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# Overview of Study of Energy

by Ron Kurtus (revised 9 July 2013)

Energy is a property of matter related to motion.

>> Energy is the capacity for doing work. A force does work when it moves an object against a resistive force. Work is also the change in KE and thus the change in velocity.

An object has kinetic energy if it is moving. If there are some constrained or pent-up forces, preventing the object to move, the object is said to have potential energy. There are various subsets or forms of both kinetic and potential energy. such as heat, electrical, chemical, and nuclear energy.

Questions you may have include:

• What is kinetic energy?
• What is potential energy?
• What are subsets of kinetic and potential energy?

This lesson will answer those questions. Useful tool: Units Conversion

## Kinetic energy

The standard textbook definition of energy is the "ability to do work." Unfortunately, this definition does not really give a good picture of what energy is all about. We normally think of an object having energy as one that is moving. The energy of a moving object is called kinetic energy and is abbreviated as KE.

The properties of kinetic energy are that the greater the mass of a moving object, the greater its energy will be. Also, the faster it goes, the greater its energy. That energy is proportional to the square of the velocity.

The formula for calculating the kinetic energy of an object is

KE = ½ mv²

where:

• m is the mass of the object
• v is its speed of velocity and is the velocity squared or v times v
• ½ mv² is one-half times m times

Note that the velocity of the object must be much less than the speed of light. When the speed of an object—such as an atomic particle—approaches the speed of light (c), its kinetic energy approaches E = mc², according to the Theory of Relativity.

## Potential Energy

There are situations when an object has the potential to start moving and gain kinetic energy. Often there are forces acting on the object, but the forces aren't yet sufficient to move the object.

### Potential due to gravity

If you hold an object a distance from the floor, it has the potential to start moving, once you let it go. The force of gravity is pulling on the object, giving it potential energy. The equation is

PE = mgh

where:

• PE is the potential energy
• m is its mass
• g is the acceleration of gravity (32 ft/s² or 9.8 m/s²)
• mg is the weight of the object (m times g)
• h is the height of the object from the floor or ground

### PE becomes KE

If you drop the object, its potential energy will become the kinetic energy of motion (PE = KE).

Since PE = mgh and KE = ½ mv², then:

mgh = ½ mv²

You can determine the speed it will be traveling after falling a height h by solving the equation for v:

v² = 2gh

Take the square root of both sides of the equation:

v = SQRT(2gh) or v = √(2gh)

Note that the mass m cancels out of the equation, meaning that all objects fall at the same rate.

Thus, if h = 1 ft, and since g = 32 ft/s², then v² = 2*32*1 = 64 and  v = √64 = 8 ft/s.

### Other types of PE

Other examples of potential energy that could cause motion include explosive chemical compounds and a coiled spring, ready to be released. A stretched rubber band, also has potential energy.

With chemical explosives, it is difficult to calculate the potential energy without experimenting to see how much kinetic energy is released in an explosion.

With a compressed spring, there are calculations that can determine its strength and potential energy.

## Other forms or subsets of energy

Often, you will hear about other forms of energy, such as heat and electrical energy. In reality, they are also forms of potential and kinetic energy.

### Heat energy

Heat is the movement of molecules. It is the sum of the kinetic energy of an object's molecules. In many physics textbooks, they look at heat as some sort of substance and heat energy as something independent of kinetic energy. In our lessons, it is just one subset of kinetic energy.

### Electrical energy

Electrical energy is the movement of electrons. That is kinetic energy. The voltage in an electrical circuit is the potential energy that can start electrons moving. Electrical forces cause the movement to occur.

### Chemical energy

Chemical energy is potential energy until the chemical reaction puts atoms and molecules in motion. Heat energy (KE) is often the result of a chemical reaction.

### Light energy

Light is the movement of waves and/or light particles (photons). It is usually formed when atoms gain so much kinetic energy from being heated that they give off radiation. This is often from electrons jumping orbits and emitting moving photons.

### Nuclear energy

Certain elements have potential nuclear energy, such that there are internal forces pent up on their nucleus. When that potential energy is released, the result is kinetic energy in the form of rapidly moving particles, heat and radiation.

## Summary

Energy is sometimes defined as the capacity to do work. An object has kinetic energy if it is moving. If there are some constrained or pent-up forces, preventing the object to move, the object is said to have potential energy. There are various subsets or forms of both kinetic and potential energy, such as heat, chemical, electrical, light and nuclear energy.

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