Physics 9702 · AS & A Level · Energy conservation

Energy conservation — practice question

One end of a spring is clamped, and the other end is pushed in by applying a force. Figure 3.1 shows how the force $F$ on the spring changes with compression $x$. When the compression is $0.045\,\text{m}$, the spring experiences a force $F_1$. The spring constant is $800\,\text{N m}^{-1}$.
(a(i))[2]

Determine $F_1$.

(a(ii))[2]

Use Fig. 3.1 to demonstrate that, for a compression of $0.045\,\text{m}$, the spring’s elastic potential energy is $0.81\,\text{J}$.

(b(i))[1]

The toy changes the spring’s elastic potential energy into the ball’s kinetic energy. Use the information in (a)(ii) to work out the percentage efficiency of this change.

(b(ii))[3]

Determine the initial momentum of the ball as it leaves the toy.

(c(i))[2]

Calculate $h$.

(c(ii))[2]

Determine the average force from air resistance acting on the ball during its motion from A to B.

(c(iii))[1]

When air resistance acts, the ball takes time $T$ to travel from A to B. State and explain whether the time taken for the ball to travel from A to its maximum height will be more than, less than or equal to time $T$ if air resistance is absent.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hooke's law: $F = kx$

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