# Force and potential energy relationship

### Force and Potential Energy - Physics LibreTexts

Define conservative force, potential energy, and mechanical energy. Explain the . forces act? What is the relationship of potential energy to conservative force?. In physics, potential energy is the energy held by an object because of its position relative to Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends . In this section the relationship between work and potential energy is presented in more detail. Potential energy is energy which results from position or configuration. it is said to be a conservative force, and it can be represented by a potential energy function which for a one-dimensional case The integral form of this relationship is.

A quick look at the graph tells us that the slope of the curve at the origin is in fact zero.

**7 4 Force and Potential Energy**

So far so good! Lastly, there's the minus sign. As the spring-mass is pulled to the right, the graph's slope becomes positive. This should make perfect sense: We can quantitatively show just how right this relationships is. Now that you're convinced that this relationship is real, let's see if we can understand why. Why is this true?

To understand, consider the following situation pictured below. Imagine a box is lifted through a potential field, like lifting an object against gravity. Imagine also that the field is associated with a force, which is constant and pointing downwards at all points in space.

## Potential energy

The energy cannot be going to kinetic energy, because by design the kinetic energy is constant. The energy also cannot be disappearing, because of energy conservation.

The answer is that it is being transferred to potential energy. The amount of work I do on the object is given by the force I exert times the distance I moved through: Interpreting Bond Energy Pictured is the real potential energy vs.

### Potential energy - Wikipedia

What does the shape of the curve tell us about the behavior of the bond? Treat the Curve Like a Roller Coaster Track By applying the relationship between force and potential energy, you will eventually arrive upon an intuition which is akin to treating the curve like the tracks of a roller coaster. That is, you can visualize the behavior of the system by imagining the object as riding the curve like a cart subject to gravity.

What that would tell us here is that hydrogen atoms easily fall into bonds with each other. We know this because the hydrogen "cart" would easily slide into the bond well.

Imagine trying to push a cart up that extremely tall, steep hill! This includes when there are multiple forces acting on the object, all of which cancel out.

- Potential Energy

Example of stable equilibrium: Each of the images below shows an example of equilibrium. Stable Equilibrium Stable equilibrium exists if the net force is zero, and small changes in the system would cause an increase in potential energy.

Unstable Equilibrium Unstable equilibrium exists if the net force is zero, and small changes in the system would cause a decrease in potential energy. Position Graph Equilibrium occurs where the force is zero. Typically, the ground is considered to be a position of zero height. But this is merely an arbitrarily assigned position that most people agree upon. Since many of our labs are done on tabletops, it is often customary to assign the tabletop to be the zero height position.

Again this is merely arbitrary.

If the tabletop is the zero position, then the potential energy of an object is based upon its height relative to the tabletop. For example, a pendulum bob swinging to and from above the tabletop has a potential energy that can be measured based on its height above the tabletop.

## 2.5: Force and Potential Energy

By measuring the mass of the bob and the height of the bob above the tabletop, the potential energy of the bob can be determined. Since the gravitational potential energy of an object is directly proportional to its height above the zero position, a doubling of the height will result in a doubling of the gravitational potential energy. A tripling of the height will result in a tripling of the gravitational potential energy.

Use this principle to determine the blanks in the following diagram. Knowing that the potential energy at the top of the tall platform is 50 J, what is the potential energy at the other positions shown on the stair steps and the incline? Elastic Potential Energy The second form of potential energy that we will discuss is elastic potential energy.

Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow, etc. The amount of elastic potential energy stored in such a device is related to the amount of stretch of the device - the more stretch, the more stored energy. Springs are a special instance of a device that can store elastic potential energy due to either compression or stretching.

A force is required to compress a spring; the more compression there is, the more force that is required to compress it further.

For certain springs, the amount of force is directly proportional to the amount of stretch or compression x ; the constant of proportionality is known as the spring constant k. If a spring is not stretched or compressed, then there is no elastic potential energy stored in it. The spring is said to be at its equilibrium position.