Physics 5054 · O Level · Elastic deformation

Elastic deformation — practice question

Fig. 8.1 depicts an elastic rope (bungee). Its unstretched length is $0.80\,\text{m}$. A student fastens the hook at one end to a shelf and suspends an empty paint can of mass $0.70\,\text{kg}$ from the other end. The rope extends to $0.97\,\text{m}$, but it does not pass its limit of proportionality.
(a)[2]

Explain what the term limit of proportionality means.

(b(i))[1]

State what is meant by mass.

(b(ii))[2]

State what is meant by weight.

(c(i))[1]

The gravitational field strength is $10\,\text{N kg}^{-1}$. Calculate the weight of the empty paint can.

(c(ii))[1]

Calculate a value of $\dfrac{\text{load}}{\text{extension}}$ for the rope.

(d(i))[3]

Once the paint volume is $2.5 \times 10^{-3}\,\text{m}^3$, the total rope length becomes $1.70\,\text{m}$. This is the point where the rope reaches its limit of proportionality. Determine the mass of the paint in the can.

(d(ii))[3]

The student keeps pouring paint into the can until it contains a volume of $5.0 \times 10^{-3}\,\text{m}^3$. He draws a graph of the total length of the rope against the paint volume added. On Fig. 8.2, sketch the length-volume graph for the interval $0$ to $5.0 \times 10^{-3}\,\text{m}^3$.

(e)[2]

The student suddenly takes the can off the end of the stretched rope and, as it contracts, the rope springs into the air. State the energy change occurring in the rope while it contracts and jumps into the air.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: At the point where extension is not directly proportional to load/force

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