Work in Physics – The Basics Explained

Introduction

In everyday life, the word “work” often means doing a task: reading a book, cooking, or writing notes. But in physics, the concept of work is much more specific.

If you hold a book in your hands for hours, you feel tired, so in everyday sense, you are doing work. But according to physics, no work is done on the book because it has not moved.

So, what does work really mean in physics? How do we calculate it? What are the different types of work? Why is it so important in understanding energy and power?

Let’s explore the basics of work in physics step by step.

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Definition of Work in Physics

In physics:

Work is said to be done when a force is applied on an object and the object is displaced in the direction of the force.

This definition highlights two essential conditions:

1. A force must be applied.
2. There must be a displacement of the object in the direction of the force.

If either condition is missing, no work is done.

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Formula for Work

The mathematical expression for work is: W=F⋅d⋅cos⁡θW = F \cdot d \cdot \cos \thetaW=F⋅d⋅cosθ

Where:

• WWW = Work done (Joules)
• FFF = Magnitude of force applied (Newtons)
• ddd = Displacement of the object (meters)
• θ\thetaθ = Angle between force and displacement

Key Points

• If θ=0∘\theta = 0^\circθ=0∘ → force and displacement are in the same direction → W=FdW = FdW=Fd.
• If θ=90∘\theta = 90^\circθ=90∘ → force is perpendicular to displacement → W=0W = 0W=0.
• If 0∘<θ<90∘0^\circ < \theta < 90^\circ0∘<θ<90∘ → work is positive.
• If 90∘<θ≤180∘90^\circ < \theta \leq 180^\circ90∘<θ≤180∘ → work is negative.

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SI Unit and Dimensions of Work

• SI Unit: Joule (J)
  • 1 Joule = Work done when a force of 1 Newton displaces an object by 1 meter in the direction of the force.
• Dimensional Formula:

[W]=[M1L2T−2][W] = [M^1 L^2 T^{-2}][W]=[M1L2T−2]

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Conditions for Work to be Done

For work to occur in physics, three essential conditions must be satisfied:

1. Force must be applied.
   • If no force, no work.
2. Displacement must occur.
   • If an object does not move, no work is done (even if force is applied).
3. Component of force in direction of displacement.
   • Only the effective force in the displacement direction contributes to work.

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Types of Work

1. Positive Work

• When force and displacement are in the same direction.
• Energy is transferred to the object.

Examples:

• Pushing a car forward.
• Lifting a box upwards.
• Acceleration of a moving body.

2. Negative Work

• When force and displacement are in opposite directions.
• Energy is taken from the object.

Examples:

• Friction acting on a sliding object.
• Air resistance slowing a ball.
• Force of gravity on a ball thrown upward.

3. Zero Work

• When force is perpendicular to displacement.
• No energy transfer occurs.

Examples:

• A satellite moving in circular orbit (gravitational force is perpendicular to velocity).
• Carrying a load while walking horizontally.

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Work Done by a Variable Force

When the force is not constant, the formula becomes: W=∫x1x2F(x) dxW = \int_{x_1}^{x_2} F(x) \, dxW=∫x1​x2​​F(x)dx

• The area under Force vs Displacement graph gives the work done.
• Useful in springs, non-uniform motion, and varying forces.

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Work and Energy Relationship

• Work-Energy Theorem:

Work done on a body=Change in kinetic energy of the body\text{Work done on a body} = \text{Change in kinetic energy of the body}Work done on a body=Change in kinetic energy of the body

This shows work is the mechanism through which energy is transferred.

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Graphical Representation

1. Force vs. Displacement Graph
   • For constant force: straight line; area under the line = work.
   • For variable force: curved line; total area under curve = work.
2. Work vs. Time Graph
   • The slope gives power (rate of doing work).

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Real-Life Examples of Work in Physics

• Weightlifting: Positive work while lifting, negative work while lowering.
• Friction: Always does negative work on moving bodies.
• Walking: Legs apply force, displacement occurs → positive work.
• Braking a Car: Brakes apply force opposite to motion → negative work.
• Earth-Moon System: Gravity does no work on the Moon because force is perpendicular to displacement (circular orbit).

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Numerical Examples

Example 1: Positive Work

A force of 50 N pushes a box by 5 m on a smooth floor. Find the work done. W=Fd=50×5=250 JW = Fd = 50 \times 5 = 250 \, JW=Fd=50×5=250J

👉 Work done = 250 Joules.

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Example 2: Work with Angle

A man pulls a cart with a force of 100 N at an angle of 60° with horizontal, moving it 10 m. Find work done. W=Fdcos⁡θ=100×10×cos⁡60∘W = Fd \cos \theta = 100 \times 10 \times \cos 60^\circW=Fdcosθ=100×10×cos60∘ W=1000×0.5=500 JW = 1000 \times 0.5 = 500 \, JW=1000×0.5=500J

👉 Work done = 500 Joules.

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Example 3: Negative Work

A 20 N frictional force acts on a sliding box, which moves 4 m. Find the work done by friction. W=Fdcos⁡180∘=20×4×(−1)=−80 JW = Fd \cos 180^\circ = 20 \times 4 \times (-1) = -80 \, JW=Fdcos180∘=20×4×(−1)=−80J

👉 Work done = –80 Joules (negative).

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Importance of Work in Physics

1. Foundation of Energy Concepts – Work explains how energy is transferred.
2. Basis of Power – Power is defined as rate of doing work.
3. Practical Applications – Used in machines, engines, construction, sports.
4. Engineering and Technology – Design of brakes, lifts, pulleys depends on work principles.

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Misconceptions About Work in Physics

• Holding a heavy object = Work?
  • In everyday sense, yes. In physics, no (no displacement).
• Walking with a bag = Work?
  • Physically tiring, but force is vertical while displacement is horizontal → zero work on bag.
• Circular motion = Work by gravity?
  • No, because force and displacement are perpendicular.

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Advanced Concept: Work in Conservative and Non-Conservative Forces

• Conservative Forces (e.g., gravity, spring force): Work done is path-independent, depends only on initial and final positions.
• Non-Conservative Forces (e.g., friction, air drag): Work depends on path, leads to energy dissipation.

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Summary Table

Aspect	Work in Physics
Definition	Energy transfer when a force causes displacement
Formula	W=Fdcos⁡θW = Fd\cos\thetaW=Fdcosθ
SI Unit	Joule (J)
Conditions	Force, displacement, and component of force along displacement
Types	Positive, Negative, Zero
Graph	Area under Force–Displacement graph
Relation	Work = Change in Kinetic Energy