M2 June 2014 (R) Q5

EdexcelOld spec13 marksWork-Energy Principle

5.

Figure 3: plane inclined at 30 degrees with A above B on a line of greatest slope, AB = 5 m
Figure 3

A particle \(P\) of mass 2 kg is released from rest at a point \(A\) on a rough inclined plane and slides down a line of greatest slope. The plane is inclined at 30\(^\circ\) to the horizontal. The point \(B\) is 5 m from \(A\) on the line of greatest slope through \(A\), as shown in Figure 3.

(a) Find the potential energy lost by \(P\) as it moves from \(A\) to \(B\). (2)

The speed of \(P\) as it reaches \(B\) is 4 m s\(^{-1}\).

(b)
(i) Use the work-energy principle to find the magnitude of the constant frictional force acting on \(P\) as it moves from \(A\) to \(B\).
(ii) Find the coefficient of friction between \(P\) and the plane. (7)

The particle \(P\) is now placed at \(A\) and projected down the plane towards \(B\) with speed 3 m s\(^{-1}\). Given that the frictional force remains constant,

(c) find the speed of \(P\) as it reaches \(B\). (4)
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