How do I calculate elastic potential energy?

In summary, the cart with the smaller mass moved at a higher velocity after the spring was compressed. The cart with the smaller mass had more kinetic energy.
  • #1
alicia12131415
3
1
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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  • #2
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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  • #3
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?
 
  • #4
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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  • #5
I will, thank you for checking my work. Have a wonderful weekend.
 
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Related to How do I calculate elastic potential energy?

1. What is elastic potential energy?

Elastic potential energy is the potential energy stored in an elastic material when it is stretched or compressed. This energy is stored in the form of strain, which is the amount of deformation or change in shape of the material.

2. How is elastic potential energy calculated?

The formula for calculating elastic potential energy is E = 1/2 kx^2, where E is the elastic potential energy, k is the spring constant of the material, and x is the displacement or change in length of the material from its equilibrium position.

3. What are some examples of elastic potential energy?

Some examples of elastic potential energy include a stretched rubber band, a compressed spring, a stretched trampoline, and a compressed diving board. These objects all have the potential to return to their original shape and release stored energy when the stretching or compression force is removed.

4. How does elastic potential energy differ from other forms of potential energy?

Elastic potential energy is a type of potential energy that is stored in elastic materials, while other forms of potential energy, such as gravitational potential energy and chemical potential energy, are stored in different types of systems. Elastic potential energy is also unique in that it is directly related to the amount of deformation or strain in the material, rather than its position or chemical composition.

5. How is elastic potential energy used in real-life applications?

Elastic potential energy is used in a variety of real-life applications, including in the design of springs for mechanical devices such as car suspension systems, in the storage of energy in compressed air tanks, and in the design of elastic materials used in sports equipment such as tennis rackets and trampolines. It is also an important concept in the study of earthquakes and the behavior of elastic materials under stress and strain.

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