The intuitive meaning of work is quite different from the scientific definition of work. In everyday activity, the term 'work' is used equally for mental work and for physical work (involving muscular force) as is clear from the following examples.
(i) You may read a book or exert yourself mentally in thinking about a simple or difficult problem.
(ii) You might be holding a weight without moving.
(iii) You may be carrying a load and moving with uniform velocity.
(iv) You may be trying hard to move a huge rock which does not move despite your best efforts, though you may get completely exhausted in the process.
In all these cases, according to scientific definition, you are not doing any work.
Scientific conception of work
In physics, the term work is used in a special technical sense and has a much more precise definition which follows from the following examples.
(i) When a box is pushed on a floor by applying a force and it moves through some distance, work is said to be done. In this case, the applied force displaces the box.
(ii) When we pull a trolley by applying a force and it moves through some distance, work is again said to be done.
(iii) When we lift a box through a height, we have to apply force. In this case, the applied force does work in lifting the box.
From all the examples given above, it follows that work is done if :
No work is said to be done if any of the two conditions is not satisfied.
Work: When Constant Force is Acting in the Direction of Displacement
A body A is kept on a smooth horizontal surface. A force F is applied as shown. This force acts on the body for some time during which the displacement of the body is s. In such a case work is defined as follows.
Work done by a force on a body is the product of force and displacement of the body in the direction of the force.
Work = Force × Displacement
⇒ W = F × s
Work is a scalar quantity. This means that it has no sense of direction.
Unit of Work
In cgs system unit of work = erg
1 erg = If a force of one dyne displaced a body through a distance of one centimetre then work is 1 erg
1erg = 1 dyne × 1 cm
In SI unit of work is = joule(J)
When a force of 1N acts on an object and the object moves a distance of 1m in the direction of the force, the work done by the force is 1J.
Definition of one Joule
When F = 1N, s = 1m, then W = 1J
If a displacement of 1m is produced by a force of 1N acting in the direction of displacement then the work done by the force is 1J.
1J= 1 N x 1 m = 105 dyne × 102 cm =107 erg
1. When s = 0, W = 0, i.e. work done by a force on a
body is zero if the displacement of the body is zero. For example, when you push a wall with a force F, then the displacement of the wall is zero. Therefore, the work done by force F on the wall is zero.
2. When you sit on a chair and prepare a lesson in two hours, you may feel tired. But according to physics, no work is done.
3. If you hold a briefcase for one hour and do not move the briefcase, then s = 0. Therefore, work done by you on the briefcase is zero.
Work: When a Constant Force is Acting at an Angle to the Displacement
Let us consider a body A lying on a smooth horizontal surface. A constant force F acts at an angle q to the horizontal. The body is displaced through distance in the horizontal direction. Here the complete force F is not responsible to displace the body. A part of the force acting in the direction of displacement is responsible for displacing the body. This horizontal part is F cos θ. Work done in this case is defined as 'work done by a constant force acting at an angle to the displacement is the product of component of force in the direction of displacement and the displacement of the body'.
Work = Component of force in the direction of displacement x Displacement
W = (F cos θ ) × s
W = F s cos θ
Work done is maximum when force acts in the direction of displacement.
Case-1 : Work done is positive when θ is acute. This is because cos q is positive, Work done is maximum when θ = 0°. This is because the maximum value of cos θ = 1. This happens when force acts in the direction of displacement.
Case-2 : When the angle between force and displacement is 90°, i.e. when θ = 90°, then
cos θ = 0 cos 90° = 0
Some examples where work done is zero because θ = 90°
(a) Work done by centripetal force
When a stone is whirled in a horizontal circle, then centripetal force acts at 90° to the displacement. Therefore, work done by centripetal force is zero.
(b) Work done by coolie
When a coolie moves on a horizontal surface, he applies a force on the load kept on his head in vertically upward direction. Therefore, θ = 90°. Therefore, work done by the force applied by coolie is zero.
(c) Motion of the Earth around the Sun
Work done by the centripetal force (which is the gravitational pull of sun on earth) acting on earth is zero. Because centripetal force is perpendicular to the displacement.
[Remember the displacement is always tangential and centripetal force is always radially inward. The angle between radius and tangent is 90°].
Case-3 : When angle between force and displacement is 180°, i.e. when q =180° then cos 180° = -1.
In this case work done is negative.
Let us take an example where work done is negative because θ = 180°
A block A is pushed by the force F and displaced through s. Work done by applied force,
W = F × s × cos 0°
Work done by frictional force,
W = f × s × cos 180°