4.7 Bulk Properties of Solids

Figure 1 shows the variation of tensile stress with tensile strain for two wires X and Y, which have the same dimensions, but are made of different materials. The materials fracture at the points F_x and F_Y respectively. 

Figure 1

State, with a reason, two properties of wire X.

State, with a reason, two properties of wire Y.

Wire X originally has a length of 1.35 m. A force of 200 N is used to extend wire X to 1.51 m. 

Calculate the energy stored in wire X if it extends a further 30 mm.

State and explain which wire would be more suitable for use as cables and structural beams. 

A type of exercise device is used to provide resistive forces when a person applies compressive forces to its handles. The stiff spring inside the device compresses as shown in Figure 1.

Figure 1

The force exerted by the spring over a range of compressions was measured. The results are plotted on the graph shown in Figure 2. 

Figure 2

State, with a reason, whether the spring obeys Hooke’s law over the range of values tested.

Use the graph in Figure 2 to calculate the spring constant, stating an appropriate unit.

Derive the formula for the energy stored by the spring using a graph of force against extension.

State and explain whether the material chosen for the spring for the device in Figure 1 should exhibit elastic or plastic behaviour.

Nichrome is a common alloy used to make coins and heating elements in electrical appliances. It consists of 80 % by volume of nickel and 20 % by volume of chromium. 

Determine the mass of nickel and the mass of chromium required to make a wire of nichrome of volume 0.50 × 10^-3 m³.           

Density of nickel = 8.9 × 10³ kg m^–3

Density of chromium = 7.1 × 10³ kg m^–3

Calculate the density of nichrome.

The radius of the nichrome wire is 5.7 mm. The wire breaks when a force of 72 kN is applied to the wire. 

Calculate the breaking stress of nichrome, stating an appropriate unit.

Hence, or otherwise, explain why nichrome is a suitable material for making coins.

Figure 1 shows a bungee jumper about to step off a raised platform. The jumper comes to a halt for the first time when their centre of mass has fallen through a distance of 25 m. The bungee rope has an unextended length of 18 m and a stiffness of  410 N m^–1. 

Ignore the effects of air resistance and the mass of the rope in this question. Treat the jumper as a point mass located at the centre of mass. 

 Figure 1

Using the extension of the bungee rope, calculate the resultant force acting on the jumper when they reach the lowest point in the jump.

The extension of the rope is 1.6 m when the acceleration of the jumper is zero. 

Calculate the mass of the bungee jumper.

The extension of the bungee rope is 2.4 m when the jumper’s centre of mass has fallen through a distance of 16 m. 

Use the principle of conservation of energy to calculate the speed of the jumper in this position.         

The bungee jump operator intends to use a bungee rope of the same unextended length but with much less stiffness. The rope is to be attached in the same way as before. 

Explain, with reference to the kinetic energy of the jumper, how the force on the jumper will be affected by this change as they are slowed down by the new rope.