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:
Fs = -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.
- 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