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

1. 1
   A steel wire of length 2.50 m and cross-sectional area 0.50 mm² supports a load of 80 N. The Young modulus of steel is 2.0 × 10¹¹ Pa, and the wire obeys Hooke's law.

   (a)

   What is the stress in the wire?

   [1 mark]

   • A1.6 × 10² Pa
   • B1.6 × 10⁵ Pa
   • C6.3 × 10⁻⁹ Pa
   • D1.6 × 10⁸ Pa

   (b)

   What is the strain in the wire?

   [1 mark]

   • A1.3 × 10³
   • B8.0 × 10⁻⁴
   • C2.0 × 10⁻³
   • D8.0 × 10⁻⁷

   (c)

   Calculate the extension of the wire.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student stretches a copper wire of diameter 0.60 mm and original length 1.80 m. A load of 50 N produces an extension of 1.4 mm.

   (a)

   What is the cross-sectional area of the wire?

   [1 mark]

   • A1.1 × 10⁻⁶ m²
   • B1.9 × 10⁻³ m²
   • C2.8 × 10⁻⁷ m²
   • D7.1 × 10⁻⁸ m²

   (b)

   What is the Young modulus of the copper?

   [1 mark]

   • A2.3 × 10¹¹ Pa
   • B1.8 × 10⁸ Pa
   • C7.8 × 10⁻⁴ Pa
   • D5.7 × 10¹⁰ Pa

   (c)

   Explain why a long, thin wire is used in an experiment to measure the Young modulus of a metal.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A metal rod of original length 0.400 m and cross-sectional area 1.0 × 10⁻⁴ m² is tested in tension until it breaks. The stress–strain graph is a straight line through the origin up to a stress of 2.8 × 10⁸ Pa, where the strain is 1.4 × 10⁻³. The breaking stress of the rod is 4.5 × 10⁸ Pa.

   (a)

   Calculate the Young modulus of the metal.

   [3 marks]

   (b)

   Calculate the force needed to break the rod and the extension of the rod at the end of the straight-line section.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In a core practical, a student determines the Young modulus of a metal in the form of a long thin wire. The wire is clamped at one end and passes over a pulley at the other, where masses can be added to a hanger. The student has a micrometer, a metre rule, a ruler to measure the extension and a set of slotted masses.

   (a)

   Describe how the student should carry out the experiment and use the results to determine the Young modulus of the metal.

   [6 marks]

   (b)

   The student measures a length of 2.000 m ± 0.002 m and a diameter of 0.38 mm ± 0.01 mm. The gradient of the force–extension graph is 1.13 × 10⁴ N m⁻¹ with an uncertainty of 2%. She calculates a Young modulus of 2.0 × 10¹¹ Pa. Determine the percentage uncertainty in the Young modulus, and evaluate which measurement limits the accuracy of the result most and how this could be reduced.

   [6 marks]

   Total for question 4: 12 marks

End of questions