A ball with a mass of #40 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 #1/5 m# when the ball was released. How high will the ball go?

1 Answer
May 5, 2017

Answer:

The height is #=0.82m#

Explanation:

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The spring constant is #k=16kgs^-2#

The compression is #x=1/5m#

The potential energy is

#PE=1/2*16*(1/5)^2=0.32J#

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=2/0.04*0.32=16#

#u=sqrt16=4ms^-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=16-2*9.8*h#

#h=16/(2*9.8)=0.82m#