Mathematical Equations Related to the Work and Power of a Force

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A force only performs Work if there is displacement of the body on which it acts. That way, if a person at rest holds an object, he is not doing Work. Analyzing this way, we can relate these events to the following mathematical equation for the Work performed by a force: , where τ (Greek letter tau) = work, F = force and d = displacement.

In some situations the work is done more quickly. For example, a marathon course was taken by two people at different times. In this case, we say that the person who completed the route in less time developed a higher average power in relation to another person. Based on this definition, the mathematical equation responsible for calculating the power of a body is given by the expression: , where ∆t: time variation.

Example 1

Determine the work done by a force of intensity 250 N (Newton) applied to a body, which moves for 20 meters in the same direction as the force.

τ = F * d
τ = 250 * 20
τ = 5000 N/m
τ = 5000 J (joule)

Example 2

A force of 40 N intensity is applied to a body, displacing it for 5 meters in the direction and direction of the force, for 10 seconds. Based on this information calculate:

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a) the work performed by force.
b) the average power of this force.

a) τ = F * d
τ = 40 * 5
τ = 200 N/m
τ = 200 J (joule)


by Mark Noah
Graduated in Mathematics
Brazil School Team

Equations - Math - Brazil School

Source: Brazil School -
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