Work Done in Physics — CBSE Class 9 Explained

Why Force Without Displacement Produces Zero Work and How Physics Redefines “Work”

You have held a heavy bag of rice at a bus stand for twenty minutes. Your arms ached. You sweated.

 

You were exhausted. And according to physics — you did zero work. If that feels like physics is being unfair, you are in exactly the right place.

The Porter Who Was Told He Did Nothing

Birju carries luggage for passengers at Kanpur railway station. He has done this for eleven years. On a busy Saturday in March, a man hands him two large suitcases — each around 15 kilograms — and asks him to wait while he buys a platform ticket.

Birju stands there. Both suitcases in hand. Arms straining. Fifteen minutes pass.

The man returns, tips Birju twelve rupees, and walks away. Birju watches him go, arms still sore, back aching.

Now here is the strange part. A physicist standing on that platform would look at those fifteen minutes and say: Birju did no work on those suitcases during the wait.

Not less work. Not reduced work. Zero work.

Birju would have a few words in response. But the physicist would not be wrong. And once you understand what physics actually means by work — you will find the physicist is making a precise and genuinely useful distinction, not an insulting one.

What Physics Notices That Everyday Language Misses

In ordinary life, work means effort. Strain. Time spent. Exhaustion. By that definition, Birju worked enormously.

But effort alone does not move anything. Strain alone changes nothing in the physical world. Birju’s muscles pulled upward on the suitcases continuously — and the suitcases went nowhere. They remained exactly where they started, at the same height, in the same position.

Physics is not interested in effort. Physics is interested in change. Specifically — did the force cause the object to move?

When Birju finally lifts the suitcases and walks thirty metres down the platform to Coach B3, something changes. The suitcases move. They travel a distance in the direction of the force applied. The physical world is now different from how it was before.

That change — force applied, object displaced in the direction of that force — is what physics calls work.

No displacement, no work. Displacement perpendicular to force, no work either. Work only exists when force and displacement share a direction, and both are non-zero.

Birju’s fifteen minutes of waiting produced real fatigue. Physics simply has a different question — and for that question, displacement is the only answer that counts.

The Name and the Formula

The scientific term for this is Work Done.

Work is defined as the product of force applied on an object and the displacement of the object in the direction of the force.

Scientists gave it a formula:

W = F × s

• W = Work done, measured in Joules (J)
• F = Force applied, measured in Newtons (N)
• s = Displacement in the direction of force, measured in metres (m)

One Joule is the work done when a force of one Newton displaces an object by one metre in the direction of the force.

And the condition that makes Birju’s wait equal to zero: if either F or s is zero — or if force and displacement point in completely different directions — the product is zero. Work is zero.

How Work is Calculated — Step by Step

Birju has collected himself and is now walking those thirty metres to Coach B3. Each suitcase weighs 15 kg. He lifts them 0.5 metres off the ground before walking.

Calculating work done against gravity (lifting phase):

Step 1: Identify the force. To lift the suitcases, Birju must apply a force equal to their weight.

Weight = mass × g = 15 × 10 = 150 N per suitcase. Two suitcases: 300 N total.

Step 2: Identify the displacement in the direction of force. He lifts them 0.5 metres upward. Force is upward. Displacement is upward. Same direction.

Step 3: Apply the formula.

W = F × s = 300 × 0.5 = 150 Joules

Birju did 150 Joules of work in the lifting phase alone.

Now the walk — thirty metres horizontally:

Here is where students are often surprised. While walking horizontally with the suitcases, Birju’s arms are applying force upward to hold the bags. But the displacement is horizontal — sideways.

Force direction: upward. Displacement direction: horizontal. These are perpendicular — they form a 90° angle.

When force and displacement are perpendicular, the work done by that force is zero.

Birju still walked 30 metres. His legs did work against the friction with the floor. But his arms — holding the suitcases up — did zero work on the suitcases during the walk.

Two phases. Same man. Same luggage. Different answers — because the relationship between force direction and displacement direction changed.

The Formula — Don’t Panic

Every variable in this formula appeared in Birju’s story. You already calculated with it above. This is just making the structure visible.

W = F × s

When force and displacement are not in exactly the same direction, the full formula uses the angle between them:

W = F × s × cos θ

• θ (theta) = angle between the direction of force and the direction of displacement
• When θ = 0° (same direction): cos 0° = 1, so W = F × s — maximum work
• When θ = 90° (perpendicular): cos 90° = 0, so W = 0 — no work done
• When θ = 180° (opposite directions): cos 180° = −1, so W = −F × s — negative work

Negative work is real. When friction acts on a moving object, it acts opposite to the displacement. Friction does negative work — it removes energy from the system rather than adding it. This is why objects slow down.

At the Class 9 level, most problems use θ = 0° — force and displacement in the same direction. But knowing the angle version tells you exactly why the horizontal walk produced zero work from Birju’s arms: the angle was 90°.

Where Work Shows Up Every Day

Pushing a stalled scooter: A man in Patna pushes his scooter 50 metres to the nearest mechanic. Force applied forward. Displacement forward. Work done = F × 50. The physical world changed — the scooter moved. Real work, by every definition.

A satellite orbiting Earth: Gravity pulls the satellite toward Earth’s centre. The satellite moves in a circular orbit — always perpendicular to the pull of gravity. Angle between force and displacement: always 90°. Work done by gravity on the satellite: zero. This is why a satellite in a stable circular orbit does not spiral inward — gravity does no work on it.

Brakes on a bicycle: The brake pads apply a friction force opposite to the direction of motion. Force and displacement are in opposite directions — an angle of 180°. Work done by friction is negative. The bicycle slows down because energy is being removed from it. Negative work is not a mistake. It is physics describing energy leaving a system.

A coolie lifting goods onto a truck: Force upward. Displacement upward. Same direction. Maximum work done. Every kilogram lifted, every metre of height gained — all of it counts, and all of it appears in the formula.

Where Students Drop Marks

Mistake 1 — Confusing effort with work. Many students write: “The man held the box for an hour, so he did a lot of work.” But look at what the story showed us — displacement must occur in the direction of force. Holding without moving means displacement is zero. W = F × 0 = 0. Effort is real. Fatigue is real. Work, in the physics definition, is zero.

Mistake 2 — Ignoring the direction condition. A student calculates W = F × s for a person carrying a load horizontally and gets a non-zero answer because they multiply the holding force by the horizontal distance. The direction mismatch eliminates that work entirely. Force direction and displacement direction must be checked before applying the formula.

Mistake 3 — Treating negative work as an error. Students often assume work must be positive or that they have calculated incorrectly. Negative work is a correct and meaningful result — it means energy is being removed from the object. Friction, braking, and air resistance all do negative work on moving objects. Write it with confidence.

The ELIS Ladder — For Every Level

Level 1 — Class 6 to 8 In physics, work only happens when a force moves an object in the direction of that force. Holding something heavy without moving it is zero work. Pushing something and making it move is real work. Work = Force × Displacement. The unit of work is the Joule.

Level 2 — Class 9 CBSE Work done W = F × s, where F is the net force in Newtons and s is the displacement in metres. Work done is zero when: force is zero, displacement is zero, or force and displacement are perpendicular. Work can be positive (force and displacement in the same direction) or negative (force and displacement in opposite directions). One Joule = one Newton-metre. Work is a scalar quantity — it has magnitude but no direction.

The work-energy theorem states: the net work done on an object equals the change in its kinetic energy. W(net) = ΔKE = ½mv² − ½mu². This connects the work chapter directly to the energy chapter that follows.

Level 3 — Class 11, 12, and Beyond. The full expression W = ∫F · ds handles variable forces — forces that change in magnitude or direction over the path of motion. The dot product F · ds = F ds cos θ captures the directional relationship at every infinitesimal step of displacement.

Work is frame-dependent: the same event produces different work values when measured from different reference frames. A passenger sitting still in a moving train does zero work on the seat in the train’s reference frame. In the ground frame, the seat has been displaced, and work calculations differ. Neither is wrong — both are frame-specific descriptions of the same physical event.

One important limitation of the W = Fs model taught in Class 9: it assumes a constant force over the entire displacement. In real systems — a spring being compressed, a rocket burning fuel — force varies continuously. The integral form exists precisely because constant-force situations are the exception rather than the rule at higher levels.

In Five Sentences, Three, and One

In five sentences: Physics defines work as force multiplied by displacement in the direction of that force. If there is no displacement, or if force and displacement are perpendicular, the work done is zero. This is why holding a heavy object without moving it counts as zero work in physics, despite the effort involved. Work can be positive when force and displacement share a direction, and negative when they oppose each other. The unit of work is the Joule — one Joule equals one Newton of force acting over one metre of displacement.

In three sentences: Work in physics requires both force and displacement in the same direction — effort alone is not enough. The formula W = F × s captures this precisely, and becomes zero whenever force and displacement are perpendicular or opposite. Negative work is real and meaningful — it describes energy being removed from a moving object.

In one sentence: Physics calls it work only when force actually moves something — and the direction of that movement decides how much.

Practice Questions

1. A force of 40 N moves an object through a displacement of 5 metres in the direction of the force. Calculate the work done.
2. A woman holds a 10 kg bag of grain stationary above her head for three minutes. How much work does she do on the bag? Explain your answer.
3. A coolie carries luggage horizontally for 20 metres. The upward holding force is 200 N. How much work does the holding force do on the luggage during the horizontal walk?
4. A braking force of 150 N acts on a bicycle moving forward, bringing it to rest over 4 metres. Calculate the work done by the braking force and state whether it is positive or negative.
5. Using the work-energy theorem, explain what happens to the kinetic energy of an object when negative work is done on it.

Students Ask These Questions

Q: Why does physics use such a different definition of work from everyday life? Because physics needs a definition that connects precisely to energy and motion — two things that can be measured, calculated, and predicted. Effort and fatigue are real human experiences, but they do not help calculate how fast an object moves or how high it can be lifted. The physics definition of work is narrow by design — that narrowness is what makes it useful.

Q: Is work a vector or a scalar? Work is a scalar — it has magnitude but no direction. Even though force and displacement are both vectors, their combination through the dot product (F · s · cos θ) produces a single number with no directional component. This surprises students who expect the result of combining two vectors to also be a vector. Work tells you how much energy transferred — not which way.

Q: Can work be done on an object that is not moving at all? No. Displacement is a non-negotiable requirement. A force applied to a wall for an hour does zero work on the wall because the wall does not move. The person’s muscles are doing internal biological work — chemical energy is being used — but no mechanical work is done on the wall itself.

Q: What is the connection between work and energy? Work is the mechanism by which energy transfers into or out of an object. When positive work is done on an object, its energy increases — usually its kinetic energy (speed increases) or potential energy (height increases). When negative work is done, its energy decreases. The work-energy theorem formalises this: net work done = change in kinetic energy. Energy and work share the same unit — the Joule — because they measure the same physical quantity from different perspectives.

Q: If a satellite does not have work done on it by gravity, why does it keep moving in a circle? Gravity still acts on the satellite — it provides the centripetal force that keeps the satellite turning rather than flying off in a straight line. But because gravity is always perpendicular to the satellite’s velocity in a circular orbit, it does no work — it changes the direction of motion without changing the speed. The satellite’s kinetic energy remains constant even though a force is continuously acting on it. Direction can change without work being done — only speed change requires net work.

Related reading: Kinetic and Potential Energy — Class 9 CBSE | Newton’s Laws of Motion — Class 9 | Power and Energy — Class 9 CBSE