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Home Page of Peggy E. Schweiger

Work

Work
work is done in physics when a force is applied on an object and there is a displacement parallel to the direction of the force. No work is done unless there is a displacement parallel to the direction of the force. The force doing the work could be a component of the applied force. It would be the component parallel to the displacement.

The general form of the work equation is:

W = F d
where W is the work, F is the force acting in the direction of the displacement, d

Here is an example of a situation where a force is applied and no work is done: A man holds a 50 N weight. No work is done (even though he must exert a force to hold the weight) because there is no displacement parallel to the direction of the weight.

Here is an example of a situation where there is a force applied and there is displacement and no work is done against the object's weight: A man walks around the room holding a 50 N weight. The object's weight acts down. For work to be done against the weight there has to be displacement in the direction of the weight (either up or down). There is none so no work is done against the weight. There is work done against friction as the man walks around the room.

Positive work   -the displacement and the force are in the same direction.

Negative work   - displacement and the force are in opposite directions.

picture of force applied at an angle

In the drawing, F is applied at angle q to the horizontal. The force doing the work is the horizontal component of the force since it is the component that is parallel to the horizontal displacement. In this type of situation, the form of the work equation would be

W = F cos q d

Joule
the SI unit of work.
1 J = 1 N m, or one Joule equals one Newton meter

Work can be represented graphically. If you plot force vs displacement, the area under the curve represents the work done.

graphical representation of work

Calculus application: Integration is used to find the area under a curve. If you integrate this curve, you have found the work done.

Power
rate of doing work.
P = W / t
where P is the power dissipated, W is the work done, and t is time in seconds

Watts
the SI unit of power
1 W = 1 J/ 1 sec, or one watt equals one joule per second

Machine
A device that changes the force doing the work. A machine multiplies your force, not work. A machine allows you to apply less force, but you apply it over a greater distance. No machine is 100% efficient; there is always work done against friction.

Simple machine
There are six types of simple machines. A compound machine is simply a combination of one or more simple machines.

Types of simple machines:

Work input
the work you do with the machine.
Wi = (force that you apply)(distance you apply it over)

Work output
the work the machine does for you
Wo = (weight of the object)(height object is raised)

Efficiency
the ratio of work output to work input. Efficiency gives you an idea of how much work is being lost in overcoming friction. In an ideal machine with no friction, the efficiency would be 100%. (I abbreviate efficiency as "eff") In our world containing friction, work output always is less than work input.
eff = Wo / Wi

Ideal mechanical advantage
tells you how much the machine would multiply your effort force (the force that you apply) by if there were no friction; abbreviated IMA
IMA = d / h
where d is the distance that you apply your force over and h is the height the object is raised

Mechanical advantage
tells you how much the machine multiplies your effort force by with friction; abbreviated MA
MA = W / F
where W is the weight of the object and F is the force that you apply

Efficiency can also be expressed in terms of advantage:

eff = MA / IMA

Energy Notes

Work Sample Problems

Energy Sample Problems

Work Homework

Energy Homework