A ball with a mass of #350 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 #7/4 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-11-22T13:56:57

The height is #=4.02m#

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

The compression is #x=7/4m#

The potential energy is

#PE=1/2*9*(7/4)^2=13.78J#

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 acceleration 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=0.35kg#

#PE_(ball)=13.78=0.35*9.8*h#

#h=13.78*1/(0.35*9.8)#

#=4.02m#

The height is #=4.02m#