A ball with a mass of #140 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 #7/3 m# when the ball was released. How high will the ball go?

1 Answer
May 11, 2018

Answer:

The height reached by the ball is #=31.75m#

Explanation:

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

The compression of the spring is #x=7/3m#

The potential energy stored in the spring is

#PE=1/2kx^2=1/2*16*(7/3)^2=43.56J#

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=0.140kg#

#PE_(ball)=43.56=0.140*9.8*h#

#h=43.56*1/(0.140*9.8)#

#=31.75m#

The height reached by the ball is #=31.75m#