A ball with a mass of #200 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #64 (kg)/s^2# and was compressed by #7/4 m# when the ball was released. How high will the ball go?

1 Answer
Apr 22, 2017

Answer:

The height is #=0.5m#

Explanation:

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The spring constant is #k=64kgs^-2#

The compression is #x=7/4m#

The potential energy is

#PE=1/2*64*(7/4)^2=98J#

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=2/0.2*98=9.8#

#u=sqrt9.8=3.13ms^-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=9.8-2*9.8*h#

#h=9.8/(2*9.8)=0.5m#