Elastic Potential Energy and spring

In summary, the object is hanging from a vertical spring with a spring constant of 40.0 N/m. When pulled down 0.200 m from the point of release (h = 0), the object has a translational kinetic energy of 0.81 J and a gravitational potential energy of 4.7088 J. The elastic potential energy at this point is 0 J. The total mechanical energy (E) at this point is 5.5188 J.
  • #1
wallace13
31
0
A 2.40 kg object is hanging from the end of a vertical spring. The spring constant is 40.0 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


I have already found kinetic and gravitational potential energy. I need to find elastic potential energy at h=0, .2, and .4m

Elastic Potential Energy= .5kx squared


.5(40)(.2)squared= .8 J

.8 J is the incorrect answer, but i know .5kx squared is the right equation... what am I doing wrong??


At this height (.2 above the release point) I found the correct kinetic energy to be .81 J and the correct gPE to be 4.7088 J
 
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  • #2
I'm confused over the point of release and the equilibrium point.
Looks to me like the point of release is h = 0, x = -0.2.
So at h = 0.2, x = 0 and the Elastic PE = 0.
 
  • #3
.

To find the elastic potential energy, you need to use the equation .5kx², where k is the spring constant and x is the displacement from the equilibrium position. In this case, the equilibrium position is at h=0, so x=.2m. Plugging in the values, we get:

Elastic Potential Energy = .5(40)(.2)² = .8 J

So, the elastic potential energy at h=0.2m is also .8 J. You may have made a calculation error or used the wrong values for k or x in your previous calculation. Double check your values and equations to make sure they are correct.
 

Related to Elastic Potential Energy and spring

1. What is elastic potential energy?

Elastic potential energy is the energy stored in an object when it is stretched or compressed, such as a spring. This energy is due to the elastic potential of the material, which allows it to return to its original shape after being deformed.

2. How is elastic potential energy calculated?

The formula for calculating elastic potential energy is: E = 1/2kx², where E is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

3. What is the relationship between elastic potential energy and spring constant?

The higher the spring constant, the more elastic potential energy is stored in the spring. This means that a stiffer spring will require more force to stretch or compress, resulting in more energy being stored in it.

4. How does the mass of an object affect elastic potential energy?

The mass of an object has no direct effect on elastic potential energy. However, the displacement of the object from its equilibrium position will impact the amount of elastic potential energy stored in the spring. The greater the displacement, the more energy will be stored.

5. Can elastic potential energy be converted into other forms of energy?

Yes, elastic potential energy can be converted into other forms of energy, such as kinetic energy, when the object is released from its stretched or compressed position. This is why springs are often used in devices such as catapults and trampolines.

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