A ball with a mass of #600 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 #3/5 m# when the ball was released. How high will the ball go?

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Answer 1 · 2017-04-02T08:42:19

The height is #=0.49m#

The energy stored in the spring will be converted to kinetic energy and this will give the initial speed of the ball.

Mass is #m=0.6kg#

Spring constant is #k=16kgs^-2#

Compression is #x=3/5m#

Energy in the spring #E_s=1/2kx^2#

Kinetic energy is #KE=1/2mv^2#

#1/2kx^2=1/2mv^2#

#v^2=k/mx^2#

#=16/0.6*(3/5)^2#

#=9.6m^2s^-2#

#v=sqrt9.6=3.1ms^-1#

We apply the equation of motion

#v^2=u^2+2as#

To find the greatest height

#v=0#

#u=3.1#

#a=-g=-9.8#

#s=h#

So,

#0=3.1^2-2*9.8*h#

#h=9.6/(2*9.8)#

#h=0.49m#