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?

Jul 18, 2017

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)=735/32Joules

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.

${U}_{g} = \frac{735}{32} \implies m g h = \frac{735}{32} \implies h = \frac{735}{32 m g} = \frac{735}{32 \cdot 0.16 \cdot 9.81} = 14.633 m$

So the ball will reach a height of ${h}_{\text{max}} = 14.633 m$