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

Elastic and plastic behaviour — practice question

As shown in Fig. 4.1, the spring is held horizontally by connection to points A and B. Point A is attached to a movable slider, while point B is attached to a fixed support. A cart of mass $1.7\,\text{kg}$ moves towards the slider with horizontal velocity $v$. The cart then collides with the slider. As the cart is brought to rest, the spring becomes compressed. Fig. 4.2 shows how the compression $x$ of the spring varies with the force $F$ applied to the spring. Fig. 4.2 gives the spring compression for $F = 1.5\,\text{N}$ to $F = 4.5\,\text{N}$. The cart is at rest when $F = 4.5\,\text{N}$.
(a(i))[2]

Use Fig. 4.2 to demonstrate that the spring compression satisfies Hooke’s law.

(a(ii))[2]

Determine the spring constant for the spring.

(a(iii))[3]

Determine the elastic potential energy $E_p$ stored in the spring because the cart is brought to rest.

(b)[2]

Calculate the speed $v$ of the cart when it reaches the slider. Assume that every part of the cart’s kinetic energy is converted into elastic potential energy in the spring.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Two coordinate pairs chosen to show $F/x$ is constant

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