# What is the relationship of potential energy to work

### Potential Energy

The Work Energy Principle is one of the big ideas in introductory physics There are many different types of energy: kinetic, potential, thermal. Although technically energy and work are same things, there is intuitive The ones we see over here are kinetic energy (KE) and potential energy (PE). Take the example of us, when we eat, we fill ourselves with energy, that is our potential energy, when we do work or run, we use parts of our potential energy in .

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.

### newtonian mechanics - Is potential energy and "work done" the same thing? - Physics Stack Exchange

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.

## Potential 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. When you lift up an object, you are increasing its gravitational potential energy.

Likewise, as you are lowering an object, its gravitational energy is decreasing. A General Formula for Potential Difference: The work done by an E field as it act on a charge q to move it from point A to point B is defined as Electric Potential Difference between points A and B: Clearly, the potential function V can be assigned to each point in the space surrounding a charge distribution such as parallel plates.

The above formula provides a simple recipe to calculate work done in moving a charge between two points where we know the value of the potential difference. The above statements and the formula are valid regardless of the path through which the charge is moved. A particular interest is the potential of a point-like charge Q. It can be found by simply performing the integration through a simple path such as a straight line from a point A whose distance from Q is r to infinity. Path is chosen along a radial line so that becomes simply Edr.

Note that potential function is a scalar quantity as oppose to electric field being a vector quantity.

Now, we can define the electric potential energy of a system of charges or charge distributions. Suppose we compute the work done against electric forces in moving a charge q from infinity to a point a distance r from the charge Q.

The work is given by: Note that if q is negative, its sigh should be used in the equation! With energy the approach is usually a little different. Often you can look at the starting conditions initial speed and height, for instance and the final conditions final speed and heightand not have to worry about what happens in between. The initial and final information can often tell you all you need to know. Work and energy Whenever a force is applied to an object, causing the object to move, work is done by the force.

If a force is applied but the object doesn't move, no work is done; if a force is applied and the object moves a distance d in a direction other than the direction of the force, less work is done than if the object moves a distance d in the direction of the applied force. The physics definition of "work" is: The unit of work is the unit of energy, the joule J. Work can be either positive or negative: If the force has a component in the direction opposite to the displacement, the force does negative work.

## Potential energy

If you pick a book off the floor and put it on a table, for example, you're doing positive work on the book, because you supplied an upward force and the book went up. If you pick the book up and place it gently back on the floor again, though, you're doing negative work, because the book is going down but you're exerting an upward force, acting against gravity. If you move the book at constant speed horizontally, you don't do any work on it, despite the fact that you have to exert an upward force to counter-act gravity.

Kinetic energy An object has kinetic energy if it has mass and if it is moving.

It is energy associated with a moving object, in other words. For an object traveling at a speed v and with a mass m, the kinetic energy is given by: