A spring is mounted horizontally with one end secured. A block is then pressed against the opposite end so that the spring is compressed, as shown in Fig. 4.1. When the block is let go, it speeds up across a horizontal frictionless surface while the spring returns to its natural length. As shown in Fig. 4.2, the block moves away from the spring with a speed of $2.3\,\text{m s}^{-1}$. The block’s mass is $250\,\text{g}$ and the spring constant is $420\,\text{N m}^{-1}$. Assume that Hooke’s law is obeyed at all times and that every bit of the spring’s elastic potential energy becomes kinetic energy of the block.
(a)[2]
Calculate the kinetic energy of the block as it leaves the spring.
(b)[2]
Calculate the compression of the spring immediately before the block is released.
(c(i))[2]
Once it has left the spring, the block travels along the surface and strikes a barrier at a speed of $2.3\,\text{m s}^{-1}$. It then rebounds at a speed of $1.5\,\text{m s}^{-1}$ and returns along its original line. The block remains in contact with the barrier for $0.086\,\text{s}$. Calculate the change in momentum of the block during the collision.
(c(ii))[1]
Calculate the average resultant force exerted on the block during the collision.
(d)[1]
The maximum compression $x$ of the spring is now altered so that the kinetic energy $E_K$ of the block as it leaves the spring is also changed. Assume that, each time, every bit of elastic potential energy in the spring is transferred to the kinetic energy of the block. On Fig. 4.3, sketch a graph to show how $E_K$ varies with $x$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$E = \frac{1}{2}mv^2$” …