# Where does spring (Hooke's law) energy come from?

• LennoxLewis
In summary: That clears up a lot. In summary, springs can store energy in the form of compressive or tensile stress and release it when the force is released.
LennoxLewis
I'm talking about just any kind of F = k.x spring, with E = 1/2 k x ^2. Why can doors be closed by something that appears to have no energy source? Why can automatic guns reload requiring a battery source? (okay, maybe a bad example because they use the gas produced).

Energy is stored as compressive (or tensile) stress due to elastic deformation. Elastic deformation is often represented at the molecular level by springs, but at the atomic level, tensile and compressive stress are stored in terms of molecular rearragement. Going from that detailed level to a macroscopic/thermodynamic description is not simple.

LennoxLewis said:
I'm talking about just any kind of F = k.x spring, with E = 1/2 k x ^2. Why can doors be closed by something that appears to have no energy source? Why can automatic guns reload requiring a battery source? (okay, maybe a bad example because they use the gas produced).

The energy comes from whatever source compresses the spring.

CS

Ie, your arm in the case of the door. That example is simply a manifestation of conservation of energy.

Here is how my textbook puts it:

We can expand the U(x) function, whatever it is, to a Taylor expansion. So,

U(x) = U(0) + U'(0)x + .5U''(0)x^2 + ...

As long as x remains small (which is what Hooke's law is accurate for), the first three terms in this series should be a good approximation. The first term is a constant, and, since we can always subtract a constant from U(x) without affecting any physics, we may redefine U(0) to be zero. Because x = 0 is an equilibrium points, U'(0) = 0 and the second term in the series is automatically zero. Because the equilibrium is stable, U''(0) is positive. Renaming U''(0) as k, we conclude that for small displacements it is always a good approximation to take U(x) = .5kx^2.

stewartcs said:
The energy comes from whatever source compresses the spring.

CS

That is true, but I'm more interested in how you get the energy back. For example, you could say for a can falling down on earth, "the person who threw that can in the air gave it the gravitational potential", and that's true, but it doesn't give any insight on how that energy is released if you don't know about gravity.

Same thing but now about springs.

LennoxLewis said:
That is true, but I'm more interested in how you get the energy back. For example, you could say for a can falling down on earth, "the person who threw that can in the air gave it the gravitational potential", and that's true, but it doesn't give any insight on how that energy is released if you don't know about gravity.

Same thing but now about springs.

Refer to post #2 by Andy. He has explained where the energy is stored. It is returned once the force applied to compress it is released. Essentially the deformation it experienced is reversed back to an equilibrium state. The elastic potential energy of the spring moves from a higher ordered state to a lower ordered state (i.e. a higher potential to a lower potential). The spring's natural state is its equilibrium position or zero-potential energy state. The spring "desires" to be there naturally.

Take a look here for some info on potential energy:

http://hyperphysics.phy-astr.gsu.edu/Hbase/pegrav.html#pe

CS

stewartcs said:
Refer to post #2 by Andy. He has explained where the energy is stored. It is returned once the force applied to compress it is released. Essentially the deformation it experienced is reversed back to an equilibrium state. The elastic potential energy of the spring moves from a higher ordered state to a lower ordered state (i.e. a higher potential to a lower potential). The spring's natural state is its equilibrium position or zero-potential energy state. The spring "desires" to be there naturally.

Take a look here for some info on potential energy:

http://hyperphysics.phy-astr.gsu.edu/Hbase/pegrav.html#pe

CS

Okay, thanks.

## 1. Where does the energy in a spring come from?

The energy in a spring comes from the force applied to it. When a force is applied to a spring, it causes the atoms and molecules within the spring to stretch and compress, storing potential energy within its structure.

## 2. How does Hooke's law relate to the energy in a spring?

Hooke's law states that the force applied to a spring is directly proportional to the amount of stretch or compression in the spring. This means that as the spring is stretched or compressed, more energy is stored within it according to Hooke's law.

## 3. Can the energy in a spring be changed or manipulated?

Yes, the energy in a spring can be changed or manipulated by altering the force applied to it or by changing the properties of the spring itself, such as its stiffness or length.

## 4. Does the energy in a spring ever run out?

No, the energy in a spring does not run out as long as the spring retains its elasticity and is not permanently deformed. The energy can be released and reused multiple times as the spring is stretched and compressed.

## 5. Is the energy in a spring always positive?

The energy in a spring can be either positive or negative, depending on the direction of the force applied. When the force is applied in the same direction as the displacement of the spring, the energy is positive. When the force is applied in the opposite direction, the energy is negative.

• Mechanics
Replies
3
Views
862
• Introductory Physics Homework Help
Replies
3
Views
492
• Introductory Physics Homework Help
Replies
2
Views
721
• Mechanics
Replies
4
Views
6K
• Mechanics
Replies
1
Views
1K
• Mechanics
Replies
26
Views
3K
• Mechanics
Replies
4
Views
1K
• Mechanics
Replies
2
Views
2K
• Mechanics
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K