CIE AS Physics

Topic Questions

ASPhysicsCIETopic Questions6. Deformation of Solids6.1 Deformation: Stress & Strain

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First teaching 2020

Last exams 2024

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6.1 Deformation: Stress & Strain

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11 mark

A student wanted to measure the Young modulus of a wire, to do this they needed to take a number of measurements.

 In which row could the measurement not be made directly with the listed apparatus?

 

Measurement

Apparatus

A

B

C

D

extension of wire

area of cross-section of wire

original length of wire

mass of load applied to a wire

vernier scale

micrometer screw gauge

metre rule

electronic balance

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21 mark

What is the unit of the Young modulus?

  • N m–2

  • N m

  • N m–1

  • N m2

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31 mark

Which of the following is the definition of the ultimate tensile stress of a material?

  • the maximum inter-atomic force before the atomic bonds of the material break 

  • the maximum force that can be applied to a bar of the material before it bends

  • the maximum tensile force in a wire of the material before it breaks

  • the maximum stretching force per unit cross-sectional area before the material breaks 

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41 mark

A material is extended elastically within the limit of proportionality. What is equal to the Young modulus of the material?

  • gradient of the stress-strain graph 

  • area under the force-extension graph 

  • area under the stress-strain graph 

  • gradient of the force-extension graph

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51 mark

An experiment was carried out to determine the Young modulus of steel using a steel wire.

 The uncertainties in the measurements are given below.

 

Measurement

Uncertainty

load on wire

length of wire

diameter of wire

extension

±2%

±0.2%

±1.5%

±1%

 

What is the percentage uncertainty in the Young modulus?

  • 6.2%

  • 4.7%

  • 1.8%

  • 1.3%

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61 mark

A glass rod was put under stress and strain until it broke. The graph of this is shown below.

cie-ial-images247png

Which of the following statements is correct about the glass rod?

  • the glass shows plastic deformation

  • when the cross-sectional area of the rod is doubled, the ultimate tensile stress of the rod is halved

  • Hooke’s law is obeyed for all values of stress up to the breaking point

  • the glass is ductile

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71 mark

Two wires S and T, with the same initial dimensions, were put under stress and strain, the graph shows the results up to their breaking points.

cie-ial-images248png

Which statement is not correct?

  • material S has a larger ultimate tensile stress

  • material S extends elastically

  • material S extends more than material T when loaded with the same force

  • material S is brittle

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81 mark

The graphs below show the stress-strain graphs of three materials. The graphs do not have the same scales.

 cie-ial-images249png

The three materials are copper, rubber and glass.

 Which materials are represented by the graphs?

 

1

2

3

A

B

C

D

rubber

rubber

glass

copper

copper

glass

copper

glass

glass

copper

rubber

rubber

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91 mark

The stress-strain graph for bone is shown below.

cie-ial-images250png

What is the Young modulus of bone?

  • 2 × 106 N m−2

  • 2 × 108 N m−2

  • 1 × 106 N m−2

  • 1 × 108 N m−2

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101 mark

A student wanted to determine the spring constant of a spring. They did this by using different loads to the extend the spring by varying amounts.

To find the spring constant, which quantities are required?

  • the elastic limit, extensions and the length of the spring

  • the loads and the extensions of the spring 

  • the elastic limit and the loads

  • the loads and the length of the spring

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11 mark

A student connected two springs, one with spring constant k1 = 4 kN m–1 and the other with spring constant k2 = 2 kN m–1 as shown in the diagram below.

cie-ial-images258png

When a load of 80 N is applied, what is the total extension?

  • 60 cm 

  • 6 cm 

  • 4 cm

  • 1.3 cm

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21 mark

A glass-reinforced plastic rod and a nylon rod attached, as shown, was used to make a composite rod.

cie-ial-images259png

Each rod has a length of 1.00 m and the same cross-sectional area. The Young modulus En of the nylon is 2.0 GPa, and the Young modulus Ep of the plastic is 40 GPa

 The composite rod will break when its total extension reaches 3.0 mm.

 What is the greatest tensile stress that can be applied to the composite rod before it breaks?

  • 5.7 cross times 10 to the power of 6 space end exponent P a

  • 5.7 cross times 10 to the power of 9 space P a

  • 7.1 cross times 10 to the power of negative 14 end exponent space P a

  • 7.1 cross times 10 to the power of negative 2 space end exponent P a

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31 mark

A child with a mass of 40 kg was standing on a diving board. The diving board has a length of 5.0 m and is hinged at one end then supported by a spring 2.0 m from the hinged end. The spring has a spring constant of 10 kN m–1

cie-ial-images260png

What is the extra compression of the spring caused by the child standing on the end of the board?

  • 16 cm 

  • 9.8 cm

  • 1.6 cm 

  • 1.0 cm

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41 mark

Three springs are arranged vertically, as shown.

cie-ial-images261png

Springs X and Y are identical and have a spring constant k. Spring Z has a spring constant of 3 k.

 What is the increase in the overall length of the arrangement when a force W is applied as shown?

  • fraction numerator 4 W over denominator 3 k end fraction

  • fraction numerator 5 W over denominator 6 k end fraction

  • 4 k W

  • fraction numerator 7 space k W over denominator 2 end fraction

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51 mark

The diagram shows a metal cube is placed between two board and compressed elastically by two opposing forces F. The cube has a length of each side of l

cie-ial-images262png

How will ∆l, the amount of compression, relate to l ?

  • increment l space alpha space l

  • increment l space alpha space l squared

  • increment l space alpha space 1 over l squared

  • increment l space alpha space 1 over l

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61 mark

A metal wire that is supported vertically from a fixed point has a load of 84 N applied to the lower end. The wire has a cross-sectional area of 0.02 mm2 and obeys Hooke’s law. The length of the wire increases by 0.30 %.

What is the Young modulus of the metal wire?

  • 1.4 cross times 10 to the power of 12 space end exponent P a

  • 1.4 space cross times 10 to the power of 9 space P a

  • 1.4 cross times 10 to the power of 8 space P a

  • 1.4 space cross times space 10 to the power of 5 space P a

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71 mark

Two wires S and T is joined, S has a length of 3.0 m and T a length of 1.0 m, both wires have a uniform cross-sectional area.

cie-ial-images263png

When a load was hung from the wires S stretched by 1.5 mm and T by 1.0 mm.

 The same load is then hung from a second wire of the same cross-section, consisting of 1.0 m of metal S and 3.0 m of metal T.

 What is the total extension of this second wire?

  • 3.5 mm

  • 2.5 mm

  • 5.0 mm

  • 4.8 mm

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81 mark

Two steel wires X and Y that both obey Hooke’s law were used in an experiment. Wire X has a length l  and a cross-sectional area A. Wire Y has a length of 2 l, and cross-sectional area of  A over 2  .

 What is the ratio fraction numerator t e n s i o n space i n space X over denominator t e n s i o n space i n space Y end fraction  when both wires are stretched to the same extension?

  • 1 fourth

  • 4 over 1

  • 2 over 1

  • 1 half

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91 mark

In order to measure the mass of flour a set of scales needs to have high sensitivity for small masses and a low sensitivity with larger masses.

 To achieve this two springs are used with different spring constants k. One has a lower spring constant than the other.

 Which of the following sets of springs would be suitable for this purpose?

cie-ial-physics-images-6-1-h-9-answer

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101 mark

The springs in the diagram all have the same spring constant. They were arranged in a different formation with a different load, as shown in the diagram.

 Which arrangement has the largest extension?

cie-ial-physics-images-6-1-h-10-answer

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11 mark

Two materials with the same dimensions were loaded to fracture; the graph shows the force-extension of these.

cie-ial-images251png

Which of the following would describe the behaviour of the materials?

  • both materials are plastic

  • both materials have the same ultimate tensile stress

  • both materials are brittle

  • both materials obey Hooke’s law

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21 mark

A metal tube with a thin wall thickness w is shown in the diagram. The thickness of the wall is small when compared to the diameter of the tube.

cie-ial-images253png

A force T applied parallel to the axis of the tube puts the tube under tension. It is proposed that making the wall thicker would reduce the stress on the tube.

 If the tube diameter and the tension remain the same, which wall thickness would half the stress?

  • 4w

  • 2w

  •  square root of 2 W end root

  • W over 2

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31 mark

A steel metal wire has the following properties:

    diameter = 5.0 × 10–4 m

   Young modulus = 2.0 × 1011 Pa

   tension = 20 N

 The string snaps and contracts elastically.

 By what percentage does a length l of a piece of the string contract?

  • 1.3 cross times 10 to the power of negative 2 end exponent percent sign

  • 1.3 cross times 10 to the power of negative 4 end exponent percent sign

  • 5.1 cross times 10 to the power of negative 4 end exponent percent sign

  • 5.1 space cross times space 10 to the power of negative 2 end exponent percent sign 

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41 mark

The Young modulus of a metal wire is dependent on which property?

  • spring constant 

  • ductility 

  • ultimate tensile stress 

  • elastic limit

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51 mark

The Young modulus E and the force per unit extension k describes the behaviour of a wire under tensile stress.

 For a wire of length L and cross-sectional area A, what is the relationship between E and k ?

  • E equals fraction numerator A over denominator k L end fraction

  • E equals fraction numerator k A over denominator L end fraction

  • E equals fraction numerator k L over denominator A end fraction

  • E equals fraction numerator L over denominator k A end fraction

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61 mark

A steel bar, shown in the diagram, has a circular cross-section that is under tension T.

diagram-7

The diameter of the thinner portion is half the diameter of the wider portion.

What is the value of fraction numerator s t r e s s space o n italic space t h e italic space w i d e italic space p o r t i o n over denominator s t r e s s italic space o n italic space t h e italic space n a r r o w italic space p o r t i o n end fraction ?

  • 4.0

  • 2.0

  • 0.50

  • 0.25

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71 mark

A student wanted to find the young modulus of a wire. The equation for the young modulus E is:

                  E equals fraction numerator 4 F l over denominator pi d to the power of italic 2 x end fraction

 The student extended the wire with a known force and made a series of measurements.

 Which measurement has the largest effect on the uncertainty in the value of the calculated Young modulus?

 

Measurement

Symbol

Value

A

B

C

D

length of wire before force applied

force applied

extension of wire with force applied

diameter of wire

l

F

x

d

2.043 ± 0.002 m

19.62 ± 0.01 N

5.2 ± 0.2 mm

0.54 ± 0.02 mm

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81 mark

A spring was stretched with increasing load. The graph of the results is shown below.

cie-ial-images255png

What is the spring constant?

  • 0.080 N m–1

  • 0.13 N m–1

  • 2.7 N m–1

  • 8.0 N m–1

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91 mark

The graph below shows the stress-strain for a metal.

cie-ial-physics-mcq-6-1-q19

When the strain on the rod is 0.010, what is the strain energy per unit volume of a rod made from this metal?

  • 10 kJ m−3

  • 10 MJ m−3

  • 100 kJ m−3

  • 1.0 MJ m−3

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101 mark

A steel spring was stretched to a length of 55 cm when a 25 N weight was hung from it. The spring has a spring constant of 150 N m–1.

 What was the original length of the spring?

  • 0.61 m

  • 0.72 m

  • 0.38 m 

  • 0.49 m 

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