AQA A-Level Physics: Mechanics and Materials

A wire made from a ductile metal (such as copper) and a rod made from a brittle material (such as cast iron) are each stretched by a steadily increasing tensile force until they break. The behaviour is recorded as a stress-strain graph for each material.

Describe and explain how the stress-strain behaviour of the ductile metal differs from that of the brittle material as the force is increased to fracture. In your answer you should refer to the limit of proportionality, the elastic and plastic regions, the yield point, and what happens at fracture for each material.

(6 marks)

A small ball is projected horizontally with a speed of 18 m s⁻¹ from the edge of a cliff. The point of projection is 32 m above the level sea below. Air resistance is negligible.

Quantity	Value
Horizontal launch speed, $u$u	18 m s⁻¹
Height of cliff above sea, $h$h	32 m
Gravitational field strength, $g$g	9.81 m s⁻²

(a) Calculate the time taken for the ball to reach the sea. (2 marks)

(b) Calculate the horizontal distance from the base of the cliff to the point where the ball lands. (1 mark)

(c) Calculate the speed of the ball as it hits the sea and the angle below the horizontal at which it strikes. (3 marks)

A student investigates how a length of metal wire extends under load. The wire has an unstretched length of 2.00 m and a cross-sectional area of $4.0 \times 10^{-7} \ \text{m}^2$4.0×10−7 m2. The student records the extension of the wire for a series of increasing loads:

Force / N	0	8	16	24	32	40
Extension / mm	0	0.20	0.40	0.60	0.80	1.10

(a) Use the data to state, with a reason, the largest force for which the wire obeys Hooke's law. (2 marks)

(b) Using the readings within the Hooke's-law region, calculate the Young modulus of the metal. (2 marks)

(c) Calculate the elastic strain energy stored in the wire at the limit of proportionality. (1 mark)

A uniform scaffolding plank of length 4.0 m and weight 240 N rests horizontally on two supports. Support A is at the left-hand end of the plank and support B is 3.0 m from A. A worker of weight 600 N stands on the plank 2.5 m from the left-hand end.

Quantity	Value
Length of plank	4.0 m
Weight of (uniform) plank	240 N
Position of support A	left-hand end (0 m)
Position of support B	3.0 m from A
Weight of worker	600 N
Position of worker	2.5 m from A

(a) By taking moments about support A, calculate the upward force exerted by support B on the plank. (3 marks)

(b) Hence calculate the upward force exerted by support A on the plank. (2 marks)

A tennis ball of mass 58 g is initially at rest when it is struck by a racket. During the contact the force the racket exerts on the ball varies with time. The force rises linearly from zero to a peak of 840 N at 2.5 ms, then falls linearly back to zero at 5.0 ms, so the force-time graph is a triangle of base 5.0 ms and height 840 N.

Quantity	Value
Mass of ball	58 g
Peak contact force	840 N
Total contact time	5.0 ms
Force-time shape	triangle (0 → 840 N → 0)

(a) Use the force-time graph to determine the change in momentum of the ball during the contact. (2 marks)

(b) Hence calculate the speed with which the ball leaves the racket. (2 marks)

(c) Calculate the average force exerted on the ball during the contact. (1 mark)

The Young modulus is a property used to compare the stiffness of different materials.

(a) Define the Young modulus, naming the two quantities it relates and stating its SI unit. (2 marks)

(b) State the condition that must be satisfied for the Young modulus of a material to have a constant value. (1 mark)