Work , Power and Energy
- Work is said to be done when a force produces some displacement in a body.
- The amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of force.
Work = Force x Displacement of point of application in the direction of force or W= Fx S
- –If there is no motion produced in the body even if a force acts on it, the work done is said to be zero, e. no work is done.
- If a force F is acting on a body and it displaces the body such that the displacement is at an angle 0 to the direction of force, then:
Work done = Force x Component of displacement
in the direction of force
or W= F x S cos θ
- If the displacement. is in the direction of force, e. θ= 0°, then cos 0° = 1.
W= Fx S
In this case, the work done is maximum and positive.
- If the displacement is normal to the direction of force, e. θ = 90°, then cos 90° = 0.
W= F x S cos 90″ = F x 0= 0
Hence, the work done is zero.
- If the displacement is in a direction opposite to the force. e. θ = 180° cos 180°= —1.
W= F x S cos 180° = –FxS
In this case, the work done is negative. This is usually the case when force opposes the motion or tries to stop a moving body.
- Work done by the force of gravity, W = mgh,
where m = mass of the body, g = acceleration due to gravity, and h = height of the body from the earth’s surface.
The work done by the force of gravity is the same whether a person comes down from a certain height using a staircase or he comes down from the same height using a lift.
Since both force and displacement are vector quantities, therefore, work is a scalar quantity. In vector form, it is written as:
- The SI unit of work is joule abbreviated as J 1 joule of work is said to be done when a force o 1 newton displaces a body through 1 metre,in it own direction.
- The MKS unit of work is kg m2 s2
- The CGS unit of work is 1 erg of work said to be done when a force of 1 dyne displaces
body through 1 cm in its own direction.