A-LevelPhysicsDeformation of solids9702/22 · May/June 2020 · Q59 Marks
One end of a wire is attached to a fixed point. A force F is applied to the wire to cause extension x. The variation with F of x is shown in Fig. 5.1. [Figure 5.1] The wire has a cross-sectional area of 4.1×10⁻⁷m² and is made of metal of Young modulus 1.7 × 10¹¹ Pa. Assume that the cross-sectional area of the wire remains constant as the wire extends.
- (a)State the name of the law that describes the relationship between F and x shown in Fig. 5.1.[1]
- (b)(i)the stress[2]
- (b)(ii)the strain.[2]
- (c)The resistivity of the metal of the wire is 3.7×10⁻⁷Ωm. Determine the change in resistance of the wire when the extension x of the wire changes from x = 0.48 mm to x = 0.60 mm.[3]
- (d)A force of greater than 45N is now applied to the wire. Describe how it may be checked that the elastic limit of the wire has not been exceeded.[1]
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Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] Hooke's (law)
- [C1] σ = F/A
- [A1] = 36/ (4.1 x 10-7) = 8.8 × 107 Pa
- [C1] Young modulus = σίε or F/Aε
- [A1] ε = 8.8 × 107 / (1.7 × 1011) = 5.2 × 10-4
- [C1] R = ρL/A
- [C1] ΔR = ρΔx / A
- [A1] = 3.7 x 10-7 × 0.12 × 10–3 / (4.1 × 10-7) = 1.1 x 10-4 Ω
- [B1] remove the force/F and wire returns to original length
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