Exploring Energy of a Vertical Spring System

In summary, the conversation discusses the energy of a system consisting of a vertical spring with a mass attached. The equations for the energy change as the reference point is changed, but the zero point for calculating the elastic restoring force must remain at the old equilibrium point.
  • #1
nothing123
97
0
Hi,

If we have a vertical spring with a mass attached to it, how does the energy of the system work. Let's say we set the zero point as the point where the spring is unstretched (basically with no mass attached). Then at the top we have zero kinetic, zero spring potential as well as zero gravitational potential. As it passes through its new equilibrium point, it will have negative gravitational and positive elastic potential and kinetic energy so 1/2kx^2 + 1/2mv^2 - mgh which rearranged is mgh - 1/2kx^2 = 1/2mv^2. Now let's say we take the zero point to be where the new equilibrium point is. At the top, we have gravitational potential as well as spring potential. As it passes through the equilibrium point, it would only have kinetic. By conservation of energy, mgh + 1/2kx^2 = 1/2mv^2. Why are the two equations different if we change the reference point?

Thanks.
 
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  • #3
zero point

Hi nothing123! :smile:
nothing123 said:
… Now let's say we take the zero point to be where the new equilibrium point is …

Your equations are completely confusing me (especially since h is related to x). :confused:

But if by "zero point", you mean for calculating the elastic restoring force, it has to be the "old" equilibrium point … that's how springs work! :smile:

(unless, I suppose, you take g out of the equation completely :rolleyes:)
 

1. What is a vertical spring system?

A vertical spring system is a physical system that consists of a spring attached to a fixed point at one end and a mass at the other end, with the spring oriented vertically. When the mass is displaced from its equilibrium position, the spring exerts a restoring force that causes the mass to oscillate up and down around its equilibrium position.

2. How does a vertical spring system store energy?

A vertical spring system stores energy in the form of potential energy. When the mass is displaced from its equilibrium position, the spring stretches or compresses, storing elastic potential energy. As the mass oscillates, the energy is transferred between kinetic energy and potential energy, but the total energy of the system remains constant.

3. What factors affect the energy stored in a vertical spring system?

The energy stored in a vertical spring system depends on the spring constant, which is a measure of the stiffness of the spring, and the displacement of the mass from its equilibrium position. A stiffer spring or a larger displacement will result in a greater amount of energy stored in the system.

4. How can the energy of a vertical spring system be calculated?

The energy of a vertical spring system can be calculated using the formula E = 1/2kx^2, where E is the energy stored in the system, k is the spring constant, and x is the displacement of the mass from its equilibrium position. This formula assumes that there is no friction or other external forces acting on the system.

5. How is the energy of a vertical spring system used in real-world applications?

The energy stored in a vertical spring system can be harnessed and used in various real-world applications. For example, it is used in shock absorbers to dampen vibrations in vehicles, in pogo sticks and trampolines for bouncing, and in watches and clocks for keeping time. It is also an essential concept in the study of mechanical waves and oscillations in physics.

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