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.
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
- 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
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
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
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
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