Work and Potential Energy | Research & Encyclopedia Articles

Work and Potential Energy

Work is performed whenever a force moves an object. When a person lifts an object, he or she is performing work. More work is done if the object is heavier or if it is lifted higher. Work, then, depends on the force acting on the object as well as the distance it is moved. The amount of work done (W) can be calculated by multiplying the magnitude of the force acting on an object (F) by the distance the object moves (d), using the equation W = F. d. Force and distance are vector quantities, that is, they have both a magnitude and a direction. The direction of the force and distance are important in work calculations, as will be discussed below. Using the English system of measurement, the force is measured in pounds (lb) and the distance is measured in feet (ft). The product of the two, or the work done, is then measured as foot-pounds (ft-lb). With the metric, or SI, system, the unit of force is the Newton (N) and the unit of distance is the meter (m). The resulting unit for work is the Newton-meter (N-m), otherwise known as the joule (J), named after the English physicist James Prescott Joule. One joule is equal to 0.7376 ft-lb. The unit for work, the joule, is the same as the unit for energy. When work is performed, energy is transferred from one object to another through mechanical means.

It is important to understand that work is only performed when an object moves. For example, work is not performed when the velocity of an object is perpendicular to the direction of the force. An object in circular motion about another object can be said to be moved by the other object, and yet no work is being done. Also, if a person holds a 12-lb (53.5 N) box of books while standing still, he is not performing any work. However, if the person lifted the box off the ground, say a distance of 3 ft (1 m), he is performing work. The work performed by the person is the product of the force times the distance, or 12 times 3, or 36 ft-lb (or 53.5 N-m, or 53.5 J). Work is also only done if the force is exerted in the same direction as the movement. If a person holds the 12-lb box of books, he is exerting a force in the upward direction on the box (against the force of gravity). If this person is holding the 12-lb box of books while traveling in a car, even though the box is moving, the person does no work on the box because the force he is exerting is not in the same direction as the motion of the box.

A common demonstration of this phenomenon in a physics class is to ask a student to come to the front of the class. The student is instructed to hold a heavy book at arm's length. As the student sweats and strains, the instructor explains that no work is being done. Why then does the student feel as though an effort is being made? The student is experiencing the force of gravity on the book, that is, gravitational potential energy (discussed below). Even though no work is being done (no displacement occurs), a force is very much present.

Sometimes a force is exerted on an object at an angle, causing the object to move. An example of this would be a person pushing a stroller. In order to find the work done by the person, you first must know the amount of force exerted on the stroller handle (F) as well as the angle the stroller handle makes with the direction of motion (t). To calculate the work done in this example, you could draw the force and displacement as vector quantities and determine the resultant vector using vector addition, or you could use a different equation for work: W = Fdcos(t). For example, if a mother pushes a stroller with a force of 5.6 lb (25 N) from her car to the entrance of a grocery store a distance of 60 feet (20 m), and the handle of the stroller makes an angle of 75° with the ground, how much work has she done? Using the equation W = Fdcos(t) and the metric units; 25 N x 20 m x cos(75) = 129 J.

The effect of doing work is the transfer of energy to an object. This energy can take the form of heat, as explained in the first law of thermodynamics. This law states that the increase of thermal energy of a system is the sum of the heat added to it and the work done on it. The energy can take other forms. For example, if the person in the above example lifted the 12-lb box of books 3 feet, placing it on a shelf, the person transferred energy to the box. The box, sitting on the shelf, has the potential to fall, crushing anything sitting on the floor beneath. The box would then do work on the surface of the object it crushes as the surface moves closer to the ground. Energy is the ability to do work, so the box sitting on the shelf has energy.

Energy can take many forms. An object in motion, such as a falling box of books, can do work on another object when a collision occurs, by exerting a force on the object, moving it through a distance. Because an object in motion has the ability to do work, it has energy. This energy of motion, the ability to do work upon collision, is called kinetic energy. A box of books on a shelf, even though it is not moving, also has energy. The box has the potential to fall due to the force of gravity. The box, therefore, has what is called gravitational potential energy. The box-Earth system has stored the energy in their combined gravitational field. Potential energy is stored energy, giving an object the potential to do work. When the object performs the work, the potential energy is changed into kinetic energy.

Gravitational potential energy (PE) depends on the mass of the object (m) as well as its height (h). The height of an object is its distance above a defined zero level, known as the reference level. The reference level is usually the floor of a room or Earth's surface, but it could be the lowest shelf on a bookcase, the top of a table, or the third rung of a ladder. The reference level is arbitrary, but it must be defined. The potential energy of an object is then calculated using its height with respect to this reference level. The amount of potential energy in an object can be calculated using the equation PE = mgh, where g is equal to the acceleration due to gravity, 9.8 m/s2. The weight of an object is its mass multiplied by the acceleration due to gravity, or mg. Weight is a force. The potential energy equation can then be rewritten as PE = Fh. This is strikingly similar to the equation for work! Using English units, the force, or weight, would be measured in pounds and the height in feet, so the units for potential energy would be foot-pounds. Using the SI system, the unit for force would be kg-m/s2 (equivalent to Newtons) and the unit for height would be meters, so the units for potential energy would be Newton-meters, or joules. The units for energy are the same as the units for work.

In the example of the 12-lb box of books on a shelf, the gravitational potential energy of the box is 12 lb times 3 feet, or 36 ft-lb (53.5 J). Notice that the amount of work done by placing the box on the shelf is the same as the potential energy gained by the box. This example demonstrates that work is simply a method of transferring energy to an object. The amount of work done on the object is equal to the potential energy, or energy of position, gained by the object. This relationship illustrates the law of conservation of energy, that the energy in a system is never lost even though it may change forms. Other forms of potential energy include electromagnetic potential energy (for example, the potential energy generated by water turning turbines in a hydroelectric power plant), and nuclear potential energy (the potential energy of atoms in nuclear reactions, where mass can be converted into energy).