Question

A ball with a mass of `160 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `15 (kg)/s^2` and was compressed by `7/4 m` when the ball was released. How high will the ball go?

Answer 1

We will use the principle of conservation of enegry.

Explanation:

So when the spring is compressed the elastick potential energy is

`U_e=1/2k(Δx)^2=1/2*15(7/4)^2=(15*49)/(2*16)=735/32`Joules

When the spring is released the potential energy converts into kinetic and then to gravitational potential energy.
At the top of it's trajectory the ball has only potential energy which is equal to the spring's potential energy.

`U_g=735/32=>mgh=735/32=>h=735/(32mg)=735/(32*0.16*9.81)=14.633m`

So the ball will reach a height of `h_"max"=14.633m`