Question

A cylinder with mass mm is initially released from the rest with the spring unstretched, and the block falls down until a point where it starts bouncing back (going upward). At this instant, what is the stretch amount in the spring ?

(Figure 1)

A cylinder with mass  is initially released from the rest with the spring unstretched, and the block falls down until a point where it starts bouncing back (going upward). At this instant, what is the stretch amount in the spring ?

mg/(4k)

4mg/k

mg/k

mg/(2k)

2mg/k

Answer 1

The spring streches until the speed of the body is zero. The initial speed of the body is zero. There is no change in kinetic energy when the cylinder reaches the bottom most point during its journey.

Hence the loss in gravitational potential energy is used in increasing elastic potential energy.

Initially the spring is relaxed hence there is no initial elastic energy in spring there is only final elastic energy in spring

Let the body descends by x then the elongation in spring is also x.

mg x = 1/2 k x2

mg = 1/2 k x

x = 2mg / k

Last Option.