What is the maximum kinetic energy in the following mass spring system:
A 3.0 kilogram mass is attached to a spring having a spring constant of 30 N/m. The mass is pulled 0.20 meter from the spring's equilibrium position and released.
The sum of the kinetic energy and potential energy in a system is a constant. Only the form of the energy changes.
For a spring with a spring constant of 30 N/m, the energy stored is equal to (1/2)*k*x^2 where x is the distance by which the spring is compressed or extended from its equilibrium position.
Here we have the mass attached to the spring given as 3 kilogram and the spring is pulled by 0.2 m from its equilibrium position.
Initially, the sum of the kinetic and potential energy in the system is KE + PE = 0 + (1/2)*30*0.2^2
=> 0 + 0.6
When the spring returns to its equilibrium position all the energy is in the form of kinetic energy and the potential energy is 0.
Therefore the maximum kinetic energy in the system is 0.6 J.