E1.5 Work, Energy and Power (Work):

In general, the work done by a force is equal to the product of the force and the displacement of its point of application in the direction of the force. 

Work (symbol: W): is defined as transfer of energy by force from one object to another object. If one object transfers energy to a another object , then said that the first object does work on the second object.

Suppose, a force is applied on an object and object is displaced from its position due to the application of the force. It is said to be work done by the force. There are three major component to work: 'Force, Displacement and Cause'. In order to force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement (the physics classroom).

Mathematically,

Work is defined as the product of force and displacement of an object in the direction of force.

i.e. $W = \vec{F}.\vec{d}$ .......... (i)

Where; W  =  Work done; 

              F  =  Force; 

              d  =  Displacement.

If $\theta$ is the angle between $\vec{F}$ and $\vec{d}$ then, 

Work done by the force (W) = Force * distance moved in direction of force.

$W = F . d\; Cos \theta$ .......... (ii)

If the force and and displacement are in the same direction, then $\theta = 0^{0} \;\;(i.e.\;\; Cos0^{0} = 1)$ From the equation (ii), we have

∴ $W = Fd$ .......... (iii)

Note: Here, no work is done by $F\;Sin\theta$ component because displacement in the direction of this component is zero.

---

» Unit of work is joule ($J$), in SI system. It's dimensional is [$M\;L^2\; T^{-2}$].

Relation between Joule and erg is,

$1\;J = 1\;N * 1\;m = 10^5\; dyne * 100\;cm = 10^7\;erg $

Work is a scalar quantity, it has no property of direction but only magnitude. When the force is one Newton and the distance moved is one meter, then the work done is one Joule.

Another Example: A force of 50 N moving through a distance of 10 m does 50 * 10 = 500 Joule of work. (This is also a measure of the energy transferred to the object).

---

» The angle measure is defined as the angle between the force and the displacement.

Case (i): The force vector and the displacement vector are in the same direction. That is, the angle between $F$ and $d$ is $0$ degrees. A force acts rightward upon an object as it is displaced rightward.

Case (ii): The force vector and the displacement vector are in opposite direction. That is, the angle between $F$ and $d$ is $180$ degrees. A force acts leftward upon an object that is displaced rightward.

Case (iii): The force vector and the displacement vector are at right angles to each other i.e. angle between $F$ and $d$ is $90$ degrees. If the force is perpendicular to the direction of displacement , work done is zero. 

Example: A waiter who carried a tray full of meals above his hand. The force supplied by the waiter on the tray is an upward and the displacement of the tray is a horizontal with a waiter speed. In this case, the angle between the force and displacement is $90$ degrees. If we calculated the work done by waiter on the tray, the result would be zero.

Return to Main Menu