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 #27 (kg)/s^2# and was compressed by #12/4 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-10-02T10:06:08

The height is #=48.43m#

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The spring constant is #k=27kgs^-2#

The compression is #x=12/4m#

The potential energy in the spring is

#PE=1/2kx^2=1/2*27*(12/4)^2=121.5J#

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 #=0.256kg#

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

#PE_(ball)=121.5=0.256*9.8*h#

The height is #h=121.5*1/(0.256*9.8)#

#=48.43m#