A ball with a mass of #256 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #32 (kg)/s^2# and was compressed by #24/5 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-07-03T15:34:01

The height is #=146.9m#

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The spring constant is #k=32kgs^-2#

The compression is #x=24/5m#

The potential energy in the spring is

#PE=1/2*32*(24/5)^2=368.64J#

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)=368.64=0.256*9.8*h#

#h=368.64*1/(0.256*9.8)#

#=146.9m#