Translational/gravitational/elastic/total energy problem

[Rival]

A 1.80 kg object is hanging from the end of a vertical spring. The spring constant is 34.0 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

that is supposed to be a table where h is given and you have to find everything else...

i can figure out Pe-gravity by mgh but i cannot get the PE-elastic.

if i get PE-elastic i can solve for the rest

Kevin

 

[himanshu121]

PE elastic is the energy stored in the spring it $$\frac{kx^2}{2}$$

Where x is the elongation from normal situation

 

[M98Ranger]

,

To solve for the elastic potential energy, we can use the equation PE = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position. In this problem, the equilibrium position is at h = 0, so we can use the given displacement values to calculate the elastic potential energy at each h position.

Here is the completed table with the calculated values:

h(m) KE(J) PE-gravity(J) PE-elastic(J) E(J)
0 0 0 0 0
0.200 1.96 0.352 0.0688 2.38
0.400 3.92 0.704 0.275 4.90

To calculate the elastic potential energy at h = 0.200m, we can use the given displacement of 0.200m and the spring constant of 34.0 N/m:

PE-elastic = 1/2(34.0 N/m)(0.200m)^2 = 0.0688 J

Similarly, for h = 0.400m, we can use the displacement of 0.400m and the same spring constant to calculate the elastic potential energy:

PE-elastic = 1/2(34.0 N/m)(0.400m)^2 = 0.275 J

Once we have all the values for kinetic energy, gravitational potential energy, and elastic potential energy, we can calculate the total mechanical energy by adding them together:

E = KE + PE-gravity + PE-elastic

Therefore, for h = 0.200m, the total mechanical energy is:

E = 1.96 J + 0.352 J + 0.0688 J = 2.38 J

And for h = 0.400m, the total mechanical energy is:

E = 3.92 J + 0.704 J + 0.275 J = 4.90 J

I hope this helps! Let me know if you have any further questions.