OCR A-Level Physics: Motion, Forces and Materials

A student stretches a length of copper wire by hanging increasing loads from it and recording the extension, then plots a stress-strain graph. The graph rises in a straight line from the origin, then begins to curve; at a clear point the strain increases sharply for very little extra stress, after which the curve rises more gently to a maximum before the wire breaks. Copper is a ductile metal.

Describe and explain the key features of the stress-strain graph for this copper wire as the stress is increased steadily from zero up to fracture. In your answer you should refer to the gradient of the straight-line region, the elastic limit and yield, the plastic region, the ultimate tensile stress, and what the area under the graph represents.

(6 marks)

In a sports-science test, a ball is launched from ground level with the data below. Air resistance is negligible, and the ground is horizontal. Treat the horizontal and vertical motions independently.

Quantity	Value
Launch speed, $u$u	24 m s⁻¹
Launch angle above horizontal, $\theta$θ	35°
Gravitational field strength, $g$g	9.81 m s⁻²

(a) Calculate the initial horizontal and initial vertical components of the launch velocity. (2 marks)

(b) Calculate the time of flight (the time from launch until the ball returns to ground level). (2 marks)

(c) Hence calculate the horizontal range of the ball. (2 marks)

A student investigates a length of metal wire of original length 2.00 m and cross-sectional area 1.5 × 10⁻⁷ m². She hangs increasing loads from the wire and measures the extension each time:

Load / N	0	10	20	30	40	50
Extension / mm	0	0.68	1.36	2.04	2.72	4.10

(a) Use the data to show that the wire obeys Hooke's law up to a load of 40 N, but not at 50 N. (2 marks)

(b) Using the Hooke's-law region only, determine the Young modulus of the wire. (3 marks)

A uniform horizontal shop sign is a rigid beam of weight 120 N and length 1.6 m. It is attached to a wall by a hinge at one end (point P) and held horizontal by a single vertical cable attached 1.2 m from the hinge. A small hanging lantern of weight 40 N is fixed to the far end of the beam (1.6 m from the hinge). The beam is in equilibrium.

(a) By taking moments about the hinge P, calculate the tension in the vertical cable. (3 marks)

(b) Hence calculate the magnitude and direction of the vertical force exerted by the hinge on the beam. (2 marks)

A toy launcher fires a small dart using a single spring of spring constant 250 N m⁻¹. To load the launcher, the spring is compressed by 8.0 cm from its natural length. The dart has a mass of 0.020 kg, and the spring obeys Hooke's law over this range. Assume all the stored elastic energy is transferred to the kinetic energy of the dart.

(a) Calculate the elastic strain energy stored in the compressed spring. (2 marks)

(b) Hence calculate the maximum speed at which the dart leaves the launcher. (2 marks)

When a wire is stretched, engineers describe its behaviour using tensile stress, tensile strain and the Young modulus.

(a) Define tensile stress and tensile strain, and state the SI unit of each. (2 marks)

(b) Write down the equation that defines the Young modulus in terms of stress and strain, and state its SI unit. (1 mark)