Stress, strain and the Young modulusEdexcel International A Level Physics: Subtopic test

1. 1
   A steel wire of original length 2.50 m and diameter 0.80 mm hangs vertically from a rigid support. A load of 120 N is attached to the lower end of the wire and the wire extends by 3.0 mm. The wire obeys Hooke's law.

   (a)

   What is the cross-sectional area of the wire?

   [1 mark]

   • A5.0 × 10⁻⁷ m²
   • B2.0 × 10⁻⁶ m²
   • C6.4 × 10⁻⁷ m²
   • D5.0 × 10⁻¹⁰ m²

   (b)

   What is the tensile stress in the wire?

   [1 mark]

   • A2.4 × 10⁵ Pa
   • B2.4 × 10⁸ Pa
   • C6.0 × 10⁷ Pa
   • D1.2 × 10⁻³ Pa

   (c)

   Calculate the Young modulus of the steel.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A ductile metal wire of cross-sectional area 2.0 × 10⁻⁷ m² is stretched until it breaks. The stress is directly proportional to the strain up to a stress of 2.4 × 10⁸ Pa, and the wire breaks when the stress reaches 3.6 × 10⁸ Pa.

   (a)

   What force is needed to break the wire?

   [1 mark]

   • A1.8 × 10¹⁵ N
   • B0.72 N
   • C72 N
   • D720 N

   (b)

   A graph of stress (vertical axis) against strain (horizontal axis) is plotted for the wire. What does the gradient of the straight section represent?

   [1 mark]

   • AThe stiffness of the wire
   • BThe breaking stress
   • CThe extension of the wire
   • DThe Young modulus of the metal

   (c)

   A second wire is made of the same metal but has twice the diameter. State and explain how its breaking stress and the force needed to break it compare with the first wire.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student determines the Young modulus of a copper wire. One end of the wire is clamped to a bench and the wire passes over a pulley, with masses added to the free end. The original length of the wire, measured from the clamp to a marker with a metre rule, is 2.00 m. The mean diameter of the wire, measured with a micrometer screw gauge, is 0.50 mm. The student plots a graph of force against extension, which is a straight line through the origin of gradient 1.2 × 10⁴ N m⁻¹.

   (a)

   Explain why the student uses a long, thin wire.

   [3 marks]

   (b)

   Use the data to determine the Young modulus of copper.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An engineer is choosing between steel and a ceramic for a cable that must support a steady load of 1.0 × 10⁶ N. Steel has a breaking stress of 5.0 × 10⁸ Pa and a Young modulus of 2.0 × 10¹¹ Pa, and its stress-strain graph shows a long region of plastic deformation before it fractures. The ceramic has a breaking stress of 3.0 × 10⁸ Pa and a Young modulus of 3.5 × 10¹¹ Pa, and its stress-strain graph is a straight line up to the point where it fractures suddenly. Before choosing, the engineer checks the manufacturer's Young modulus value for the steel by testing a thin steel wire in the laboratory.

   (a)

   Describe how the engineer could determine the Young modulus of a thin steel wire in the laboratory, including how the results are used.

   [6 marks]

   (b)

   Evaluate which material, steel or the ceramic, the engineer should choose for the cable.

   [6 marks]

   Total for question 4: 12 marks

End of questions