Work power energy

WORK

Whenever a force acting on a body, displaces it in its direction, work is said to be done by the force. Work done by a force is equal to scalar product of force applied and displacement of the point of application,

W=F. d

    

Note : Work is a scalar quantity

1.1 WORK DONE BY A CONSTANT FORCE

If the direction and magnitude of a force applied on a body is constant, the force is said to be constant. Work done by a constant force,

W = Force × component of displacement along force

    = displacement × component of force along displacement                                                                                                                        

The work done will, be W = (F cos ѳ)d

                                          = F(d cos ѳ) ѳ

In vector form,   W=F.d

Note: The force of gravity is the example of constant force; hence work done by it is the example of work done by a constant force.

1.2 WORK DONE BY A VARIABLE FORCE

If the force applied on a body is changing its direction or magnitude or both, the force is said to be variable. Suppose a variable force causes displacement in a body from position  to position To calculate the work done by the force the path from  to  can be divided into infinitesimal elements, each element is so small that during displacement of body through it, the force is supposed to be constant. If dr̅ be small displacement of point of application and F̅ be the force applied on the body, the work done by force is 

dW=F̅.dr̅                             

The total work done in displacing body from  to  is given by

                                   

1.4 NATURE OF WORK DONE→

(1) POSITIVE WORK

W=Fs cosѳ

If the angle Ѳ is acute (Ѳ < 90°) then the work is said to be positive. The positive work signifies that the external force favours the motion of the body.

. When a body falls freely under the action of gravity (Ѳ =0°), the work done by gravity is positive.

. When a spring is stretched, stretching force and the displacement both are in the same direction. So work done by stretching force is positive.

(2) Negative work

W=Fs cosѳ

If the angle Ѳ is obtuse (Ѳ > 90°).

Then the work is said to be negative.

It signifies that the direction of force is such that it opposes the motion of the body.

. Work done by frictional force is negative when it opposes the motion.

. Work done by braking force on the car is negative.