7.1 Work Done by a Constant Force

Last updated at September 16, 2026 by

What is work and what is not work?
  • GIF Watch: what is work and what is not work Animation for "What is work and what is not work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — In science, work is done only when we apply a force AND the object moves. Beat 2 — If the object does not move, no work is done — no matter how much force we apply. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • In science, work is done only when we apply a force AND the object moves.
  • If the object does not move, no work is done — no matter how much force we apply.
Case Work done or not?
Lifting an object Work done — force applied, object moves up
Dropping an object Work done — gravity pulls it, object moves down
Pushing an object and it moves Work done — force applied, object moves
Pushing a wall NO work done — force applied, but wall does not move
Pulling an object and it moves Work done — force applied, object moves
Pulling a heavy stone and it doesn't move NO work done — force applied, but no displacement
What is the definition of work?
GIF Watch: what is the definition of work Animation for "What is the definition of work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work is done by a force on an object, when the force displaces the object in the direction of the force. (At a Glance, page 136). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • Work is done by a force on an object, when the force displaces the object in the direction of the force.
Important points about work
  • Formula —
Work = Force × Displacement in the direction of the force,
W = F × s
  • Unit
Its unit is Joule
One Joule of energy is used up (or work is done) when a force of one Newton moves an object a distance of exactly one metre
So
1 Joule = 1 N × 1 m
  • While describing work done, always specify which force does the work, and on which object.
Example 1
  • GIF Watch: what is the definition of work Animation for "What is the definition of work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work is done by a force on an object, when the force displaces the object in the direction of the force. (At a Glance, page 136). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • Suppose we push a box with a force of 10 N.
  • The box moves 2 m in the direction of the force.
  • We note down the Force applied
    • Force = 10 N
  • We note down the Displacement
    • Displacement = 2 m
  • We calculate Work
    • Work = Force × Displacement
    • Work = 10 N × 2 m
    • Work = 20 J
Example 2 — Lifting 1 bag to 1 m
  • GIF Watch: what is the definition of work Animation for "What is the definition of work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work is done by a force on an object, when the force displaces the object in the direction of the force. (At a Glance, page 136). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • We lift a wheat bag of mass 5 kg slowly to a height of 1 m.
  • We apply an upward force equal to the gravitational force on the bag.
    • Force = 50 N
  • Displacement = 1 m
  • Work = Force × Displacement
  • Work = 50 N × 1 m
  • Work = 50 J
Example 3 — Lifting 3 bags one after the other to 1 m
GIF Watch: what is the definition of work Animation for "What is the definition of work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work is done by a force on an object, when the force displaces the object in the direction of the force. (At a Glance, page 136). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • Now we lift 3 such bags, one after the other, to the same height of 1 m.
  • Each bag needs — Force = 50 N, Displacement = 1 m, Work = 50 J
  • Total Work = 50 J + 50 J + 50 J
  • Total Work = 150 J
  • This is 3 times the work of lifting 1 bag.
  • If a machine using fuel lifts the bags, it will need 3 times more fuel for 3 bags.
Example 4 — Lifting all 3 bags together to 1 m
GIF Watch: what is the definition of work Animation for "What is the definition of work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work is done by a force on an object, when the force displaces the object in the direction of the force. (At a Glance, page 136). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • Now we lift all 3 bags together to the same height of 1 m.
  • We need a force 3 times larger.
    • Force = 3 × 50 N = 150 N
  • Displacement = 1 m
  • Work = Force × Displacement
  • Work = 150 N × 1 m
  • Work = 150 J
  • Same as Example 3 — because we did the same task.
  • Main Idea — Applying a larger force over the same distance = proportionally more work.
Example 5 — Lifting 1 bag to 3 m 
GIF Watch: what is the definition of work Animation for "What is the definition of work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work is done by a force on an object, when the force displaces the object in the direction of the force. (At a Glance, page 136). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • Now we lift a single bag, but to a height of 3 m.
  • Force = 50 N
  • Displacement = 3 m
  • Work = Force × Displacement
  • Work = 50 N × 3 m
  • Work = 150 J
  • This is 3 times the work of lifting the same bag to 1 m.
  • Main Idea — Applying the same force over a larger distance = proportionally more work.
Suppose we push a box horizontally. Is it work?
  • Yes, it is work.
  • Work does not depend on the direction being up or down.
  • GIF Watch: what is the definition of work Animation for "What is the definition of work". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work is done by a force on an object, when the force displaces the object in the direction of the force. (At a Glance, page 136). Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • The displacement can be in the vertical direction, in a horizontal direction, or any other direction for that matter.
  • The formula remains the same — W = F × s, where s is the displacement in the direction of the force.
What is a Force-Displacement Graph? How to make it?
  • A force-displacement graph shows how much force acts on an object at each point of its displacement.
  • How to make it:
    • On the X-axis, take displacement of the object (in the direction of force), in metre.
    • On the Y-axis, take force on the object, in newton.
    • For every displacement, mark the force acting at that point, and join the points.
      Example: A constant force of 10 N acts on an object as it moves from 0 to 1 m.
      At every displacement (0.2 m, 0.4 m, 0.6 m …), the force stays 10 N.
      So the graph is a straight horizontal line at 10 N.
    • GIF Watch: what is a Force-Displacement Graph? How to make it Animation for "What is a Force-Displacement Graph? How to make it". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — A force-displacement graph shows how much force acts on an object at each point of its displacement. Beat 2 — How to make it:. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
How do we find work done from a force-displacement graph?
  • Work done = area under the force-displacement graph between the initial and the final positions.
    Example: In the graph above, force = 10 N, displacement = 0 to 1 m.
    The area under the graph is a rectangle.
    Area = 10 N × 1 m
    So Work done = 10 J
    We can check with the formula too — W = F × s = 10 × 1 = 10 J. Same answer.
  • GIF Watch: how do we find work done from a force-displacement graph Animation for "How do we find work done from a force-displacement graph". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work done = area under the force-displacement graph between the initial and the final positions. Beat 2 — This method works even when the force is NOT constant — just find the area under the graph between the initial and final positions. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • This method works even when the force is NOT constant — just find the area under the graph between the initial and final positions.
  • GIF Watch: how do we find work done from a force-displacement graph Animation for "How do we find work done from a force-displacement graph". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — Work done = area under the force-displacement graph between the initial and the final positions. Beat 2 — This method works even when the force is NOT constant — just find the area under the graph between the initial and final positions. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
When is work done equal to zero?
  • We know that
Work done = Force × displacement
W = F × s
  • So if Force is 0, work done is also 0
  • If displacement s is 0, work done is 0
Case Condition Example
No force F = 0 No force acting on an object, no work done on it
No displacement s = 0 Pushing a rigid wall — wall does not move, work done on wall = 0
Why do we feel tired even when work done is zero?
GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • We push a wall, the wall does not move, so scientifically we did no work on the wall.
  • But our muscles repeatedly expand and contract, and use up the internal energy of our body.
  • So we feel tired even though, in a scientific sense, we have not done any work on the object.
  • Also, displacement can be either positive or negative.
  • So work done can also be positive or negative. Lets see when.
When is work done positive?
  • When the displacement is in the SAME direction as the applied force, work done by the force is positive.
    Example: We push a wheelchair. Our force and the wheelchair's displacement are in the same direction. We do positive work on the wheelchair.
  • GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
When is work done negative?
  • When the displacement is in the direction OPPOSITE to the force, work done by the force is negative.
    Example: A goalkeeper stops a football. She applies force opposite to the ball's motion, so opposite to displacement. She does negative work on the ball.
  • GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • Note — The ball and the goalkeeper both apply equal and opposite forces on each other. The ball does positive work on the goalkeeper, while the goalkeeper does negative work on the ball. 
What if displacement is perpendicular to the direction of force?
  • If a force acts in a direction perpendicular to the displacement of an object, the work done by that force is zero.
  • Why? Because there is no displacement in the direction of the force.
    Example: A girl carries a box while walking.
    She applies an upward force to balance the box's weight.
    But the box moves horizontally.
    Force is upward, displacement is horizontal — perpendicular to each other.
    So work done by her force on the box = 0.
  • GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • In higher grades, you will learn how to calculate work done when force and displacement are at an angle to each other.
📘 Example 7.1 (NCERT)
While exercising, a girl lifts a dumbbell and slowly lowers it down. Identify when the girl does positive work on the dumbbell and when she does negative work on it.
GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • The girl applies a force equal to the weight of the dumbbell to lift it up.
  • Moving UP — her force is in the direction of displacement, so she does positive work.
  • Moving DOWN — the force she applies to hold it is opposite to the displacement, so she does negative work.
📘 Example 7.2 (NCERT)
While saving a goal, a goalkeeper's hand moved back by 15 cm as she stopped a ball while applying a force of 200 N. How much work did the goalkeeper do on the ball in stopping it?
GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
  • The goalkeeper applied force opposite to the ball's motion, so her work is negative.
  • Displacement is taken as negative — the ball moves opposite to the applied force.
  • Work done = force × displacement in the direction of force
  • Work done = 200 N × (– 0.15 m) = – 30 J
  • 🤔 Pause and Ponder 1 (from the book)
    In the previous chapter, a weightlifter is shown holding a barbell steady in her hands. Is she doing any work on the barbell while holding it steady?
    GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
    View answer Hide answer
    Answer
    • No. The barbell is steady, so its displacement s = 0.
    • Work done = F × s = F × 0 = 0.
    • She feels tired because her muscles use internal energy, but scientifically no work is done on the barbell.
  • 🤔 Pause and Ponder 2 (from the book)
    Is the work done by friction on the stack of coins that travels on a rough surface — positive, negative or zero?
    GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
    View answer Hide answer
    Answer
    GIF Watch: why do we feel tired even when work done is zero Animation for "Why do we feel tired even when work done is zero". A short looping GIF, three or four beats, drawn in the flat classroom style of the chapter. Beat 1 — We push a wall, the wall does not move, so scientifically we did no work on the wall. Beat 2 — But our muscles repeatedly expand and contract, and use up the internal energy of our body. Beat 3 — So we feel tired even though, in a scientific sense, we have not done any work on the object. Label every arrow and quantity, name the direction each force or motion acts in, and hold the last frame for a moment before the loop starts again.
    • Negative.
    • The coins move forward, but friction acts opposite to motion — so force and displacement are in opposite directions.
    • Hence friction does negative work on the coins.
📝 Important points — 7.1 Work Done by a Constant Force
Point Detail
Work formula W = F × s (displacement in direction of force)
SI unit joule (J), 1 J = 1 N × 1 m = 1 kg m² s⁻²
From graph Work = area under force-displacement graph
Zero work F = 0, or s = 0, or force ⊥ displacement
Positive work Force and displacement in same direction
Negative work Force and displacement in opposite directions
Always specify Which force does the work, and on which object
🚀 Ready to Go Beyond
  • Force and displacement have both magnitude and direction.
  • Work, however, does not have a direction — it is described using a number with a positive or a negative sign.
💡 Worth remembering
  • Work needs BOTH — a force AND a displacement in its direction.
  • Feeling tired ≠ doing work.
  • The sign of work only tells the relative direction of force and displacement, not "good" or "bad" work.
✅ Quick self-check
  1. A porter stands still with a heavy bag on his head. How much work does he do on the bag?
    View Answer Hide Answer
    • The porter is standing still, so displacement of the bag s = 0.
    • Work done = F × s = F × 0
    • Work done = 0 J
  2. A ball rolls on the ground and slows down due to friction. What is the sign of work done by friction?
    View Answer Hide Answer
    • The ball moves forward, but friction acts opposite to the motion.
    • Force and displacement are in opposite directions.
    • Work done by friction is negative.
  3. A force of 5 N moves an object 2 m in the direction of the force. Find the work done.
    View Answer Hide Answer
    • W = F × s
    • W = 5 N × 2 m
    • W = 10 J

Key terms and units

Term Meaning Unit
Work Force × displacement in direction of force joule (J)
Joule Work done when 1 N moves an object by 1 m 1 J = 1 N m
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