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Home Minds On Work and Energy Mission WE1 Work Help Help 4

Mission WE1 Work

The Question

Which of the following are examples of work being done (either positive or negative) upon an object?

Define Help

Definition of Work:
When a force acts upon an object to cause (or to hinder) a displacement, work is done upon the object. Mathematically, work is the dot product of the force and displacement for such a situation.

Think About It

As the definition of work implies, there are three ingredients of work: force, displacement, and cause. There must obviously be a force acting upon an object; the object must be displaced or moved from its position. And there must be a cause-effect relationship between the force and the motion. So in analyzing each scenario, ask "Is there a force that is acting upon an object to cause that object to be displaced or moved from its position?"

Don't be Fooled

There are two sources of confusion with regard to work. First, many students simply regard a situation of a force acting upon an object as being a sufficient signal that work is being done. But don't be fooled! The force must do more than act upon the object; it must cause the object to move. If an object doesn't move, then one can be certain that no work is done upon it.

The second source of confusion has to do with the cause-effect relationship between F and d. The force must cause the displacement that is observed. If the force acts at right angles to the direction of movement, then the force is NOT doing work upon the object. Mathematically, this would be the situation in which the angle Θ is 90 degrees and the cosine (Θ) is 0. See Formula Frenzy section.

Formula Fix

Mathematically, work (W) is calculated from knowledge of the force (F) that acts upon an object, the displacement (d) that the force causes, and the angle (Θ) between the force and displacement vectors. The formula is

W = F • d • cosine(Θ)

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