Physics 9702 · AS & A Level · Momentum and Newton's laws of motion

Momentum and Newton's laws of motion — practice question

A helicopter is shown in Fig. 3.1 with a cable hanging down from it towards the sea below. A man with mass $80\,\text{kg}$ rescues a child with mass $50.5\,\text{kg}$. Both are fastened to the cable and are raised from the sea to the helicopter. The lifting takes place in three stages: first a period of uniform acceleration, then a period of constant velocity, and finally it ends with a period of uniform deceleration.
(a)[1]

Calculate the total weight of the man and child.

(b(i))[2]

Calculate the cable tension while the initial acceleration is $0.570\,\text{m s}^{-2}$.

(b(ii))[1]

Calculate the cable tension while the man and child move at constant velocity of $2.00\,\text{m s}^{-1}$.

(c)[2]

During the final deceleration, the cable tension is $1240\,\text{N}$. Calculate this deceleration.

(d(i).1)[1]

Calculate the duration for which the man and child are accelerating uniformly.

(d(i).2)[1]

Calculate the period over which the man and child move with uniform deceleration.

(d(ii))[2]

The duration of constant velocity is $20\,\text{s}$. On Fig. 3.2, sketch a graph showing how the velocity of the man and child varies with time throughout the whole lifting process.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Using $W = mg$, the weight is $130.5 \times 9.81 = 1280\,\text{N}$.

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