Mathematical Equations Related to the Work and Power of a Force

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:

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)

B)


by Mark Noah
Graduated in Mathematics
Brazil School Team

Equations - Math - Brazil School

Source: Brazil School - https://brasilescola.uol.com.br/matematica/equacoes-matematicas-relacionadas-ao-trabalho-potencia-.htm

Studies prove: caffeine helps in reducing body fat

According to research published in the journal BMJ Medicine, high levels of caffeine in the blood...

read more

Ways to behave in public and be confident

Having confidence in yourself is a big challenge for people who are always facing a large audienc...

read more
Woman adopts elderly cat to give 'peaceful death' to the animal, but is surprised

Woman adopts elderly cat to give 'peaceful death' to the animal, but is surprised

In 2016, a 27-year-old woman known only as Júlia reported on her forum account reddit that she we...

read more