A ball with a mass of #640 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #36 (kg)/s^2# and was compressed by #5/8 m# when the ball was released. How high will the ball go?

1 Answer
Apr 18, 2017

Answer:

The height is #=1.12m#

Explanation:

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The spring constant is #k=36kgs^-2#

The compression is #x=5/8m#

The potential energy is

#PE=1/2*36*(5/8)^2=7.03J#

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=2/0.64*7.03=21.97#

#u=sqrt21.97=4.69ms^-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=21.97-2*9.8*h#

#h=21.97/(2*9.8)=1.12m#