Question

A 0.16 kg ball is dropped from rest onto a spring with spring constant 42 N/m, as shown. If it compresses the spring by a distance y = 0.19 m before coming to rest, from what height above the spring was it dropped? Ignore air resistance and friction.

A.0.04 m

B. 0.48 m

C. 0.17 m

D. 0.29 m

Answer 1

Let the ball was dropped from height h m  above the spring .

So the potential energy of the ball = mgh ........(1)

where m= mass of the ball =0.16 kg

g = acceleration due to gravity=9.8 m/s2

This potential energy of the ball will transfer to the spring when it falls on the spring .

Now

potential energy of the spring =1/2 kx^2 .........(2)

where k = spring constant =42 N/m

x = compression of spring =0.19m  

equating equation 1 and equation 2 we get

mgh =0.5 kx^2

Or , 0.16×9.8×h = 0.5 ×42×(0.19)^2

Or, h =0.483

Answer : B) 0.48m