# Ke and pe relationship

### The Relationship Between Kinetic and Potential Energy - Physics - Ashley Nestler There is a direct relation between gravitational potential energy and the mass of an object. More massive objects have greater PEgrav = mass • g • height. The mechanical energy of an object is equal to the sum of the potential plus kinetic energies, i.e. E = PE + KE, and is a direct measure of the total energy. This video defines and describes kinetic and potential energy. You'll learn how different types of energy can be classified as potential and kinetic. You'll also find out how kinetic and potential energy are transformed.

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.

### Potential Energy

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. 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.

### Work and Energy Conservation

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. The details of problems involving frictional work will be left for a more advanced course in the subject.

## The relationship between potential energy and kinetic energy

Another case to consider involves an object traveling on a level ground which is brought to rest by an external force.

Since the force is applied over a finite distance, then work is done on the mass which decelerates it to a stop. The total work required to bring the system to a halt is simply given by the initial kinetic energy; there is no change in potential energy if it travels at the same height on the ground so that the kinetic energy is removed from the object by the external forces.

In order to reinforce the concepts noted above, consider the following examples which explore the motion of everyday objects as they move in the presence of forces which change either the position or velocity of the masses.

A helicopter drops a 20 kg package from rest at a height of m from the ground. Since the package is held motionless above the ground, we see that the initial mechanical energy is simply the potential energy it has while in the helicopter no KE: A 5 kg cannonball is fired from the ground straight up into the air such that it rises to a height of 50 m.

Note that if we ignore air friction, this is the same as the initial speed of the cannonball when it was fired from the cannon. Then we can use the height of the cannonball above the ground to determine the potential energy from the formula: Using the same idea of energy conservation, we relate the potential energy lost by the cannonball to the kinetic gained: It crashes into the wall and is brought to rest by the forces acting from the wall.