel = 1.90 × 1011 Pa

answer = ...................................... m2

(3) (Total 8 marks)

Q6.A manufacturer of springs tests the properties of a spring by measuring the load applied each time the extension is increased. The graph of load against extension is shown below.

(a) State Hooke’s law.

........................................................................................................................

........................................................................................................................

........................................................................................................................ (2)

(b) Calculate the spring constant, k, for the spring. State an appropriate unit.


spring constant ......................................... unit ............... (3)

(c) Use the graph to find the work done in extending the spring up to point B.

work done ............................................ J (3)

(d) Beyond point A the spring undergoes plastic deformation.

Explain the meaning of the term plastic deformation.

........................................................................................................................

........................................................................................................................ (1)

(e) When the spring reaches an extension of 0.045 m, the load on it is gradually reduced to zero. On the graph above sketch how the extension of the spring will vary with load as the load is reduced to zero.

(2)

(f) Without further calculation, compare the total work done by the spring when the load is removed with the work that was done by the load in producing the extension of 0.045 m.

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........................................................................................................................

........................................................................................................................ (1)

(Total 12 marks)

Q7.An aerospace engineer has built two differently designed wings. One wing is made from an aluminium alloy and the other is made from a carbon fibre composite.

The engineer tests a sample of each material by applying a varying stress.


(a) Tick (✓) two of the boxes in the table below to indicate which are properties of the

material from which the wing is made.

breaking stress

stiffness constant, k

tensile strain

tensile stress

Young modulus

(1)

(b) Below is the stress−strain graph that the engineer obtains for the aluminium alloy.

(i) The engineer has labelled a point Q on the graph. This is a point beyond which the

behaviour of the material changes irreversibly. State the name for this point.

............................................................................................................... (1)

(ii) Use the graph to determine the Young modulus of the aluminium alloy. Show your working.


Young modulus = ................................................ Pa (2)

(c) The engineer who carried out the experiment to obtain the stress−strain graph decided to stretch another sample to a strain of 0.10. She then gradually reduced the stress to zero.

Show by drawing on the graph how you would expect the stress to vary with strain as the stress is reduced.

(2)

(d) Calculate the volume of 25.0 kg of the aluminium alloy.

density of aluminium alloy = 2.78 × 103 kg m–3.

volume = ................................................ m3

(1)

(e) 1.28% of the aluminium alloy’s volume is copper. Calculate the mass of pure aluminium needed to make 25.0 kg of the aluminium alloy.

density of pure aluminium = 2.70 × 103 kg m–3.

mass of pure aluminium = ................................................ kg (2)

(Total 9 marks)


M1. (a) density = (1) 1

(b) (i) volume of copper = × 0.8 ×10–3 (= 0.56 × 10–3 m3)

(volume of zinc = 0.24 × 10–3 m3)

mc (= ρcVc) = 8.9 × 103 × 0.56 × 10–3 = 5.0 kg (1) (4.98 kg)

mz = × 0.8 × 10–3 × 7.1 × 103 = 1.7 (kg) (1)

(allow C.E. for incorrect volumes)

(ii) mb (= 5.0 +1.7) = 6.7 (kg) (1) (allow C.E. for values of mc and mz)

ρb = = 8.4 × 103 kg m–3 (1)

(allow C.E. for value of mb) [or ρb = (0.7 × 8900) + (0.3 × 7100) (1) = 8.4 × 103 kg m–3 (1)]

max 4

[5]

M2.use of mg with g = 9.8[ use of g 10 – 1] B1

energy = ½ F l = ½ (1200 × 9.8) × 0.03 M1

= 180 J [176] [omission of g will score only 1] A1

[3]


M3.(a) tensile stress = (1)

tensile strain = (1)

mention of tensile and original (1) (3)

(b) diameter of wire (1) in several places [or repeated] (1) using a micrometer (1) (original) length of wire (1) using a metre rule (or tape measure) (1)

(max 4)

(c)

(2)

[9]

M4. (a) (i) the lines are not straight (owtte) (1)

(ii) there is no permanent extension (1) (or the overall/final extension is zero or the unloading curve returns to zero extension)

(iii) (area represents) work done (on or energy transfer to the rubber cord) or energy (stored) (1) not heat/thermal energy

3

(b) the mark scheme for this part of the question includes an overall assessment for the Quality of Written Communication

QWC descriptor mark range

good- excellent

The candidate provides a comprehensive and coherent description which includes nearly all the necessary procedures and measurements in a logical order. The descriptions should show awareness of how to apply a

5-6


variable force. They should know that measurements are to be made as the force is increased then as it is decreased. In addition, they should know how to calculate/measure the extension of the cord. At least five different masses/’large number’ of masses are used. Minimum 7 masses to reach 6 marks. The diagram should be detailed.

modest- adequate

The description should include most of the necessary procedures including how to apply a variable force and should include the necessary measurements. They may not have described the procedures in a logical order. They may not appreciate that measurements are also to be made as the cord is unloaded. They should know that the extension of the cord must be found and name a suitable measuring instrument (or seen in diagram – label need not be seen)/how to calculate. The diagram may lack some detail.

3-4

poor- limited

The candidate knows that the extension or cord length is to be measured for different forces – may be apparent from the diagram. They may not appreciate that measurements are also to be made as the cord is unloaded. They may not state how to calculate the extension of the cord. The diagram may not have been drawn.

1-2

incorrect, inappropriate

or no response

No answer at all or answer refers to unrelated, incorrect or inappropriate physics.

0

The explanation expected in a competent answer should include a coherent selection of the following physics ideas.

diagram showing rubber cord fixed at one end supporting a weight at the other end or pulled by a force (1)

means of applying variable force drawn or described (eg use of standard masses or a newtonmeter) (1)

means of measuring cord drawn or described (1)

procedure

measured force applied ( or known weights used) (1)

cord extension measured or calculated (1)

repeat for increasing then decreasing length (or force/weight) (1)

extension calculated from cord length – initial length (1) [9]


M5. (a)

Suitable scale on both axes (eg not going up in 3s) and > ½ space used

≥ points correct (within half a small square)

line is straight up to at least stress = 2.5 × 108 and curve is smooth beyond straight section

3

(b) understanding that E = gradient (= Δy/Δx)

allow y/x if line passes through origin

= 1.05 × 1011 (Pa) (allow 0.90 to 1.1) ecf from their line in (a)

if answer outside this range and uses a y value ≥ 2

when values used from table;

• two marks can be scored only if candidates line passes through them

• one mark only can be scored if these points are not on their line 2

(c) correct rearrangement of symbols or numbers ignoring incorrect

powers of ten, eg A =

correct substitution in any correct form of the equation,

eg =

allow incorrect powers of ten for this mark


= 1.6 × 10–4 (1.5789) (m2) 3

[8]

M6.(a) Force proportional to extension

up to the limit of proportionality (accept elastic limit) dependent upon award of first mark

Symbols must be defined Accept word equation

allow ‘F=kΔL (or F ∝ ΔL) up to the limit of proportionality ’ for the second mark only

allow stress ∝ strain up to the limit of proportionality’ for the second mark only

2

(b) Gradient clearly attempted / use of k=F / ΔL

k = 30 / 0.026 = 1154 or 31 / 0.027 = 1148

correct values used to calculate gradient with appropriate 2sf answer given (1100 or 1200)

1100 or 1200 with no other working gets 1 out of 2

OR 1154 ± 6 seen

Do not allow 32/0.0280 or 33/0.0290 (point A) for second mark.

AND load used >= 15 (= 1100 or 1200 (2sf) )

32 / 0.028 is outside tolerance. 32/0.0277 is just inside.

Nm−1 / N / m (newtons per metre) (not n / m, n / M, N / M) 3

(c) any area calculated or link energy with area / use of 1 / 2FΔL

(or 0.001 Nm for little squares)

35 whole squares, 16 part gives 43 ± 1.0 OR equivalent correct method to find whole area

0.025 Nm per (1cm) square × candidates number of squares and correctly evaluated OR (= 1.075) = 1.1 (J) (1.05 to 1.10 if not rounded)

3


(d) permanent deformation / permanent extension

Allow: ‘doesn’t return to original length’; correct reference to ‘yield’ e.g. allow ‘extension beyond the yield point’ do not accept: ‘does not obey Hooke’s law’ or ‘ceases to obey Hooke’s law’,

1

(e) any line from B to a point on the x axis from 0.005 to 0.020

straight line from B to x axis (and no further) that reaches x axis for 0.010<=ΔL<= 0.014

2

(f) work done by spring < work done by the load

Accept ‘less work’ or ‘it is less’ (we assume they are referring to the work done by spring)

1

[12]

M7.(a)

breaking stress ✓

stiffness constant, k

tensile strain

tensile stress

Young modulus ✓

1

(b) (i) elastic limit ✓

only one attempt at the answer is allowed 1

(ii) ( E = 300 × 106 / 4 × 10-2 = 7.5 × 109 )

7.5 (Pa) ✓ allow 7.4 to 7.6 (Pa)

× 109 ✓

first mark is for most significant digits ignoring the power of 10. E.g. 7500 gains mark

2


(c) straight line beginning on existing line at a strain of 0.10 and hitting the strain axis at

a lower non-zero value ✓

line that ends on the x -axis with strain between 0.045 and 0.055 ✓(only allow if first

mark is given)

ie accuracy required ± one division 2

(d) 8.99 × 10-3 (m3) ✓ condone 1 sig fig

allow 9.00 × 10-3

1

(e) 0.9872 × 8.99 × 10-3 or = 8.8749 × 10-3 (m3) ✓

allow CE from 4d

(m = ρV )= 2700 × 8.8749 × 10-3 = 24 (kg) ✓ (23.962 kg)

allow CE from first part, e.g. if 1.28% was used gives 0.311 kg

V =0.9872 × (d)

m = 2.665 × (d)

1.28% of vol = 1.15 × 10-4 m3

2

[9]

materials exam style questions 54 marks

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