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.

In the figure shown when the massless spring is in released state its

1.	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» 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))`

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