- A spring of natural length \(a\) has one end attached to a fixed point \(A\). The other end of the spring is attached to a package \(P\) of mass \(m\).
The package \(P\) is held at rest at the point \(B\), which is vertically below \(A\) such that \(A B = 3 a\).
After being released from rest at \(B\), the package \(P\) first comes to instantaneous rest at \(A\). Air resistance is modelled as being negligible.
By modelling the spring as being light and modelling \(P\) as a particle,
- show that the modulus of elasticity of the spring is \(2 m g\)
- Show that \(P\) attains its maximum speed when the extension of the spring is \(\frac { 1 } { 2 } a\)
- Use the principle of conservation of mechanical energy to find the maximum speed, giving your answer in terms of \(a\) and \(g\).
In reality, the spring is not light.
- State one way in which this would affect your energy equation in part (b).