5 A block, of mass 12 kg , lies on a horizontal surface. The block is attached to a particle, of mass 18 kg , by a light inextensible string which passes over a smooth fixed peg. Initially, the block is held at rest so that the string supports the particle, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{828e8db1-efcf-4878-8292-ba5bbd80115c-3_346_716_1557_715} The block is then released.

1. Assuming that the surface is smooth, use two equations of motion to find the magnitude of the acceleration of the block and particle.
2. In reality, the surface is rough and the acceleration of the block is \(3 \mathrm {~ms} ^ { - 2 }\).
   1. Find the tension in the string.
   2. Calculate the magnitude of the normal reaction force acting on the block.
   3. Find the coefficient of friction between the block and the surface.
3. State two modelling assumptions, other than those given, that you have made in answering this question.