October 2020 Paper 3 Mechanics Q1

1. A rough plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan\alpha = \dfrac{3}{4}\)

A brick \(P\) of mass \(m\) is placed on the plane.

The coefficient of friction between \(P\) and the plane is \(\mu\)

Brick \(P\) is in equilibrium and on the point of sliding down the plane.

Brick \(P\) is modelled as a particle.

Using the model,

For parts (c) and (d), you are not required to do any further calculations.

Brick \(P\) is now removed from the plane and a much heavier brick \(Q\) is placed on the plane.

The coefficient of friction between \(Q\) and the plane is also \(\dfrac{3}{4}\)

Brick \(Q\) is now projected with speed \(0.5\ \text{m s}^{-1}\) down a line of greatest slope of the plane.

Brick \(Q\) is modelled as a particle.

Using the model,