     Next: Power Up: Work and Energy Previous: Work and Energy

# Work

Suppose a force acts on an object over a certain distance. The work done on that object is defined as follows: We assume in this and the following that the direction of the force and the direction of the motion are the same, and also that the force is constant; otherwise, a more complicated definition of work is used. This definition of work again agrees with our intuitive notion of work: one does more work on an object by pushing on it with a larger force and/or by moving it a larger distance. Note that forces without motion do no work. For example, if you push hard against a wall, you will eventually get very tired, but you will not do any work unless you actually move the wall in the direction you are pushing.

The units of work can be inferred from its definition; they are the units of force times the units of distance, or Newton-meters (N m). This combination of units is given the special name of Joules (J). For example, if you push on a box with a force of 4 N in order to slide it across a rough floor a distance of 3 meters, the total work that you do on the box is (3 x 4) = 12 Joules. Again this assumes that the force is always exactly in the same direction as the motion. In fact if a force is exerted in a direction perpendicular to the motion, no work at all is done. Suppose you carry a pail of water weighing 7 N over a distance of 10 m. In order to hold the pail up against gravity you must exert a vertical force of 7 N on the pail. The motion, however, is horizontal, and the force you are exerting does no work, even though you might get tired of holding the pail after a while. Work only involves the useful part of a force, namely the part that is effective in causing the motion. Thus, the vertical force which keeps the pail from falling does not contribute to the motion in the horizontal direction and therefore does no work.

Interestingly, it is possible to do negative work as well, and in most cases you would get just as tired as if you were doing positive work. This happens when the force is exerted in a direction that is directly opposite to the motion of the object being pushed. How can this happen? Suppose you are trying to stop a car that is rolling towards you by pushing against it. Clearly, if you push hard enough, you will succeed in slowing the car down, but in the process you will be moving backwards as the car continues to roll towards you. In this case the force you exert is in the opposite direction of the motion, and is considered to be negative. This is not as non-sensical as it may sound. By Newton's third law, the car is exerting an equal and opposite force on you, and is consequently doing positive work on you. So when you do negative work on an object, that object in reality is doing positive work on you.     Next: Power Up: Work and Energy Previous: Work and Energy
modtech@theory.uwinnipeg.ca
1999-09-29