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

Elastic and plastic behaviour — practice question

A spring has one end secured in place and its other end fastened to the frame of a pulley. A cable runs around the pulley wheel. The spring is extended to a fixed length with the aid of the cable and pulley. Fig. 3.1 gives the view from above of the spring, cable and pulley. The spring follows Hooke’s law and has a spring constant $k$ of $250\,\text{N m}^{-1}$. A force $F$ acts on the spring. The tension in the cable is $T$. The pulley is in equilibrium.
(a)[2]

On Fig. 3.2, draw labelled arrows to indicate the directions of the forces acting on the pulley.

(b(i))[1]

The force $F$ is $110\,\text{N}$. Find $T$.

(b(ii))[2]

Calculate the extension of the spring.

(c(i))[2]

A second identical spring with the same spring constant of $250\,\text{N m}^{-1}$ is now connected to the pulley as well, as shown in Fig. 3.3. The tension in the cable is unchanged. The pulley is once again in equilibrium. Determine the extension of the springs.

(c(ii))[2]

The elastic potential energy stored in the spring in Fig. 3.1 is $E_1$. The total elastic potential energy stored in the two springs in Fig. 3.3 is $E_2$. Calculate the ratio $\frac{E_1}{E_2}$.

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