Four solid steel rods, each of length 2.0 m and cross-sectional area 250 mm², equally support an object weighing 10 kN. The weight of the object causes the rods to contract by 0.10 mm. The rods obey Hooke’s law.

What is the Young modulus of steel?

• 2.0 × 10⁸ N m^–2

• 2.0 × 10¹¹ N m^–2

• 8.0 × 10⁸ N m^–2

• 8.0 × 10¹¹ N m^–2

A wire is attached at one end to a fixed point. A tensile force F is applied to the other end of the wire, causing it to extend. This is shown on the graph by the line OSP.

The force F is then gradually reduced to zero and the wire contracts. This is shown on the graph by the line PQ.

Which area on the graph represents the work done by the wire as it contracts?

• OSTO

• OSPRO

• QPRQ

• OSPQO

A wire X is stretched by a force and gains elastic potential energy E.

The same force is applied to wire Y of the same material, with the same initial length but twice the diameter of wire X. Both wires obey Hooke’s law.

What is the gain in elastic potential energy of wire Y?

• 0.25E

• 0.5E

• 2E

• 4E

The stress-strain graphs for loading and unloading four different materials are shown.

Which material exhibits purely elastic behaviour?

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Two wires X and Y are made from the same material. Wire Y has twice the diameter and experiences twice the tension of wire X. The wires obey Hooke’s law and have the same original length.

Wire X has extension e.

What is the extension of wire Y?

• e/4

• e/2

• e

• 2e

What is represented by the gradient of a graph of force (vertical axis) against extension (horizontal axis) for a wire obeying Hooke’s law?

• elastic limit

• spring constant

• stress

• Young modulus

Forces are applied to the ends of a rod so that its length increases. The variation with load L of the extension e of the rod is shown.

The point P is the elastic limit.

Which shaded area represents the work done during the plastic deformation of the rod?

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A metal cylinder is able to withstand a compressive force of 4.0 kN without deforming plastically.

The cylinder has cross-sectional area A and would be at its elastic limit when a stress σ is applied.

What is a possible pair of values for (i) A (m²) and (ii) σ (MPa)?

• (i) 1.5 × 10^–5 (ii) 50

• (i) 1.5 × 10^–5 (ii) 80

• (i) 7.5 × 10^–5 (ii) 50

• (i) 7.5 × 10^–5 (ii) 80

The diagram shows a wire of diameter D and length L that is firmly clamped at one end between two blocks of wood. A load is applied to the wire which extends its length by x.

A second wire is made of the same material, but of diameter 2D and length 3L. Both wires obey Hooke’s law.

What is the extension of the second wire when the same load is applied?

• 2/3 x

• 3/4 x

• 4/3 x

• 3/2 x

Two wires, one made of brass and the other of steel, are stretched in an experiment. Both wires obey Hooke’s law during this experiment.

The Young modulus for brass is less than the Young modulus for steel.

Which graph shows how the stress varies with strain for both wires in this experiment?

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