__WORK DONE BY A CONSTANT FORCE__

The work done by a constant force acting on an object is equal to the product of the magnitudes of the displacement and the component of the force parallel to that displacement.

W= Fd

In **condition a**, there is a force but no displacement, no work is done.

In **condition b**, the force is parallel to the displacement.

In **condition c**, the force is at angle to the displacement.

** Note**: If the force is at an angle to the displacement, as in the condition c, this form of the work should be used:

W= F_{‖}D = (F cos θ) d

** Unit of work**: Newton ▪ meter (N▪m)

1 N▪m is called 1 joule

** Note**:

- If the force (or a component) is in the direction of motion, the work done is positive.
- If the force (or a component) is opposite to the direction of motion, the work done is negative.

__WORK DONE BY A VARIABLE FORCE__

The force exerted by a spring varies linearly with the displacement:

F_{s} = -kx

A plot of force versus displacement allows us to calculate the work done as:

__THE WORK-ENERGY THEOREM: KINETIC ENERGY__

The net force acting on an object causes the object to accelerate, changing its velocity:

a = (V^{2} – V_{0}^{2 }) / 2x

We can use this relation to calculate the work done:

W = F*x = m (V ^{2} – V_{0}^{2 }) / 2x . x*

= 1/2mv^{2} – 1/2mv_{0}^{2}

Kinetic energy is therefore defined:

*K= 1/2mv ^{2}*

*(kinetic energy)*

**SI unit of energy**= Joule (J)

The net work on an object changes its kinetic energy.

Q.1. A force of 10N causes a displacement of 2m in a body in its own direction. Calculate the work done by force.

- 30 J
- 40 J
- 20 J
- 10 J

Ans. c

Q.2. How much force is applied on a body when 150 joule of work is done in displacing a body through a distance of 10m in the direction of force?

- 15 N
- 20 N
- 33 N
- 25 N

Ans a

Q.3. An engine does 54000 J by exerting a force of 6000 N on it. What is the displacement of force?

- 9 m
- 11 m
- 13 m
- 9.5 m

Ans. a

Q.4. A force of 10 N on a body at an angle of 60 degree with the horizontal direction displaces the body through a distance of 2 m along the surface of a floor. Calculate the work done. (cos 60=1/2)

- 10 J
- 11 J
- 10.5 J
- 11.2 J

Ans. a

Q.5. A body of mass 2 kg is moving with a speed of 20 m/s. Find the kinetic energy.

- 400 J
- 100 J
- 50 J
- 200 J

Ans. a