Work and Energy

Discover the fascinating world of work in physics! Learn how force and displacement combine to create work, understand the difference between positive and negative work, and master the calculations with real-world examples.

Applied Force (F)
Displacement (s)
Work Done
W = F × s
0 J
Energy Transfer
Work
0 J
Kinetic Energy
0 J
Force & Displacement Angle
0°
Positive Work
Work Formula
W = F × s × cos(θ)
Work is defined as the product of force and displacement in the direction of force.
W
Work
Joule (J)
F
Force
Newton (N)
s
Displacement
Meter (m)
Force Vector Components
🚗
Positive Work
A car accelerates forward. The engine force and displacement are in the same direction.
W = F × s × cos(0°)
W = +1000 J
Force and displacement in same direction → Positive Work
🛑
Negative Work
A car brakes to stop. The friction force opposes the direction of motion.
W = F × s × cos(180°)
W = -800 J
Force opposite to displacement → Negative Work
💪
Zero Work
A person pushes against a wall. Force is applied but there's no displacement.
W = F × 0
W = 0 J
No displacement → Zero Work
Positive Work
+1000 J
Energy transferred TO the object
Negative Work
-800 J
Energy taken FROM the object
Zero Work
0 J
No energy transfer occurs
Activity 10.1: Work in Daily Life

Analyze different activities and determine when work is done in physics:

Questions to Ask:

  • What is the work being done on?
  • What is happening to the object?
  • Who or what is doing the work?

Examples:

  • Studying: Mental effort with no physical displacement → No work in physics
  • Pushing a wall: Force applied but no displacement → No work
  • Climbing stairs: Force applied AND displacement occurs → Work is done

Conclusion: Only activities involving both force and displacement constitute work in physics!

Activity 10.2: Identifying Work Situations

Situations where Work IS Done:

  • Push a pebble: Pebble moves when force is applied
  • Pull a trolley: Trolley moves in direction of force
  • Lift a book: Book rises up when lifted
  • Kick a football: Ball moves due to applied force

Situations where Work is NOT Done:

  • Push against wall: No displacement occurs
  • Hold heavy load: No displacement occurs
  • Object moves without force: No applied force

Key Point: For work to be done, BOTH force and displacement in the direction of force are required!

Activity 10.3: Force vs Displacement

Force but No Displacement:

  • Pushing against immovable wall
  • Holding weights stationary above head
  • Car engine running but car not moving

Displacement but No Applied Force:

  • Ball rolling on smooth surface (inertia)
  • Skateboard coasting down a hill
  • Satellite orbiting Earth (no external force)

Conclusion: Work is done only when BOTH force and displacement are present! Missing either condition means no work in physics.

Activity 10.4: Types of Work

Positive Work Examples:

  • Lifting object upward: Your force (↑) + Displacement (↑) = +W
  • Pushing car forward: Force (→) + Displacement (→) = +W
  • Result: Energy is given TO the object

Negative Work Examples:

  • Gravity on lifted object: Gravity (↓) + Displacement (↑) = -W
  • Friction slowing car: Friction (←) + Displacement (→) = -W
  • Result: Energy is taken FROM the object

Amazing Fact: The same situation can involve both positive and negative work by different forces!

Example Problem 1
A force of 15 N is applied to move a box 4 meters across a horizontal floor. Calculate the work done.
Solution:
Given:
Force (F) = 15 N
Displacement (s) = 4 m
Angle between force and displacement = 0° (same direction)
Formula:
W = F × s × cos(θ)
Calculation:
W = 15 × 4 × cos(0°)
W = 15 × 4 × 1
W = 60 J
Work Done = 60 Joules
Example Problem 2
A person lifts a 20 kg bag to a height of 1.5 m. Calculate the work done against gravity. (g = 9.8 m/s²)
Solution:
Given:
Mass (m) = 20 kg
Height (h) = 1.5 m
Acceleration due to gravity (g) = 9.8 m/s²
Find Force:
F = mg = 20 × 9.8 = 196 N
Work Done:
W = F × s
W = 196 × 1.5
W = 294 J
Work Done = 294 Joules
Interactive Work and Energy Learning
Understanding Work in Physics
W = F × s × cos(θ)
Where: W = Work (Joules), F = Force (Newtons), s = Displacement (meters), θ = angle between force and displacement
Definition of Work
Work is done when a force causes displacement of an object in the direction of the force. It's the transfer of energy to an object by means of force acting through a distance.
Conditions for Work
Two conditions must be satisfied: (1) A force must be applied on the object, and (2) The object must be displaced in the direction of force. If either condition is missing, no work is done.
Types of Work
Positive Work: When force and displacement are in the same direction.
Negative Work: When force opposes displacement.
Zero Work: When there's no displacement or force is perpendicular to displacement.
Units and Dimensions
SI Unit: Joule (J) = N⋅m
CGS Unit: Erg = dyne⋅cm
Conversion: 1 J = 10⁷ erg
Dimension: [ML²T⁻²]