# Issues Determining Change in Elastic Potential Energy

• Sofa
In summary, the conversation discusses a problem where the individual attached a screengrab of the problem and their attempted solution. They used the formula ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}## and after multiple attempts, found a solution of U2=4.91J. However, they were incorrect because they interpreted the problem incorrectly and should have calculated the potential energy relative to the initial unstretched position. The potential energy equation for this problem is ##U=\frac{1}{2}kx^2## and it is important to read the problem carefully to answer what is being asked.
Sofa
Homework Statement
See attached
Relevant Equations
See attached
I've attached a screengrab of the problem (Specifically, Part B, as indicated in the image) and my attempt at a solution. Summarized, my thinking was based on using ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}##.

After using up all my attempts, the solution, as it turns out, was U2=4.91J. No variation on the above formula - or any I know, for that matter - gets me anything like that. For future reference, what exactly was I doing wrong?

Sofa said:
Homework Statement: See attached
Homework Equations: See attached

I've attached a screengrab of the problem (Specifically, Part B, as indicated in the image) and my attempt at a solution. Summarized, my thinking was based on using ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}##.

After using up all my attempts, the solution, as it turns out, was U2=4.91J. No variation on the above formula - or any I know, for that matter - gets me anything like that. For future reference, what exactly was I doing wrong?View attachment 251997
You seem to have interpreted part b as being compressed (or rather, relaxed) 0.06m relative to the stretched position in part a. They mean relative to the initial unstretched position.

The potential energy relative to the unstretched position is ##U=\frac{1}{2}kx^2## regardless of whether the spring is stretched or compressed. In part (b) you are asked for the potential energy. You calculated the change in potential energy from part (a). For future reference, read the problem carefully and asnwer what is being asked.

## 1. What is elastic potential energy?

Elastic potential energy is a type of potential energy that is stored when an elastic material, such as a spring, is stretched or compressed. It is the energy that is stored within the bonds of the material and can be released when the material returns to its original shape.

## 2. How is elastic potential energy calculated?

Elastic potential energy is calculated using the equation E = 1/2kx², where E is the elastic potential energy, k is the spring constant, and x is the displacement of the material from its resting position. The unit for elastic potential energy is joules (J).

## 3. What factors determine the amount of elastic potential energy in a system?

The amount of elastic potential energy in a system is determined by several factors, including the spring constant (k), the displacement of the material (x), and the mass of the object attached to the material. The greater the spring constant and displacement, the more elastic potential energy will be stored in the system.

## 4. How does the change in mass affect the elastic potential energy?

The change in mass can affect the elastic potential energy in a system. An increase in mass will result in an increase in the amount of elastic potential energy stored, while a decrease in mass will result in a decrease in elastic potential energy.

## 5. What are some real-life examples of elastic potential energy?

Some real-life examples of elastic potential energy include: a stretched rubber band, a compressed spring, a stretched bungee cord, a coiled hair tie, and a compressed diving board. These objects all have the ability to store and release energy due to their elastic properties.

Replies
6
Views
1K
Replies
16
Views
3K
Replies
12
Views
2K
Replies
14
Views
4K
Replies
20
Views
2K
Replies
3
Views
318
Replies
1
Views
2K
Replies
15
Views
704
Replies
2
Views
2K
Replies
29
Views
2K