M1 June 2014 Q2

EdexcelOld spec7 marksForces & Newton's LawsResolving Forces

2.

Figure 2: points A and B, 3 m apart, on a line of greatest slope of a plane inclined at 40 degrees, A above B
Figure 2

A rough plane is inclined at 40\(^\circ\) to the horizontal. Two points \(A\) and \(B\) are 3 metres apart and lie on a line of greatest slope of the inclined plane, with \(A\) above \(B\), as shown in Figure 2. A particle \(P\) of mass \(m\) kg is held at rest on the plane at \(A\). The coefficient of friction between \(P\) and the plane is \(\dfrac{1}{2}\). The particle is released.

(a) Find the acceleration of \(P\) down the plane. (5)
(b) Find the speed of \(P\) at \(B\). (2)
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