The Young modulusAQA A-Level Physics: Subtopic test

1. 1
   A steel wire of length 2.50 m and diameter 0.80 mm hangs from a fixed support and carries a load that produces a tension of 40 N. The Young modulus of the steel is 2.0 × 10¹¹ Pa and the wire obeys Hooke's law.

   (a)

   What is the tensile stress in the wire?

   [1 mark]

   • A2.0 × 10⁷ Pa
   • B6.3 × 10⁷ Pa
   • C8.0 × 10⁷ Pa
   • D1.6 × 10⁸ Pa

   (b)

   A second wire is made from a different steel. Which of the following quantities depends only on the material of a wire and not on its length or diameter?

   [1 mark]

   • AThe Young modulus
   • BThe extension produced by a given load
   • CThe tensile stress produced by a given load
   • DThe force needed to produce a given extension

   (c)

   Calculate the extension of the wire.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two rods, X and Y, have identical lengths of 1.50 m and identical cross-sectional areas of 2.0 × 10⁻⁵ m². The Young modulus of X is 1.0 × 10¹¹ Pa and the Young modulus of Y is 2.0 × 10¹¹ Pa. Both rods are used within the limit of proportionality.

   (a)

   The same tensile force is applied to each rod. How does the extension of Y compare with that of X?

   [1 mark]

   • AY extends by twice as much as X
   • BY extends by half as much as X
   • CY extends by the same amount as X because the dimensions are identical
   • DY extends by four times as much as X

   (b)

   A graph of tensile stress (vertical axis) against tensile strain (horizontal axis) is drawn for each rod. Which statement is correct?

   [1 mark]

   • AThe gradient of the graph for X is twice the gradient for Y
   • BThe gradients are the same because the rods have the same dimensions
   • CThe gradient of the graph for Y is half the gradient for X
   • DThe gradient of the graph for Y is twice the gradient for X

   (c)

   Calculate the force needed to produce an extension of 0.80 mm in rod X.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student determines the Young modulus of a copper wire. The wire is fixed at one end and passes over a pulley at the other end, where masses are added in steps. The unstretched length from the fixed end to a marker is 1.85 m. The student measures the diameter of the wire with a micrometer and obtains a mean value of 0.30 mm. A graph of force against extension is a straight line through the origin with a gradient of 4.5 × 10³ N m⁻¹.

   (a)

   Explain how the student should measure the diameter of the wire, and why this measurement is likely to be the largest source of uncertainty in the Young modulus.

   [3 marks]

   (b)

   Calculate the Young modulus of copper from the student's results.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A crane uses a steel cable of length 12.0 m and diameter 18 mm to lift a load that produces a tension of 2.5 × 10⁴ N in the cable. The Young modulus of the steel is 2.1 × 10¹¹ Pa. The designers are comparing this cable with a copper cable of the same dimensions, for which the Young modulus is 1.2 × 10¹¹ Pa.

   (a)

   Calculate the extension of the steel cable. A second steel cable of the same length has twice the diameter and carries the same load. Calculate the extension of the second cable.

   [6 marks]

   (b)

   The designers test a sample of the steel and plot a graph of stress against strain. Explain how the Young modulus is found from this graph, and use the Young moduli to compare the extension of the steel cable with that of the copper cable under the same load.

   [6 marks]

   Total for question 4: 12 marks

End of questions