A ball with a mass of #350 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #9 (kg)/s^2# and was compressed by #7/4 m# when the ball was released. How high will the ball go?

Question

A ball with a mass of #350 g# is projected vertically by a spring loaded contraption.  The spring in the contraption has a spring constant of #9  (kg)/s^2# and was compressed by #7/4 m# when the ball was released.  How high will the ball go?

Julia Aguilar · Accepted Answer

The height is #=4.02m#

The spring constant is #k=9kgs^-2#

The compression is #x=7/4m#

The potential energy is

#PE=1/2*9*(7/4)^2=13.78J#

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 #

The acceleration due to gravity is #g=9.8ms^-2#

Then ,

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

Mass of the ball is #m=0.35kg#

#PE_(ball)=13.78=0.35*9.8*h#

#h=13.78*1/(0.35*9.8)#

#=4.02m#

The height is #=4.02m#

Parker Abbott · Answer

undefined To find the maximum height the ball will reach, you can use the conservation of mechanical energy. The potential energy stored in the compressed spring is converted into kinetic energy as the ball is launched upwards. At the maximum height, all kinetic energy is converted back into potential energy. You can use the equation for potential energy to find the height.