Work, Energy and Power Concept Page - 1

Definition

Work

Work is defined as the force  in the direction of displacement times displacement. It is a scalar quantity having S.I unit Joule.
W=Fs$W=Fs$
where F$F$ is the component of force in the direction of displacement.

Definition

No work done inspite of working hard

No work is done inspite of working hard when:

1. There is no displacement of object. Example: A boy pushing a wall.
2. Displacement is perpendicular to the object. Example: Uniform circular motion.

Example

Work Done

Example: A force F⃗ =6i^−8j^N$\overrightarrow{F}=6\hat{i}-8\hat{j}N$, acts on a particle and
displaces it over 4$4$ m along the positive X-axis and then displaces it over 6$6$ m along the positive Y-axis. What is the total work done over the two displacements?

Solution: W.D=∫F⃗ .ds→$W.D=\int \overrightarrow{F}.\overrightarrow{ds}$
=(6i^−8j^).(4i^)+(6i^−8j^).(6j^)$=(6\hat{i}-8\hat{j}).(4\hat{i})+(6\hat{i}-8\hat{j}).(6\hat{j})$
(6×4)+(−8×6)=24−48=−24J$(6\times 4)+(-8\times 6)=24-48=-24J$

Definition

Work done as dot product of force and displacement

Work is force applied over distance. For e.g., lifting an object against the Earth's gravitation, driving a car up a hill etc.
W=Fd$W=Fd$
The standard unit of work is the joule (J), which is equal to newton - meter (N m).
If force is not applied in the same direction as the displacement, then also it results in work (for example, a car ascending a hill).
In this case, we will have to use the vector form of the above formula.
For a given force vector F (in newtons, in a given direction) applied to an object that undergoes displacement d (in meters), the work w (in joules) is given by the dot product of the force vector and the displacement vector as :
W=F⃗ .d⃗ $W=\overrightarrow{F}.\overrightarrow{d}$
W=Fdcosθ$W=Fdcos\theta$

Definition

Work done by a constant force

When the force is constant, the work done is defined as the product of the force and distance moved in the direction of force.
Example: Suppose a body is kept on the frictionless surface and a force of constant magnitude of 10 N$10N$ is acting on it, due to the action of forces the body will completed a distance of 5$5$ meter, then the work done will be given as
W=Fs=10×5=50 Joule$W=Fs=10\times 5=50Joule$

Definition

Relationship between units of work

Some units of work are:

1. SI unit: 1 J=1 Nm$1J=1Nm$
2. CGS unit: 1 erg=10−7 J$1erg={10}^{-7}J$
3. Litre atmosphere

Definition

Work done scientifically

Following are the places where work is done scientifically:

1. Launching a rocket. 
2. Internal combustion engine in a vehicle.
3. Drawing water by a pump.
4. Work output from the turbine.

Definition

Condition for Positive, Negative & Zero work done by a force

We know that:
W=F⃗ .d⃗ =Fdcosθ$W=\overrightarrow{F}.\overrightarrow{d}=Fdcos\theta$
Sign of work done depends on the angle between force and displacement vector.
If θ=00$\theta =0^0$ - Work done is positive.
If θ=900$\theta ={90}^0$ - Work done is zero.
If θ=1800$\theta ={180}^0$ - Work done is negative.

Definition

Sign convention

Work done by the system i.e. work done by the gas is positive. Example: expansion of gas on heating. Work done on the system is negative. Example: A constant force being applied on the piston of a cylinder.

Definition

Positive and negative work

For a cyclic process, PV graph is a closed curve and the area enclosed by the curve is the work done. If the cycle is clockwise work done is positive, and if the cycle is anticlockwise work done is negative. 

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