A ball with a mass of #420 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #35 (kg)/s^2# and was compressed by #9/6 m# when the ball was released. How high will the ball go?

1 Answer
Nov 22, 2016

Answer:

The height gained by the ball is #9.57# metres approx.

Explanation:

When the ball is projected vertically, it acquires a new potential energy, while the spring acquires the compression energy because of it's compression.

#:.#Potential Energy of ball#=#Compression Energy of Spring.

#:.color(red)(mgh=1/2kx^2)# , where,

m is mass of ball,
g is acceleration due to gravity,
h is height gained by the ball,
k is spring constant,
x is compression of the spring.

So, #color(blue)(420/1000xx9.8xxh=1/2xx35xx(9/6)^2).#

#:.h=9.5663# metres #=9.57# metres. (answer).