### Definition of work done and its essential condition

Work: When a force is applied on a body and a body is displaced along the line of action of force then this is called the work done by force. Work is a scalar quantity.

Unit: $Joule$, $N-m$

Dimension: $[ML^{2}T^{-2}]$

Example: When a boy kicks a football to move it, the boy is said to have done some work.

Let us consider, A body that has mass $m$. If a force $F$ applied on a body at an angle $\theta$ and body is displaced from position $A$ to position $B$ with distance $d$ then work done by force:
$W= horizontal \: component \: of \: the \: force \times displacement$

$W=F\:cos\theta \times d$

$W=F d\:cos\theta \qquad(1)$

$W=\overrightarrow{F}. \overrightarrow{d}$

So, we can conclude from the above equation that "The work done by the force is the scalar product of the force and displacement ".

Note: When the force is applied at an angle $\theta$ then the vertical component of the force is balanced by weight $mg$ and the horizontal component of the force is responsible for the motion of the body.

Essential Condition for work to be done:

For work to be done, the following two conditions should be satisfied

• A force should act on the body.

• The body should move in the direction of the force, or opposite to it, i.e the point of application of the force should move in the direction of the force or opposite to it. In other words, the body must be displaced

• Types of Work done by force:

• Positive Work done
• Zero Work done
• Negative Work done

• Positive Work done: When a force is applied on a body and the body is displaced along in direction of the force then this is called the positive work done by force.

If $\theta=0 ^{\circ}$, then $cos0 ^{\circ} =1$

the from equation $(1)$

So Work done by force

$W=Fd$

Zero Work done: When a force is applied on a body and the body is not displaced from its position then this is called the zero work done by force.

If $\theta=90 ^{\circ}$, then $cos90 ^{\circ} =0$

then from equation $(1)$

So Work done by force

$W=0$

Negative Work done: When a force is applied on the body and a body is displaced along in the opposite direction of the force then this is called the negative work done by force.

If $\theta=180^{\circ}$, then $cos 0^{\circ} =-1$

then from equation $(1)$

So Work done by force

$W=-Fd$

** 1 Joule Work done: When $1 \: Newton$ of force is applied on a body and a body is displaced by $1\: m$ along the line of action of force then this is called the $1 \: Joule$ work done by force.**