Work Done

In Physics, the term work has a very specific meaning that is different from its everyday usage. In daily life, any physical or mental effort is often called work. However, in Physics, work is said to be done only when a force applied on an object produces displacement in the direction of the force.If a force is applied on an object but the object does not move, then no work is done in the physical sense.

Similarly, if displacement occurs without the application of force, work is not considered to be done by that force. This condition is extremely important for exams, as many questions are designed to test whether the student understands this strict definition. Thus, work in Physics depends on two essential factors: the applied force and the displacement produced due to that force.

Conditions Necessary for Work to be Done

For work to be done by a force, three conditions must be satisfied simultaneously. First, a force must act on the object. Second, the object must undergo displacement. Third, the displacement must have a component in the direction of the applied force. If any one of these conditions is missing, the work done by that force is zero. For example, pushing a rigid wall with all your strength does not result in work done, because although force is applied, displacement is zero.

This is a classic exam example. Similarly, when a stone tied to a string moves in a circular path, the centripetal force acts perpendicular to the direction of motion. Since displacement at every instant is perpendicular to the force, no work is done by the centripetal force.

Work Done by a Constant Force

When a constant force acts on an object and produces displacement in the same direction, the work done is defined as the product of the magnitude of force and the displacement.

W = F × S

Here, W represents work done, F represents the applied force, and s represents displacement. This formula is valid only when the force and displacement are in the same direction. In exams, this condition is often hidden, and students are expected to identify whether the formula can be applied directly or not.

Work Done When Force and Displacement Are at an Angle

In many real-life situations, the direction of force and displacement are not the same. In such cases, only the component of force in the direction of displacement contributes to work done.

W= F s × cosθ

Here, θ is the angle between the direction of force and the direction of displacement. If the angle is 0°, cosθ becomes 1 and work done is maximum. If the angle is 90°, cosθ becomes 0 and work done is zero. If the angle is greater than 90°, work done becomes negative. This concept is frequently tested through conceptual MCQs.

Physical Quantity Table: Work

Parameter	Description
Symbol	W
Formula	W = F s cosθ
SI Unit	Joule (J)
Scalar or Vector	Scalar quantity
Dimensional Formula	[M L² T⁻²]

SI Unit of Work

The SI unit of work is joule (J). One joule of work is said to be done when a force of one newton produces a displacement of one metre in the direction of the force.

1 J = 1 N × 1 m

In exams, joule is often confused with newton or watt. It must be remembered that joule is the unit of work and energy, not force or power.

Positive, Negative, and Zero Work

Work done can be positive, negative, or zero depending on the angle between force and displacement.
Positive work is done when force and displacement are in the same direction. For example, gravity does positive work when a stone falls freely downward.

Negative work is done when force and displacement are in opposite directions. For example, friction does negative work on a moving object because it opposes motion. Zero work is done when force is perpendicular to displacement or when there is no displacement. Examples include centripetal force in circular motion and pushing a wall without moving it.

Physical Quantity Table: Force

Parameter	Description
Symbol	F
Formula	F = ma
SI Unit	Newton (N)
Scalar or Vector	Vector quantity
Dimensional Formula	[M L T⁻²]

Special Cases of Work Done

Work Done by Gravity

When an object falls freely under gravity, gravity acts in the direction of displacement. Therefore, work done by gravity is positive. When an object is lifted upward against gravity, displacement is opposite to gravitational force. In this case, work done by gravity is negative. This distinction is important in numerical problems involving lifting or lowering objects.

Work Done by Friction

Friction always opposes motion. Therefore, the work done by friction on a moving object is always negative.
This negative work results in loss of mechanical energy, usually in the form of heat. Questions often test whether students remember that friction cannot do positive work on a sliding object.

Work Done in Circular Motion

In circular motion, the centripetal force acts toward the centre of the circle, while displacement at any instant is tangential. Since the force is always perpendicular to displacement, work done by centripetal force is zero. This is a standard conceptual question in NDA and CDS exams.

Physical Quantity Table: Displacement

Parameter	Description
Symbol	d, s, ∆s
Definition	Change in position of an object
SI Unit	metre (m)
Scalar or Vector	Vector quantity
Dimensional Formula	[L]

Work Done on an Inclined Plane

When an object moves on an inclined plane, the component of force along the plane does work. The normal reaction does no work because it is perpendicular to displacement. Friction, if present, does negative work. Gravity may do positive or negative work depending on the direction of motion. These situations are commonly used to test understanding of force components.

Example : 1 A force of 10 N acts on a body and produces a displacement of 5 m in the same direction.
Work done is:

W = F × s = 10 × 5 = 50 J

Example 2
A force of 20 N acts on an object and produces a displacement of 4 m at an angle of 60°.
Work done is:

W = 20 × 4 × cos60° = 80 × 0.5 = 40 J

Common Misconceptions About Work

Applying force always means work is done. This is incorrect because displacement is necessary.
Work done does not depend on time taken. Time is related to power, not work.
Work can be negative or zero, not only positive. This is a frequent exam trap.

Boundary Conditions of Work Concept

The classical definition of work applies only to macroscopic objects and classical mechanics.
At atomic scales or in quantum mechanics, the concept of work is treated differently, which is outside the UPSC syllabus.

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FAQs – Work Done