Spring stretch - Do I use Force or Potential Energy

In summary, the discussion revolves around the concept of equilibrium and total stretch of a spring when a mass is attached to it. While the force equation leads to x=mg/k as the equilibrium position, the energy equation shows that the maximum displacement is actually 2mg/k. This is due to the fact that at equilibrium, there is also kinetic energy present. Additionally, the energy balance should include the work done in stretching the spring, leading to a more comprehensive equation.
  • #1
Steve1971
2
0
I have read posts about this but still don't have a good handle on it. I am confused about something that I know is simple. If a mass is attached to a spring, the spring will stretch according to Hooke,s law, correct? So won't the weight, (mg) balance out the spring force of -kx? So in other words, won't x=mg/k?

My confusion is when I look at the same problem using a potential energy balance. the balance of the change in spring potential energy of 1/2kx^2 with the change in potential energy of the hanging mass mgx will result in x=2mg/k.

So the energy equation shows twice as much stretch as the force equation. Can someone please clear this up for me?
 
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  • #2
Hi Steve, :welcome:

Well observed !
The mass, when gently moving from position with spring unstretched to equilibrium, can do useful work (in theory e.g. run a clock or something).
Conversely, when lifting the weight from equilibrium to spring unstretched position, you have to add some energy (you have to do work).
 
  • #3
maybe it's equilibrium vs. total stretch that is getting me. So will the equilibrium position be mg/k?

but prior to that equilibrium, the spring will stretch as far as 2mg/k as it is oscillating?
 
  • #4
Yes, if don't have any external force to slowly lower the weight, it will oscillate. At equilibrium position you have kinetic energy as well.
What you found from energy conservation is the maximum displacement and not the equilibrium one.
 
  • #5
I think you may have left out a term. If I am not mistaken, an energy balance should include the work done in stretching the spring.

##W = -\frac{1}{2}k{x_d}^2##

So the balance looks like:

## -\frac{1}{2}k{x_d}^2 = \frac{1}{2}k{x_d}^2 - mgx_d ##

This can be solved to yield the same answer you got from a force balance.
 
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FAQ: Spring stretch - Do I use Force or Potential Energy

How does the stretch of a spring relate to force and potential energy?

When a spring is stretched, it stores potential energy in the form of elastic potential energy. This energy is stored in the bonds between the molecules of the spring, and the amount of potential energy stored is directly proportional to the amount of stretch or compression of the spring. This potential energy can also be converted into kinetic energy as the spring returns to its original shape.

When is force used in relation to spring stretch?

Force is used when the spring is stretched or compressed, as it is the force applied to the spring that causes it to stretch or compress. The amount of force applied to the spring determines the amount of stretch or compression it undergoes. The force required to stretch a spring is directly proportional to the amount of stretch, according to Hooke's Law.

Is potential energy used to calculate the stretch of a spring?

Potential energy is not used to directly calculate the stretch of a spring. However, the amount of potential energy stored in a spring can be used to determine the amount of stretch or compression it has undergone. This can be done by using the equation for elastic potential energy, which includes the spring constant and the amount of stretch or compression.

How does the spring constant affect the force and potential energy in a spring?

The spring constant, represented by the letter k, is a measure of the stiffness of a spring. A higher spring constant means that it takes more force to stretch or compress the spring, and it also stores more potential energy for a given amount of stretch. Therefore, a higher spring constant results in a greater force and potential energy in a spring.

Can you use both force and potential energy to describe the stretch of a spring?

Yes, both force and potential energy can be used to describe the stretch of a spring. Force describes the external force applied to the spring, while potential energy describes the internal energy stored in the spring. Together, they provide a complete understanding of the relationship between spring stretch and the forces and energies involved.

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