A2 October 2021 Q6

EdexcelCurrent spec11 marksHooke's LawWork-Energy Principle

6.

Figure 2: a spring on a plane inclined at angle α, fixed at X, with the package at Y a distance l up the line of greatest slope
Figure 2

A light elastic spring has natural length \(3l\) and modulus of elasticity \(3mg\).

One end of the spring is attached to a fixed point \(X\) on a rough inclined plane.

The other end of the spring is attached to a package \(P\) of mass \(m\).

The plane is inclined to the horizontal at an angle \(\alpha\) where \(\tan\alpha = \dfrac{3}{4}\)

The package is initially held at the point \(Y\) on the plane, where \(XY = l\). The point \(Y\) is higher than \(X\) and \(XY\) is a line of greatest slope of the plane, as shown in Figure 2.

The package is released from rest at \(Y\) and moves up the plane.

The coefficient of friction between \(P\) and the plane is \(\dfrac{1}{3}\)

By modelling \(P\) as a particle,

(a) show that the acceleration of \(P\) at the instant when \(P\) is released from rest is \(\dfrac{17}{15}g\) (5)
(b) find, in terms of \(g\) and \(l\), the speed of \(P\) at the instant when the spring first reaches its natural length of \(3l\). (6)
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