# Work

##     A Couple of Shockers:

Undoubtedly, you have been taught that "Work equals force times distance." Brace yourself. Work is sometimes force times distance, but not always. Work is more subtle than that, and in order to understand energy, you have to understand work to a greater depth.

If you think that "work equals force times distance," then you probably think that you automatically do work every time you exert a force. That's not true, either!

Why? Well, the work/energy equation says that work done (by the net force on an object) equals the object's change in kinetic energy. More simply:

Work = Change in Kinetic Energy

This means that if an object's kinetic energy doesn't change, then no work has been done on the object - whether or not a force has been exerted. In the diagram above, the green block is moving to the right. The red force F1 does work on the block because it has a component in the direction of motion. The blue force F2 does NOT do work on the block, because it does not have a component in the direction of motion.
Now, remember that forces cause accelerations (Newton's Second Law), but an object can accelerate by

1. speeding up, in which case the object's kinetic energy increases,
2. slowing down, in which case the object's kinetic energy decreases,
3. or changing direction, in which case the object's kinetic energy does not change.

So, an object's kinetic energy will only change if the force acting on the object changes the object's speed. This will only happen if there is a component of the force in the direction that the object moves.

Therefore, a force will do work only if the force has a component in the direction that the object moves.

Calculating work can get, well, interesting. Fortunately for the Physics 1 student, you only need to be able to calculate work done by a force in the four simple cases shown below. For the more mathematically mature, there is a formula that you can use to calculate the work done by a constant force. Some of the following pages discuss calculating work done by a variable force, but that is for AP Physics students.

## Calculating the Work Done by a Constant Force:

In Physics 1, you need to be able to calculate the work done by a force in four situations:

 Situation: Example: Work done by the force F is: The direction of the force is in the same direction the object moves. The force pushing a car along a road Force x distance The direction of the force is in the direction opposite the object's direction of motion. The force the brakes exert to stop a car -Force x distance (*See note) The direction of the force is perpendicular to the direction the object moves. The gravitational force the Earth exerts on the Moon 0 The object doesn't move. The force you exert when pushing on a wall 0

## Why?

### The Key to Understanding:

The Work/Energy Equation says that the work done on an object (by the net force on it) equals its change in kinetic energy. So, to figure out how much work is done on an object, just calculate the change in its kinetic energy...

### If the Force Acts in the Direction That the Object Moves:

This force will tend to increase the object's speed. If the object's speed increases, then its kinetic energy will increase. If the kinetic energy increases, the change in kinetic energy will be positive. Since the Work/Energy Equation guarantees that the work done equals the change in kinetic energy, the work done must be positive. A numerical example is available.

### If the Force Acts in the Direction Opposite to the Direction the Object Moves:

In this situation, the force tends to slow the object down, thereby decreasing its kinetic energy. If the kinetic energy decreases, then the change in kinetic energy is negative. Since the work done equals the change in kinetic energy, the work done by this force must be negative.

There are a couple of ways to handle this:

1. Remember that work = - force x distance in this case. So if a force of 5 Newtons acts on an object for a distance of 5 meters, and the direction of the 5 Newton force is opposite to the direction the object moves, then work done = - force x distance = -(5 Newtons)(2 meters) = -10 Joules.
2. Keep in mind that direction matters with force and distance. If the direction of the force is opposite to the direction that the object moves, one or the other of them is acting in the negative direction. If you do this, then work = force x distance in this case also. In the previous example, you would say work done = force x distance = (- 5 Newtons)(2 meters) = -10 Joules.

It really doesn't matter which method you use - just be consistent, and remember that if the direction of the force is opposite to the direction the object moves, the work done by the force is negative. A numerical example is available.

### If the Force is Perpendicular to the Direction That the Object Moves

In this case, the force does not change the speed of the object - just its direction. Since the object's speed doesn't change, its kinetic energy doesn't change. If the change in kinetic energy is 0, the work done on the object is 0, too.

### If the Object Doesn't Move

Work is not always force x distance, but work always involves motion of some sort. No distance - no work.

## Work is NOT Force!

Many beginning physicists confuse "exerting a force" with "doing work." As seen above, you have to change the kinetic energy of an object in order to do work on it - just pushing on it isn't enough. Even the fact that you may get tired - even exhausted - holding a heavy box or pushing on a wall, if the kinetic energy of the box or the wall doesn't change, you didn't do work. "Exerting a force" is NOT the same as "doing work!"     Last update November 23, 2007 by JL Stanbrough