How do I calculate elastic potential energy?

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SUMMARY

The discussion centers on calculating elastic potential energy using the formula U = (1/2)kx², where k is the spring force constant and x is the stretch length. A scenario involving two carts, one weighing 0.29 kg and the other 0.19 kg, is analyzed to determine the energy stored in a compressed spring. The kinetic energy of both carts is calculated, leading to a total elastic potential energy of 0.44326 J. The importance of rounding the final answer to match the significant digits of the given data is also emphasized.

PREREQUISITES
  • Understanding of elastic potential energy and the formula U = (1/2)kx²
  • Knowledge of kinetic energy calculations
  • Familiarity with conservation of energy principles
  • Basic algebra for solving equations involving momentum and energy
NEXT STEPS
  • Study the concept of spring force constant (k) and its determination
  • Learn about conservation of momentum in elastic collisions
  • Explore the relationship between kinetic energy and potential energy in mechanical systems
  • Practice problems involving elastic potential energy calculations with varying parameters
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Students studying physics, educators teaching mechanics, and anyone interested in understanding energy transformations in spring systems.

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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