A ball with a mass of 400 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 32 (kg)/s^2 and was compressed by 3/7 m when the ball was released. How high will the ball go?

1 Answer
Jul 2, 2016

h=32/49m

Explanation:

In the given situation, one notices that the spring energy is converted into kinetic energy which inturn is converted into potential energy. So in the end spring energy is converted into potential energy.
We'll use the near-earth potential energy equation.

So the object is placed on a spring of spring constant k=32kg/s^2 and the spring is compressed by x=3/7m
So, E=1/2kx^2=1/2*32*(3/7)^2=16*9/49

Given that the object is of mass m=0.4kg and we shall take gravity g=10m/s^2, so substituting that to the near-earth potential equation and equating it to the spring energy, we get
cancel16^4*9/49=cancel{0.4}^1*cancel10^1*h

Simplify that further and you'll get the answer I gave up there.