Density, Hooke's law and stress-strainAQA A-Level Physics: Subtopic test

1. 1
   A solid rectangular block of metal measures 4.0 cm by 5.0 cm by 2.0 cm and has a mass of 108 g.

   (a)

   What is the volume of the block in m³?

   [1 mark]

   • A4.0 × 10⁻⁵ m³
   • B40 m³
   • C4.0 × 10⁻² m³
   • D4.0 × 10⁻⁶ m³

   (b)

   What is the density of the metal?

   [1 mark]

   • A2.7 kg m⁻³
   • B2.7 × 10⁻³ kg m⁻³
   • C2.7 × 10³ kg m⁻³
   • D2.7 × 10⁶ kg m⁻³

   (c)

   A second block is made from the same metal and has the same outside dimensions, but it contains a hollow cavity. Its mass is 80 g. Calculate the volume of the cavity.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student hangs masses from a helical steel spring. A load of 4.0 N produces an extension of 0.080 m. The spring obeys Hooke's law up to its elastic limit, which is reached at a load of 6.0 N.

   (a)

   What is the spring constant of the spring?

   [1 mark]

   • A0.020 N m⁻¹
   • B0.32 N m⁻¹
   • C4.0 N m⁻¹
   • D50 N m⁻¹

   (b)

   What is the extension of the spring when the load is 3.0 N?

   [1 mark]

   • A0.080 m
   • B0.060 m
   • C17 m
   • D150 m

   (c)

   A load of 9.81 N is hung from the spring, which is greater than the elastic limit. Describe two ways in which the behaviour of the spring differs from its behaviour at loads below the limit.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A steel wire of length 2.50 m and diameter 0.50 mm hangs from a fixed support. A load of 80 N is hung from its lower end, and the wire extends by 3.0 mm. The wire is within the region where it obeys Hooke's law.

   (a)

   Define tensile stress and tensile strain, and state the unit of tensile stress.

   [3 marks]

   (b)

   Calculate the tensile stress and the tensile strain in the wire.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A lift cabin of mass 1800 kg hangs at rest from a single steel cable of circular cross-section and diameter 12 mm. The breaking stress of the steel is 1.1 × 10⁹ Pa. The engineer is also comparing the steel with a brittle ceramic fibre that has a similar breaking stress. Take g = 9.81 N kg⁻¹.

   (a)

   Calculate the stress in the cable and the factor by which the stress could be increased before the cable breaks.

   [6 marks]

   (b)

   Compare the stress-strain behaviour of the ductile steel with that of the brittle ceramic, and evaluate which material is the more suitable for the lift cable.

   [6 marks]

   Total for question 4: 12 marks

End of questions