The general form of the work equation is:

The image below shows a box being pulled by a constant force along a horizontal surface and moved a displacment d. The force is applied parallel to the surface. The amount of word done is given by

The image below shows a box being pulled by a constant force along a horizontal surface and moved a displacment d. The force is applied at an angle q to the surface. Only the component of the force (F cos q) parallel to the displacement does work in the direction of the displacemnt. The amount of work done is given by

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.

It is important to specify whether you are talking about work done by an object or work done on an object. For example, work done by gravity depends upon the vertical height. You can push an object up an incline and the amount of work done by gravity is the same for all angles of the incline.

Conservative forces Forces such as gravity, for which the work done does not depend upon the path taken are called conservative forces.

Nonconservative forces Forces such as friction, for which the work done does depend upon the path taken are called nonconservative forces.

Since work is scalar, a sign convention must be established for work.

1. Positive work   -the displacement and the force are in the same direction.
2. Positive work  the work done by a system is positive.
3. Negative work   - displacement and the force are in opposite directions. Friction does negative work (the frictional force acts in the direction opposite the motion).
4. Negative work  the work done on a system is negative

Net work The net work done on an object determines its motion. If the net work is zero, the object moves at constant speed or is at rest. The object accelerates if the net work has a value other than zero.

The moon orbiting the earth is an example of when a force is applied and there is no work done. In the figure below, the gravitational force acts inward (it is the source of the centripetal force) and the velocity of the moon is perpendicular to the gravitational force (or in a direction tangent to the circle or orbit). The moon's displacement is in the direction of the velocity vector, perpendicular to the gravitational force. Thus, there is no component of the gravitational force parallel to the displacement and the work done by the gravitational force is zero. Since the net work done by gravity is zero, the moon moves at constant speed.

In the drawing below, 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

Joule

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

Work Done by a Varying Force:

Calculus application:  Integration is used to find the area under a curve. If you integrate this curve, you have found the work done. This is useful when work is done by a varying force. The work done by a varying force in moving an object between two points is equal to the area under the curve between these two points.

In the graph below, the force is changing. The graph shows how the force varies with displacment. If one wanted to know the work done beteen two points (the shaded area of the graph), one would simply find the area under the curve (or the area of the shaded area).

Power rate of doing work.

Since is the product of force times displacement, power can also be expressed in terms of velocity (which is displacement divided by time).

Watts the SI unit of power

Another unit of power is the horsepower. 1 hp = 746 W

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.

Efficiency can also be expressed in terms of advantage:

Work-Energy Priciple  If net work is done on a particle, its speed is changed. The motion of a particle can be related to the net work done using a property called kinetic energy. If you want to change the kinetic energy of a particle, you must do net work on it.

If positive net work is done on an object, its speed (kinetic energy) increases. If negative net work is done on an object, its speed (kinetic energy) decreases. If the net work done on an object is zero, its speed (kinetic energy) remains constant.

Advanced look at the Work/Energy Theorem If the net work done is positive, the kinetic energy of the object increases by this amount of work. If the net work done is negative, the kinetic energy of the object decreases by this amount of work. The work/energy theorem is a useful tool to predict the final speed of an object. Remember, the net force causes an acceleration and the net work is the product of the net force and the displacement.

AP Multiple Choice Questions on Work

1. Be able to recognize situations when work is not done. For example, an object in circular motion does no work in one revolution (the displacement is zero!).
2. Know your that power is the rate of doing work!
3. Important: Power = Force * speed (P=Fv).
4. Be able to perform simple work and power calculations.
5. Know that the work done by the gravitational force corresponds to the change in gravitational potential energy.

AP Free Response Questions on Work

1. Very important - Know the work/energy theorem! The work done is equal to the change in kinetic energy.
2. Remember to find the component doing the work - the one parallel to the displacement.
3. Be able to calculate the work done by different forces. For example, when a box is pushed across the floor. You can calculate the work done by the applied force, the work done by the frictional force, and the net work done.
4. Be able to graphically determine work. You may be given data that involves how force varies with displacement. Work is the area under the curve (W=Fd).

Energy Notes

AP Objectives-Work

Work Sample Problems

Energy Sample Problems

Work Homework

Energy Homework

AP Work & Energy Class Problems