A ball with a mass of #80 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #9 (kg)/s^2# and was compressed by #4/5 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-06-06T12:07:11

The height is #=3.67m#

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The spring constant is #k=9kgs^-2#

The compression is #x=4/5m#

The potentialenergy in the spring is

#PE=1/2*9*(4/5)^2=2.88J#

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#

#PE_(ball)=2.88=0.08*9.8*h#

#h=2.88*1/(0.08*9.8)#

#=3.67m#