How do I calculate elastic potential energy?

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Homework Help Overview

The discussion revolves around calculating elastic potential energy in the context of a problem involving two carts and a compressed spring. The original poster expresses uncertainty about the correct formula and how to approach the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of the formula for elastic potential energy and the conservation of energy principle. Questions arise regarding the initial setup and the calculations of kinetic energy for both carts. There is also a focus on the assumptions made about the spring being ideal and massless.

Discussion Status

Some participants have provided calculations for kinetic energy and have attempted to apply conservation of energy principles. There is acknowledgment of the need to round answers according to significant figures, but no explicit consensus on the correctness of the calculations has been reached.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available and the methods they can use. The original poster's uncertainty about where to start indicates a lack of foundational understanding that is being addressed through the discussion.

alicia12131415
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Homework Statement
A 0.29-kg cart and a 0.19-kg cart are held together with a compressed spring between them. When they are released, the 0.29-kg cart moves at 1.1 m/s to the right.
How much elastic potential energy was stored in the spring before the release?
Relevant Equations
U = (1/2)kx^2
k = spring force constant
x = stretch length
Is this the correct formula to use, if not what is. I really just don't know where to start. I really just need to know where and how to start.
 
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Hello @alicia12131415,

Welcome to PF! :welcome:

alicia12131415 said:
Problem Statement
A 0.29-kg cart and a 0.19-kg cart are held together with a compressed spring between them. When they are released, the 0.29-kg cart moves at 1.1 m/s to the right.
How much elastic potential energy was stored in the spring before the release?
Relevant Equations
U = (1/2)kx^2
k = spring force constant
x = stretch length

Is this the correct formula to use, if not what is. I really just don't know where to start. I really just need to know where and how to start.
Try using conservation of energy.

What's the kinetic energy of the 0.29 kg kart? What's the kinetic energy of the 0.19 kg kart? (Hint: that last calculation is also going to involve conservation of momentum.)

I'm guessing that the problem wants you to treat the spring itself as ideal and massless.
 
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So, I got

Velocity for 0.19 kg cart:
0 = (0.29kg)(1.1m/s) + (0.19)v2f
v2f = −1.6789 m/s

Kinetic energy:
0.29 kg KE1f = (1/2)(0.29kg)(1.1m/s)2 = 0.17545 J
0.19 kg KE2f = (1/2)(0.19kg)(-1.6789m/s)2 = 0.26781 J
KEf = 0.44326 J
ΔKE = 0.44326 J - 0 J = 0.44326 J

Conservation of Energy:
KEi + PEi = KEf + PEf
PEi = ΔKE + PEf
PEi = 0.44326 J + 0 J = 0.44326 J

Is this correct?
 
alicia12131415 said:
So, I got

Velocity for 0.19 kg cart:
0 = (0.29kg)(1.1m/s) + (0.19)v2f
v2f = −1.6789 m/s

Kinetic energy:
0.29 kg KE1f = (1/2)(0.29kg)(1.1m/s)2 = 0.17545 J
0.19 kg KE2f = (1/2)(0.19kg)(-1.6789m/s)2 = 0.26781 J
KEf = 0.44326 J
ΔKE = 0.44326 J - 0 J = 0.44326 J

Conservation of Energy:
KEi + PEi = KEf + PEf
PEi = ΔKE + PEf
PEi = 0.44326 J + 0 J = 0.44326 J

Is this correct?
Looks good, but you should round the answer to match the fewest significant digits of the given data.
 
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I will, thank you for checking my work. Have a wonderful weekend.
 
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