# Compressing a Spring: Forces & Potential Energy

• ralqs

#### ralqs

(This was, incidentally, inspired by a question I saw posted recently)

When a spring w/ mass is compressed, what will the forces that it produces on both ends be? Does it depend on how the spring is moving? What if one end is attached to a wall? And what will the spring's potential energy be? Thanks a lot, and the more derivations, the better! :)

If the mass is accelerating, the forces on the mass will be slightly greater than the force on the wall due to the acceleration of the mass of the spring, but the difference would usually be very small.

## 1. What is the relationship between the force applied to a spring and its potential energy?

As a spring is compressed, the force being applied to it increases. This increase in force results in an increase in the potential energy stored in the spring. This relationship is described by Hooke's Law, which states that the force applied to a spring is directly proportional to the amount of compression or extension.

## 2. How does the mass of an object affect the potential energy stored in a compressed spring?

The mass of an object does not directly affect the potential energy stored in a compressed spring. However, the amount of force needed to compress the spring does depend on the mass of the object. Heavier objects will require more force to compress the spring, resulting in a higher potential energy being stored in the spring.

## 3. Can a compressed spring have potential energy if it is not being acted upon by an external force?

No, a compressed spring only has potential energy when it is being acted upon by an external force. Once the force is removed and the spring returns to its original shape, the potential energy is converted into kinetic energy as the spring expands.

## 4. How can the potential energy of a compressed spring be calculated?

The potential energy stored in a compressed spring can be calculated using the equation PE = 1/2kx², where PE is the potential energy, k is the spring constant, and x is the distance the spring is compressed or extended. This equation is derived from Hooke's Law, which describes the relationship between force and displacement in a spring.

## 5. Is the potential energy of a compressed spring a form of stored energy?

Yes, the potential energy stored in a compressed spring is a form of stored energy. This energy is stored in the bonds between the molecules of the spring, which are stretched or compressed when the spring is compressed or extended. This stored energy can be released as kinetic energy when the spring returns to its original shape.