A More Mathematical

Look at Work

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Work For the Trigonometrically Inclined:

In the four special cases we have investigated so far:

• force in the direction of the motion
• force in the opposite direction of the motion
• force perpendicular to the direction of the motion
• no motion

work appears to behave differently in each one. Actually, of course, this is not the case. All four cases (and much more) can be calculated from a single equation (as long as the force is constant), which is:

Where:

• F = the magnitude of the force
• = the magnitude of the displacement
• q = the angle between the force on the object and the object's displacement

(Why?) This equation fits the four special cases of motion as follows:

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If the Force is in the Direction of Motion:

In this case, q = 0^o, so:

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If the Force is in the Opposite Direction of Motion:

In this case, q = 180^o, so:

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If the Force is Perpendicular to the Direction of Motion:

In this case, q = 90^o, so:

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If the Object Being Pushed Doesn't Move:

In this case, Dx = 0, so:

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last update December 13, 2003 by JL Stanbrough