10 A body of mass 20 kg is on a rough plane inclined at angle \(\alpha\) to the horizontal.
The body is held at rest on the plane by the action of a force of magnitude \(P \mathrm {~N}\).
The force is acting up the plane in a direction parallel to a line of greatest slope of the plane.
The coefficient of friction between the body and the plane is \(\mu\).
- When \(P = 100\), the body is on the point of sliding down the plane.
Show that \(g \sin \alpha = g \mu \cos \alpha + 5\).
- When \(P\) is increased to 150, the body is on the point of sliding up the plane.
Use this, and your answer to part (a), to find an expression for \(\alpha\) in terms of \(g\).