[Figure 8.1] shows an elastic rope (bungee). The unstretched length of the rope is 0.80 m. A student uses the hook at one end to suspend the rope from a shelf and hangs an empty paint can of mass 0.70 kg from the other end. The rope stretches to a length of 0.97m but does not exceed its limit of proportionality.

1. (a)Explain what is meant by limit of proportionality.[2]
2. (b)(i)State what is meant by: mass[1]
3. (b)(ii)weight.[2]
4. (c)(i)The gravitational field strength is 10N/kg. Calculate the weight of the empty paint can.[1]
5. (c)(ii)For the rope, calculate a value for load extension[1]
6. (d)(i)The student repeatedly pours small volumes of paint into the can. When there is 2.5 × 10⁻³ m³ of paint in the can, the total length of the rope is 1.70m. This is where the rope reaches the limit of proportionality. Determine the mass of the paint in the can.[3]
7. (d)(ii)The student continues to pour paint into the can until there is a volume of 5.0 x 10⁻³ m³ in it. He notices that the elastic rope becomes harder to stretch after the limit of proportionality. He plots a graph of the total length of the rope against the volume of paint added. On Fig. 8.2, sketch the length-volume graph for the range 0 to 5.0 × 10⁻³m³.[3]
8. (e)The student suddenly removes the can from the end of the stretched rope and, as it contracts, the rope jumps into the air. State the energy change that is taking place in the rope as it contracts and jumps into the air.[2]

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