A ball with a mass of #720 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #36 (kg)/s^2# and was compressed by #9/8 m# when the ball was released. How high will the ball go?

1 Answer
Mar 3, 2018

Answer:

The height is #=3.23m#

Explanation:

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The spring constant is #k=36kgs^-2#

The compression is #x=9/8m#

The potential energy in the spring is

#PE=1/2*36*(9/8)^2=22.78J#

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 #

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

Then ,

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

Mass of the ball is #m=0.72kg#

#PE_(ball)=22.78=0.72*9.8*h#

#h=22.78*1/(0.72*9.8)#

#=3.23m#

The height is #=3.23m#