Work and Kinetic Energy

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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 = (V² –  V₀² ) / 2x

We can use this relation to calculate the work done:

 

W = Fx = m (V² –  V₀² ) / 2x . x

= 1/2mv² – 1/2mv₀²

Kinetic energy is therefore defined:

K= 1/2mv² (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.

1. 30 J
2. 40 J
3. 20 J
4. 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?

1. 15 N
2. 20 N
3. 33 N
4. 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?

1. 9 m
2. 11 m
3. 13 m
4. 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)

1. 10 J
2. 11 J
3. 10.5 J
4. 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.

1. 400 J
2. 100 J
3. 50 J
4. 200 J

Ans. a