Question

A ball with a mass of `480 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `24 (kg)/s^2` and was compressed by `8/9 m` when the ball was released. How high will the ball go?

Answer 1

6.28 m/s

Explanation:

If Spring compressed by `x` then Potential Energy stored in it
`U=1/2kx^2`
`k="spring constant" =24 (kg)/s^2`
`x="Displacement "=8/9 m`

`U=1/2(24)(8/9)^2=(24xx64)/(2xx81)=9.48 J`

After Release spring loaded contraption Potential Energy Changes into Kinetic Energy. (Conservation of Energy)
Hence Mass of 480g has Kinetic Energy `1/2mv^2`

Now Using Conservation of Energy
`"Kinetic Energy"="Potential Energy"`
`U=1/2mv^2`
`9.48=1/2(0.48)(v)^2`
`v^2=39.50`
`v=sqrt39.50`
`v=6.28 m/s`