Elastic Potential Energy homework

[bb1235]

A 2.40 kg object is hanging from the end of a vertical spring. The spring constant is 41.0 N/m. The object is pulled 0.200 m downward and released from rest. Complete the table below by calculating the translational kinetic energy, the gravitational potential energy, the elastic potential energy, and the total mechanical energy E for each of the vertical positions indicated. The vertical positions h indicate distances above the point of release, where h = 0.

h (m) KE (J) PE-gravity (J) PE-elastic (J) E (J)
0
0.200
0.400

I know how to get PE-Gravity, mgh. And i know Trans kinetic= 1/2mv^2 but I am having trouble coming up with V^2.

And with PE elastic= 1/2kx^2 but i can't get the correct number for x. Is x the I-.200 plus h

 

[G01]

x is the displacement of the spring from it's equilibrium position. i.e. How far the spring is compressed or stretched.

Once you are able to calculate the initial elastic potential energy, you should be able to find K.E. at any point in the objects motion.

HINT: Remember that mechanical energy is conserved.

 

[RTW69]

The movement of the weight as it bobs can be modeled as simple harmonic motion (at least for the first few oscillations). The equation of that motion can be described as Y as a function of time. The first derivative of that function will be velocity as a function of time. Find the time for the desired height and use that time to find the corresponding velocity.