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 #27 (kg)/s^2# and was compressed by #9/8 m# when the ball was released. How high will the ball go?

Question

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 #27  (kg)/s^2# and was compressed by #9/8 m# when the ball was released.  How high will the ball go?

Isabella Alvarez · Accepted Answer

The height is #=3.87m#

The spring constant is #k=27kgs^-2#

The compression is #x=9/8m#

The potential energy in the spring is

#PE=1/2*27*(9/8)^2=17.09J#

This potential energy will be converted to kinetic energy when the spring is released and to potential energy of the ball

#KE_(ball)=1/2m u^2#

Let the height of the ball be #=h #

Then ,

The potential energy of the ball is #PE_(ball)=mgh#

#PE_(ball)=17.09=0.45*9.8*h#

#h=17.09*1/(0.45*9.8)#

#=3.87m#

Julia Aguilar · Answer

undefined To find the maximum height reached by the ball, you can use the equation for the maximum height in vertical motion: $ h = \frac{1}{2} \frac{k}{m} x^2 $, where $ k $ is the spring constant, $ m $ is the mass of the ball, and $ x $ is the compression of the spring. Plugging in the given values, you can calculate the maximum height.