Physics 9702 · AS & A Level · Elastic and plastic behaviour

Elastic and plastic behaviour — practice question

A bungee jumper with mass $64\,\text{kg}$ fastens one end of an elastic rope to a bridge, and the opposite end is fixed to the jumper. The jumper starts from rest at the bridge and drops into the valley below, as illustrated in Fig. 3.1. Fig. 3.2 plots how the rope tension $T$ varies with the vertical distance $h$ of the jumper below bridge level.
(a)[1]

State Hooke’s law for the rope.

(b(i))[1]

Determine the rope’s unstretched length.

(b(ii))[2]

Determine the rope’s spring constant $k$.

(c(i))[2]

For the bungee jumper when they are $120\,\text{m}$ below the bridge: show that the reduction in gravitational potential energy since leaving the bridge is $75\,\text{kJ}$.

(c(ii))[2]

For the bungee jumper when they are $120\,\text{m}$ below the bridge: show that the elastic potential energy in the rope is $75\,\text{kJ}$.

(d)[2]

Explain what can be inferred from the information in (c) about the speed of the bungee jumper at a distance of $120\,\text{m}$ below the bridge.

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