A ball with a mass of #160 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #21 (kg)/s^2# and was compressed by #3/8 m# when the ball was released. How high will the ball go?

1 Answer
Oct 21, 2017

The height is #=0.94m#

Explanation:

enter image source here

The spring constant is #k=21kgs^-2#

The compression is #x=3/8m#

The potential energy in the spring is

#PE=1/2kx^2=1/2*21*(3/8)^2=1.48J#

This potential energy will be converted to kinetic energy when the spring is released and to potential energy of the ball

#KE_(ball)=1/2m u^2#

Let the height of the ball be #=h #

Then ,

The potential energy of the ball is #PE_(ball)=mgh#

The mass of the ball is #=0.160kg#

The acceleration due to gravity is #g=9.8ms^-2#

#PE_(ball)=1.48=0.160*9.8*h#

The height is #h=1.48*1/(0.160*9.8)#

#=0.94m#