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 #32 (kg)/s^2# and was compressed by #5/7 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-05-07T08:18:45

The height is #=2.08m#

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The spring constant is #k=12kgs^-2#

The compression is #x=1/2m#

The potential energy is

#PE=1/2*32*(5/7)^2=8.16J#

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=2/0.4*8.16=40.8#

#u=sqrt40.8=6.39ms^-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=40.8-2*9.8*h#

#h=40.8/(2*9.8)=2.08m#