4 The diagram shows a block, of mass 13 kg , on a rough horizontal surface. It is attached by a string that passes over a smooth peg to a sphere of mass 7 kg , as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{965a176a-848c-478d-a748-80fc9dfe4399-3_323_974_1256_575} The system is released from rest, and after 4 seconds the block and the sphere both have speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and the block has not reached the peg.

1. State two assumptions that you should make about the string in order to model the motion of the sphere and the block.
2. Show that the acceleration of the sphere is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
3. Find the tension in the string.
4. Find the coefficient of friction between the block and the surface.