1. A plank \(P Q R\), of length 8 m and mass 20 kg , is in equilibrium in a horizontal position on two supports at \(P\) and \(Q\), where \(P Q = 6 \mathrm {~m}\).

A child of mass 40 kg stands on the plank at a distance of 2 m from \(P\) and a block of mass \(M \mathrm {~kg}\) is placed on the plank at the end \(R\). The plank remains horizontal and in equilibrium. The force exerted on the plank by the support at \(P\) is equal to the force exerted on the plank by the support at \(Q\). By modelling the plank as a uniform rod, and the child and the block as particles,

1. 1. find the magnitude of the force exerted on the plank by the support at \(P\),
   2. find the value of \(M\).
2. State how, in your calculations, you have used the fact that the child and the block can be modelled as particles.