A ball with a mass of #144 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 #6/4 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-04-23T07:33:41

The height is #=12.76m#

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

The compression is #x=6/4m#

The potential energy is

#PE=1/2*16*(6/4)^2=18J#

This potential energy will be converted to kinetic energy when the spring is released

#KE=1/2m u^2#

The initial velocity is #=u#

#u^2=2/m*KE=2/m*PE#

#u^2=2/0.144*18=250#

#u=sqrt250=15.81ms^-1#

Resolving in the vertical direction #uarr^+#

We apply the equation of motion

#v^2=u^2+2ah#

At the greatest height, #v=0#

and #a=-g#

So,

#0=250-2*9.8*h#

#h=250/(2*9.8)=12.76m#