Class 9 > Unit # 08:Energy Sources & Transfer of Energy > Work

Talha's Physics Academy

Work: Definition, Formula, and Units

Q.1 Define Work, its formula and unit.

Work

"The amount of work is the product of force and the distance moved in the direction of force."

Formula

Case 1: Force acting at an angle $\theta$

Suppose a constant force $F$ acts on a body at an angle $\theta$ with distance $d$. The work done is equal to the product of the component of the force along the line of motion ($F \cos\theta$) and the distance $d$ through which the body moves along that line:

$\text{Work} = (\text{component of force}) \times (\text{distance})$
$W = (F \cos\theta)(d) = Fd \cos\theta$

Fig: Constant force $F$ acting at an angle $\theta$ to the displacement vector $d$.

Case 2: Force acting in the direction of motion ($\theta = 0^\circ$)

Suppose a constant force $F$ acts on a body and motion takes place in a straight line in the direction of force. Then work done is equal to the product of magnitude of force $F$ and the distance $d$ through which the body moves.

In this case, $\theta = 0^\circ$ and $\cos(0^\circ) = 1$:

$W = F \cdot d \cdot (1) \quad \Rightarrow \quad W = Fd$

Fig: Force acting parallel to the direction of motion ($\theta = 0^\circ$).

Units of Work

The S.I. unit of work is the Joule (J). Other units of work include Foot-Pound and Erg.

$1 \text{ Joule} = 1\text{ N}\cdot\text{m}$

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