A ball with a mass of #300 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #32 (kg)/s^2# and was compressed by #5/6 m# when the ball was released. How high will the ball go?

1 Answer
Jun 26, 2017

Answer:

The height is #=3.78m#

Explanation:

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The spring constant is #k=32kgs^-2#

The compression is #x=5/6m#

The potential energy in the spring is

#PE=1/2*32*(5/6)^2=11.11J#

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)=11.11=0.3*9.8*h#

#h=11.11*1/(0.3*9.8)#

#=3.78m#