Work is one of the most difficult physical concepts to understand. Although we all have a good deal of first hand experience with work, that experience can be misleading. Consider, for example, the following tasks. Based on your intuition and experience, compare the amount of work required for each task.
Even though it seems "harder" to lift a thousand pound weight than a hundred pound weight, it takes exactly the same amount of work to lift a thousand pound weight 0.2 feet as a hundred pound weight two feet. In fact, all of the tasks listed above require exactly the same amount of work. One way to see, for example, that lifting a hundred pound weight two feet requires the same amount of work as lifting a fifty pound weight four feet is to imagine cutting the hundred pound weight into two equal pieces -- each weighing fifty pounds. Then lift each piece two feet. This requires exactly the same amount of work as lifting one fifty pound weight four feet and the net result is to lift the original hundred pound weight two feet.
The work done by a constant force F as an object moves a distance D is
Notice that work is measued in units of force times length. Since force is measured in units of mass times length per time2, work is measured in units of mass times length2 per time2
When gravity acts on an object whose mass is m kilograms, the force is
When this object falls a distance of h meters the work done is
Note that a joule is the amount of work done when a force of one newton acts on an object as it moves a distance of one meter.
Work and energy are two sides of the same coin. Energy is the capacity to do work. It is often useful to track the energy in a system. Consider, for example, what happens when an object falls from a height of h meters to the ground under the influence of gravity. When the object falls the work done by gravity is stored in the form of kinetic energy. The formula for the kinetic energy contained in an object of mass m whose speed is v is
Since speed is measured in units of length per time, kinetic energy is measured in units of mass times length2 per time2. As expected, these are the same units in which work is measured.
Heat is another form of energy. We usually measure heat energy using calories. One cal is equivalent to 4.186 Joules. This is roughly the amount of energy required to raise one gram of water one degree Celsius.
Copyright c 1995 by Frank Wattenberg Department of Mathematics, Montana State University, Bozeman, MT 59717.