# Work

Math Analysis - Vectors - Application of Work

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1 of 2 videos by AJ Speller

## Key Questions

color(green)(W = F cos theta * d, Newton meter

#### Explanation:

F = Force, d = displacement

Work done = Force * Displacement

$W = \vec{F} \cdot \vec{d}$

Force and displacement are vector quantities

If both F and d are in the same direction, $W = F \cdot d$

If force is exerted at an angle of $\theta$ to the direction of motion, then work done

color(green)(W = F cos theta * d

Unit of work is Joule

1 Joule = 1 Newton meter = 1 N m

Through an equation.

#### Explanation:

Work is represented by the equation,

$W = F \cdot d$

• $F$ is the force in newtons

• $d$ is the distance moved in meters

Now, the distance moved is also the displacement of the object. If the object doesn't move, even if $10$ millions newtons of force was applied, there'll still be no work done.

But, if an object moves, then work is done.

Work done defined as the scalar product of the two vectors force and displacement.

#### Explanation:

If a force $\vec{F}$ acts on a body and displaces it through $\vec{r}$ and the angle between the two vectors be $\theta$. The work done by the force is given as,

$W = \vec{F} \cdot \vec{r}$
$\implies W = F r C o s \theta$, where $F$ and $r$ are the magnitudes of $\vec{F}$ and $\vec{r}$ respectively.

## Questions

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