A ball with a mass of #400 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #45 (kg)/s^2# and was compressed by #3/4 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-05-09T10:04:22

The height is #=3.23m#

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The spring constant is #k=45kgs^-2#

The compression is #x=3/4m#

The potential energy in the spring is

#PE=1/2*45*(3/4)^2=405/32J#

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)=405/32=0.4*9.8*h#

#h=405/32*1/(0.4*9.8)#

#=3.23m#