Work , Power and Energy

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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:

W= F.S

  • 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.

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