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Kinetic Energy Concerns Movement of Matter

by Ron Kurtus (10 October 2007)

Kinetic energy is the energy of a moving object according to the equation KE = ½ mv². This equation is valid provided that the speed of the object does not approach the speed of light. Motion and kinetic energy can be a direct result of a force can be applied to a object. Also, releasing potential energy can create kinetic energy, such as with springs and chemical reactions. Most forms of energy where material is moving are kinetic energy.

Questions you may have include:

• What does the equation KE = ½ mv² mean?
• How can a force create kinetic energy?
• What are other forms of energy?

This lesson will answer those questions. There is a mini-quiz near the end of the lesson.

Useful tools: Metric-English Conversion | Scientific Calculator.

Kinetic energy equation

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 equation for calculating the kinetic energy of an object is

KE = ½ mv²

where:

• KE is the kinetic energy, usually measured in joules
• m is the mass of the object, usually measured in kilograms
• v is its speed or velocity of the object, measured in meters per second
• v² is the velocity squared or v times v
• ½ mv² is one-half times m times v²

A joule equals a newton-meter. Since a newton equals a kilogram-meter per second squared (kg-m/s²), you can see that a joule equals kg-m²/s². It is not usually designated that way, but you can see it holds by multiplying the units.

Example with different masses

If two objects were going at the same velocity, but one object had twice the mass of the other, then the energy of the heavier object would be 2 times the energy of the lighter object.

If M = 16 and m = 8

then KE_M = ½*16*v² = 8v²

and KE_m = ½*8*v² = 4v²

thus KE_M = 2KE_m

Example with different velocities

Now suppose the lighter object in the example above was going twice as fast as the heavier object. Say the object with m = 8 was going at v = 4 m/s and the object with M = 16 was going at V = 2 m/s. Then the energies would be:

KE_mv = ½ mv² = ½ * 8 * 4 * 4 = 128

KE_MV = ½ MV² = ½ * 16 * 2 * 2 = 64

Thus, the effect of higher velocity is greater than that of a greater mass.

Force results in kinetic energy

When a force is applied to an object, it accelerates the object according to the equation

F = ma

where:

• F is the force, measured in newtons
• m is the mass, usually measured in kilograms
• a is the acceleration, usually measured in meters/second/second or m/s²
• ma is m times a

Acceleration is defined as the change in velocity over a period of time. Thus, if the force is applied to an object for a certain amount of time, it will reach the velocity v and have a kinetic energy of KE = ½ mv².

Work

Work is defined as the result of a force applied over a distance, W = Fd. Since force is in newtons and distance is in meters, work is in newton-meters, which equals the units of energy, joules.

Other forms are also kinetic energy

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

Heat energy

Heat is the movement of molecules. It is the sum of their kinetic energy. 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 another form 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

A chemical reaction puts atoms and molecules in motion. Heat and radiation energy are often the result of a chemical reaction, which releases chemical potential energy.

Light energy

Light consists of 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.

Summary

Kinetic energy is the energy of a moving object according to the equation KE = ½ mv². Motion and kinetic energy can be a direct result of a force can be applied to a object. Releasing potential energy can create kinetic energy, such as with springs and chemical reactions. Heat, electrical energy and light are forms of kinetic energy.

Answers to Readers' Questions

Move with kinetic energy

Resources

The following resources provide information on this subject:

Websites

Physical Science Resources

Books

Top-rated books on Energy

Miscellaneous

Mini-quiz to check your understanding

1. What happens when you triple the velocity of a moving object?

2. How does applying a force on an object result in kinetic energy?

3. What really is heat energy?

If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.

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