A ball with a mass of #420 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #35 (kg)/s^2# and was compressed by #5/4 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-09-20T05:04:22

The height is #=6.64m#

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The spring constant is #k=35kgs^-2#

The compression is #x=5/4m#

The potential energy in the spring is

#PE=1/2kx^2=1/2*35*(5/4)^2=27.34375J#

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 #=0.420kg#

#PE_(ball)=24.34375=0.240*9.8*h#

The height is #h=24.34375*1/(0.420*9.8)#

#=6.64m#