Question

In the figure shown when the massless spring is in released state its free end is at point `B`. A very small block is ressed against the spring by a distance `delta` and the released from rest. Except the portion `BC` where coefficient of kinetic friction is `mu_(k)`, track is smooth everywhere. Determine the spring compression `delta` so that the block enters a small hole at `E`. Consider all values shown in the figure.

Answer 1

We determine the speed required at `D` so that the block falls into the hole at `E` by following a parbolic trajectory.
`v_(d)=`speed at `D`
`v_(d)=sqrt(8gd)`
Applying conservation of energy for motion from `A` to `D`
`(1)/(2)kdelta^(2)=mu_(k)mgd+mgd+(1)/(2)m(8gd) rArr delta=sqrt((2mgd)/(k)(mu_(K)+5))`