The Young Modulus (AQA AS Physics)

Exam Questions

3 hours45 questions
1a2 marks

Define the following terms: 

(i)         Tensile stress 

(ii)        Tensile strain

1b1 mark

Figure 1 below shows a stress–strain graph for a copper wire up to the point of fracture.

Figure 1

4-8-s-q--q1b-easy-aqa-a-level-physics

Use Figure 1 to determine the breaking stress of this copper wire.

1c4 marks

(i)         Use Figure 1 to calculate the Young modulus of copper 

(ii)        State an appropriate unit for your answer

1d3 marks

A certain material has a Young modulus less than copper and undergoes brittle fracture at a stress of 176 MPa.

Draw a line on Figure 1 showing the possible variation of stress with strain for this material.

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2a1 mark

Define what is meant by the Young modulus of a material.

2b4 marks

A wire has a diameter 2.0 mm. 

Calculate the cross–sectional area of the wire in m2.

2c2 marks

A tensile force of 15.0 N is applied to the wire. 

Calculate the stress produced by this tensile force.

2d3 marks

The wire has a Young modulus value of 120 GPa. 

Calculate the strain on the wire when the tensile force of 15.0 N is applied.

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3a5 marks

A student carries out an experiment which will enable them to draw a suitable graph in order to obtain a value for the Young’s modulus of a wire.

Label the apparatus shown in Figure 1 which would enable the student to obtain a value of the Young’s modulus of the wire. 

Figure 1

4-8-s-q--q3a-easy-aqa-a-level-physics

3b2 marks

State and explain safety consideration when carrying out the experiment using the apparatus you have drawn in part (a).

3c2 marks

On the axis of Figure 2 draw a graph to show the relationship between the stress and strain values which the pupil could obtain from the experiment.

          Assume that the wire is not stretched beyond the limit of proportionality.

Figure 2

4-8-s-q--q3c-easy-aqa-a-level-physics

3d1 mark

State how the Young modulus value could be obtained from the graph in Figure 2.

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4a2 marks

A sample of fishing line is subjected to a load and found to obey Hooke’s law up to a tensile stress of 20 MPa. When the tensile stress is 20 MPa the tensile strain of the fishing line is 3.0 × 10–2.

Calculate the value of the Young modulus of the fishing line in MPa.

4b2 marks

The sample of fishing line is 2.0 m. 

Calculate the extension of the fishing line when the tensile strain is 3.0 × 10–2.

4c4 marks

The fishing line has a cross–sectional area of 1.25 × 10–5 m2. The breaking stress of the wire is 25 MPa. 

Calculate the maximum tensile force which can be applied to the line.

4d3 marks

Sketch a graph on Figure 1 below to show how you expect the tensile stress to vary with strain. Mark the value of stress and corresponding strain at the limit of Hooke’s law and stress at the breaking point. 

You do not need to calculate the strain at the breaking point. 

Figure 1

4-8-s-q--q4d-easy-aqa-a-level-physics

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5a2 marks

A garden swing is suspended by a nickel wire and a copper wire. A girl of mass 40 kg sits on the seat of the swing which is made from a uniform material with a mass of 1.0 kg. The girl is sitting in the middle of the seat and the seat is horizontal and in equilibrium. This arrangement is shown in Figure 1. 

Figure 1

4-8-s-q--q5a-easy-aqa-a-level-physics

Calculate the tension in each wire.

5b2 marks

Nickel has a Young modulus value of 1.7 × 1011 Pa. When the girl is sitting on the swing the tensile stress in the nickel wire is 7.1 × 107 Pa. 

Calculate the tensile strain of the nickel wire when the girl sits on the seat.

5c3 marks

Before, the nickel wire is attached to the swing it has a length of 5.0 m. 

Calculate the extension of the nickel wire.

5d3 marks

The copper wire also has a length of 5.0 m before is attached to the swing.

 State the strain in the copper wire. Explain your answer.

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1a3 marks

An elastic cord of unstretched length 180 mm has a cross-sectional area of 0.51 mm2 and spring constant of 120 N m–1. The cord is stretched to a length of 230 mm. Assume that Hooke’s law is obeyed for this range and that the cross-sectional area remains constant. 

Calculate the tensile stress of the cord in MPa.

1b2 marks

Calculate the tensile strain of the cord.

1c2 marks

Calculate the Young Modulus for the material of the cord.

1d3 marks

Explain quantitatively how the Young Modulus of the cord would change if its diameter was twice as large. Assume the cord has a circular cross-section.

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2a3 marks

Figure 1 shows a tower crane that has three identical steel cables. The length of each steel cable is 41 m from the jib to the hook. 

Figure 1

4-8-s-q--q2a-medium-aqa-a-level-physics

The cables would break if the crane attempted to lift a load of 2.7 MN or more. 

Calculate the breaking stress of one 

Radius of each cable = 12 mm.  

2b3 marks

When the crane supports a load each cable experiences a stress of 500 MPa. Each cable obeys Hooke’s law. 

Calculate the mass of the load.

2c4 marks

The unstretched length of each cable is 41 m. 

Calculate the final length of each cable when supporting the load. Give your answer to three significant figures. 

Young Modulus of steel = 2.1 × 1011 Pa

2d3 marks

Calculate the combined stiffness constant, k, for the three cables. State an appropriate unit in your answer.      

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3a3 marks

One end of a steel wire of length 1.5 m and 3.0 mm diameter is attached to a rigid beam. A 32 g mass is attached to the free end of the steel wire and placed against the underside of the beam as shown in Figure 1. 

Figure 1

4-8-s-q--q3a-medium-aqa-a-level-physics

The mass is released and falls freely until the wire becomes taut. The gravitational potential energy of the falling mass is converted to elastic potential energy in the wire as the wire extends to a maximum of 2.0 mm. Energy converted to other forms is negligible. 

Calculate the tension in the wire.

3b2 marks

Calculate the stress in the wire.

3c2 marks

Calculate the strain in the wire.

3d2 marks

Hence, or otherwise, calculate the Young Modulus in the wire.

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4a3 marks

If lengths of rail track are laid down in cold weather, they may deform as they expand when the weather becomes warmer. Therefore, when rails are laid in cold weather they are stretched and fixed into place while still stretched. This is called pre-straining. 

The following data is typical for a length of steel rail: 

Young modulus of steel = 2.0 × 1011 Pa
Amount of pre-strain =  3.5 × 10–5 for each kelvin rise in temperature the rail is expected to 
experience. 

A steel rail is laid when the temperature is 6 °C and the engineer decides to use a pre-strain of 1.24 × 10–4. The tensile force required to make this pre-strain is 0.19 MN. 

Show that the cross-sectional area of a length of rail is about 7.7 × 10-3 m2.

4b3 marks

The elastic strain energy stored in the rail when pre-strained as in part (a) is 4.2 kJ. 

Calculate the original unstressed length of the rail.

4c2 marks

Calculate the temperature at which the steel rail becomes unstressed.

4d3 marks

State and explain whether the pre-strain that the engineer decided to use is suitable in all-weather conditions.

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5a4 marks

A rope climber of mass 70 kg has a rope of length 2.3 m and 1 cm diameter attached to their harness. The other end of the rope is attached to a ridge on a rock face and the climber can be treated like a point mass. 

The climber falls freely vertically downwards until the rope is taut as shown in Figure 1. The gravitational potential energy of the falling climber is converted to elastic potential energy in the rope as the rope extends to a maximum of 1.5 mm. Energy converted to other forms is negligible. 

Figure 1

4-8-s-q--q5a-medium-aqa-a-level-physics

Complete parts (a) to (d) using the maximum extension of the rope 

Calculate the tension in the rope.

5b2 marks

Calculate the stress in the rope.

5c1 mark

Calculate the strain of the rope.

5d2 marks

Hence, calculate the Young modulus of the material of the rope.

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1a3 marks

A student adds a series of masses to a vertical metal wire of circular cross–section and measures the extension of the wire produced. Figure 1 is a force–extension graph of the data. 

Figure 1

4-8-s-q--q1a-hard-aqa-a-level-physics

Outline how the student can determine the Young Modulus of the wire using the graph in Figure 1.

1b3 marks

The metal wire is used to make a cable of diameter 5.3 mm. The Young Modulus of the metal of the cable is 128 GPa. 

Calculate the force necessary to produce a strain of 0.30 % in the cable.

1c3 marks

The cable is used in a crane to lift a mass of 540 kg. 

Determine the maximum acceleration with which the mass can be lifted if the strain in the cable is not to exceed 0.30 %.

1d3 marks

An engineer redesigns the crane to lift a 1620 kg load at the same maximum acceleration. 

Discuss the changes that could be made to the cable of the crane to achieve this without exceeding the 0.30% strain.

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2a3 marks

Table 1 show the results of an experiment where a force was applied to a copper wire. 

Table 1

Strain / 10–3

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Stress /108 Pa

0

0.60

1.16

1.50

1.66

1.74

1.78

1.82

1.84

1.86

1.88

1.90

 

On the axes shown in Figure 1, plot the graph of stress against strain using the data in the table for the copper wire. 

Figure 1

4-8-s-q--q2a-hard-aqa-a-level-physics

2b3 marks

Use the graph drawn in part (a) to calculate the Young Modulus of copper. State an appropriate unit for your answer.

2c2 marks

Use the graph in drawn in part (a) to find the work done per unit volume in stretching the copper wire to a strain of 3.5 × 10–3.

2d2 marks

A certain material has a Young Modulus greater than copper and undergoes brittle facture at a stress of 182 MPa. 

On the graph drawn in part (a), draw a line showing the possible variation of stress with strain for this material.

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3a6 marks

As part of a quality check, a manufacturer of fishing rods selects a sample of the lines used for the rods to a tensile test. 

The sample of line used is 2.0 m long and is of constant circular cross–section of diameter 0.55 mm. Hooke’s law is obeyed up to the point when the line has been extended by 50mm at a tensile stress of 1.9 × 108 Pa.

The maximum load the line can support before breaking is 55 N at an extension of 9 cm. 

Sketch a graph on Figure 1 to show how you expect the tensile stress to vary with strain. Mark the value of stress and corresponding strain at 

(i)      the limit of Hooke’s law

(ii)     the breaking point. 

Figure 1

4-8-s-q--q3a-hard-aqa-a-level-physics

3b4 marks

A different 2.0 m fishing line sample has a larger diameter. It is made of the same material and is subject to the same force. 

Discuss the advantages and disadvantages of this fishing line compared to the first.

3c4 marks

Calculate the force needed to extend a piece of 3 m nylon fishing wire with a radius of 1.2 mm to change its surface area by 3.5 × 10–3 m2.

Assume that the cross–sectional area is kept constant throughout the extension. 

Young Modulus of nylon = 2.7 GPa.

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4a5 marks

Figure 1 shows two wires, one made of Molybdenum and the other of Titanium, firmly clamped together at their ends. The wires have the same unstretched length and the same cross–sectional area.

One of the clamped ends is fixed to a horizontal support and a mass M is suspended from the other end, so that the wires hang vertically. 

Figure 1

4-8-s-q--q4a-hard-aqa-a-level-physics

The mass M is 2 kg. 

Calculate the force on the titanium wire, F subscript T. 

            Young Modulus of Molybdenum, E subscript M = 330 GPa

            Young Modulus of Titanium, begin mathsize 16px style E subscript T end style = 110 GPa

4b4 marks

Two spring constants k subscript 1 and k subscript 2 combine in parallel in the following way:  k subscript e q end subscript equals k subscript 1 plus k subscript 2 where k subscript e q end subscript is the equivalent spring constant of the combination. 

Calculate the equivalent Young Modulus of the combination of the Molybdenum and Titanium wires. Assume this time that the force on each wire is identical.

4c5 marks

Figure 2 now shows the Molybdenum and Titanium wires joined together, now at different lengths but still with the same cross–sectional area. This combination is suspended from a fixed support and a force F is applied at the bottom end. 

Figure 2

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The two wires extend by a total of 5.4 × 10–4 m. 

Length of the Molybdenum wire = 0.90 m

Length of the Titanium wire = 1.25 m 

Calculate the individual extensions of the Molybdenum and Titanium wires.

4d4 marks

The total mass of the combination of wire is 5.3 g. 

Show that the radius of both wires is around 0.34 mm. 

            Density of Molybdenum = 10 000 kg m–3

            Density of Titanium = 4420 kg m–3

4e3 marks

Calculate the new mass of the wire if the diameter of both wires is twice as large.

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5a4 marks

In order to prevent the collapse of walls of old buildings a metal rod is often used to tie opposite walls together, as shown in Figure 1 below. 

Figure 1

4-8-s-q--q5a-hard-aqa-a-level-physics

In one case a steel tie rod of diameter 24 mm is used. When the nuts are tightened, the rod extends by 7 %. The Young Modulus of steel is 2.1 × 1011 Pa. 

Calculate the force exerted on the walls by the rod.

5b4 marks

Another part of the old building requires 6 steel bolts, each of diameter 8.5 cm. When an earthquake occurs, this produces a strain on each bolt of 5.3 × 10–4. 

Calculate the maximum force exerted on the bolts during this earthquake.

5c3 marks

The ultimate tensile stress of steel is 5.0 × 108 Pa. 

Determine the minimum number of bolts that is required to make sure the building stays intact during this earthquake.

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