A ball with a mass of #480 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #12 (kg)/s^2# and was compressed by #9/5 m# when the ball was released. How high will the ball go?

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Answer 1 · 2018-02-06T17:39:46

The height is #=4.13m#

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The spring constant is #k=12kgs^-2#

The compression is #x=9/5m#

The potential energy is

#PE=1/2*12*(9/5)^2=19.44J#

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 sacceleration 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=0.48kg#

#PE_(ball)=5.76=0.48*9.8*h#

#h=19.44*1/(0.48*9.8)#

#=4.13m#

The height is #=4.13m#