Energy and Work
Energy and work are two very central, closely related concepts in the physics of motion. In fact, energy can itself be defined as the capacity to do work. Work, in turn, is defined as the force required to move an object some distance. Therefore, a transfer of energy occurs with work as one body moves another against an opposing force, such as gravity or friction.
There are many forms of energy. Heat energy, light energy, and potential energy are examples. With regard to work, however, kinetic energy is central. Kinetic energy is the energy of motion. Because all moving matter has mass and velocity, the kinetic energy of moving objects can be expressed in terms of these. Kinetic energy, then, is defined as one-half the product of the mass of an object and the square of its velocity. Therefore, the greater the mass of a moving object, the greater is its kinetic energy. Similarly, the greater the velocity or momentum of a moving object, the greater is its energy of motion. For instance, a car moving at 20 mph (32 kph) has far more (kinetic) energy than a bicycle moving at the same speed. Likewise, an object completely at rest has negligible kinetic energy.
The relationship between kinetic energy and work is important. The work that is performed on an object is equal to the change in its kinetic energy as the result of an applied force. The greater the change in kinetic energy, or movement, of an object, the greater is the amount of work done. If, for example, a car traveling at 60 mph (96 kph) is slowed to 40 mph (64 kph), the work done by the brakes over the distance that they were applied equals the change in kinetic energy of the moving vehicle as it is slowed. Similarly, the work done by your leg muscles as you accelerate from walking to running is equal to the change in kinetic energy of your body between walking and running. Interestingly, work is not done, by muscles as a textbook is held motionless outward at arms length because there is no movement of the book, and thus no change in kinetic energy of the text.
An important principle regarding energy and work is the concept of conservation of energy. A fundamental law of nature, conservation of energy states that in any closed system, the total amount of energy is constant. Energy is not gained or lost but merely changes form or location as it is transferred. For example, the total energy is not changed when electricity is used to create heat in an electric oven. The total energy that starts as electricity is equal to the heat energy liberated plus the (lessened) electricity leaving the heating elements to complete the circuit. Electric energy is not lost, but converted into heat energy such that the total energy remains constant. Considering work, then, if the change in kinetic energy is negative, the energy of motion is not actually lost, but converted into another form, such as heat. For instance, when a baseball strikes the catcher's glove and its movement is suddenly changed, the kinetic energy of the ball is converted into heat as it comes abruptly to a halt. Similarly, with positive work, where kinetic energy is increased, energy is converted from another form into motion within a closed system.
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