A ball with a mass of #450 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #18 (kg)/s^2# and was compressed by #4/5 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-05-04T12:42:05

The height is #=1.31m#

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The spring constant is #k=18kgs^-2#

The compression is #x=4/5m#

The potential energy is

#PE=1/2*18*(4/5)^2=5.76J#

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=2/0.45*5.76=25.6#

#u=sqrt25.6=5.06ms^-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=25.6-2*9.8*h#

#h=25.6/(2*9.8)=1.31m#