A ball with a mass of #40 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #2/5 m# when the ball was released. How high will the ball go?

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Answer 1 · 2018-05-25T06:14:37

The height reached by the ball is #=3.27m#

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The spring constant is #k=16kgs^-2#

The compression of the spring is #x=2/5m#

The potential energy stored in the spring is

#PE=1/2kx^2=1/2*16*(2/5)^2=1.28J#

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=0.040kg#

#PE_(ball)=1.28=0.040*9.8*h#

#h=1.28*1/(0.040*9.8)#

#=3.27m#

The height reached by the ball is #=3.27m#