June 2024 Paper 3 Mechanics Q3

EdexcelCurrent spec7 marksForces & Newton's LawsResolving Forces

3.

Figure 3: particle P of mass m on a plane inclined at angle alpha to the horizontal
Figure 3

A particle \(P\) of mass \(m\) is held at rest at a point on a rough inclined plane, as shown in Figure 3.

It is given that

  • the plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan\alpha = \dfrac{5}{12}\)
  • the coefficient of friction between \(P\) and the plane is \(\mu\), where \(\mu \lt \dfrac{5}{12}\)

The particle \(P\) is released from rest and slides down the plane.
Air resistance is modelled as being negligible.

Using the model,

(a) find, in terms of \(m\) and \(g\), the magnitude of the normal reaction of the plane on \(P\), (2)
(b) show that, as \(P\) slides down the plane, the acceleration of \(P\) down the plane is\[\frac{1}{13}g(5 - 12\mu)\] (4)
(c) State what would happen to \(P\) if it is released from rest but \(\mu \geqslant \dfrac{5}{12}\) (1)
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