How Forces Affect Motion

Why This Matters

In Chapter 4, you learnt to describe how an object moves. You used words like position, velocity and acceleration. But you never asked the bigger question: why does the motion change at all?

Think about it. A football lies still on the ground. It does not move by itself. You have to kick it. A moving bus does not stop on its own at once — the driver has to press the brakes. A cricket ball flying towards the boundary suddenly changes direction when the bat hits it.

In every one of these cases, something had to happen to change the motion. That something is a force — a push or a pull.

This chapter answers the deepest “why” in all of motion. Why do things start moving? Why do they stop? Why is it harder to push a loaded cart than an empty one? Why does a rocket fly up with nothing below it to push against?

The answers were worked out over 300 years ago by Isaac Newton, in just three simple laws. By the end of this chapter, you will be able to look at almost any moving thing — a canoe, a walking person, a recoiling gun, a launching rocket — and explain exactly what force is doing what, and why. Let us begin.

The Big Idea

The Big Idea: A force is a push or a pull. On its own, a single fact decides everything about motion: the net force — the leftover force after you add up all the pushes and pulls on an object. If the net force is zero, the object keeps doing what it was doing (stays still, or keeps moving at the same speed in the same direction). If the net force is not zero, the object accelerates — it speeds up, slows down, or changes direction — in the direction of that net force. A bigger net force gives more acceleration; a bigger mass gives less. And every force comes in a pair: when one object pushes a second, the second pushes back equally. These three ideas are Newton’s three laws of motion, and together they explain the motion of everything from a cricket ball to a planet.

What a Force Is, and What It Can Do

You already met forces in earlier classes. Let us pull those ideas together cleanly.

A force is simply a push or a pull on an object. A force always needs two objects — one to apply it and one to receive it. Your hand (object 1) pushes a door (object 2). The Earth (object 1) pulls a falling apple (object 2).

A force can do four different things. Figure 6.1 shows all four with everyday examples.

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Force is more than just a size. Notice that whenever we describe a force, we always say which direction it acts in: friction acts opposite to motion, the Earth pulls objects downwards, like magnetic poles push apart. So a force has both a magnitude (how strong) and a direction. This makes force a quantity like velocity and acceleration, which also need a direction.

The SI unit of force is the newton. We write the unit with a small “n” (newton), but its symbol is a capital N. This is the rule for any unit named after a person: the full name starts small, the symbol is capital. So we write 5 N, not 5 n.

A light touch you can feel is about a few thousandths of a newton (a few millinewtons, where 1 mN = 10⁻³ N). To get a feel for one newton: if you rest a 100 g object on your palm, your palm pushes up on it with about 1 N.

Measuring how strong a force is

To measure a force, we use a spring balance. You have used one before to find the weight of an object.

Balanced and Unbalanced Forces

In real life, an object rarely has just one force on it. Usually several forces act at once. So what really matters is not each single force, but how they add up.

Have you ever played tug of war? Two teams pull a rope in opposite directions. Figure 6.2 uses this game to show the key idea.

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When two forces are equal in size but opposite in direction, we call them balanced forces. They cancel out. The net force is zero, and the motion does not change — the rope stays put.

When the forces do not cancel, they are unbalanced. There is a leftover force called the net force. Two simple rules let you find it:

• Forces in opposite directions: subtract the smaller from the larger. The net force points along the larger force.
• Forces in the same direction: add them. The net force points the same way as both.

For example, two people pushing a stalled car in the same direction add their pushes together. The car feels the sum of the two forces, pushing it forward.

Let us put numbers on this. Figure 6.3 shows the same two forces, 10 N and 6 N, arranged in three ways.

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The Force of Friction: Always There

Here is a puzzle. Push a heavy box on the floor gently and it does not move. You have to push harder before it slides. Why does the box “resist” you?

The reason is friction — a force that appears between two surfaces in contact, acting opposite to the direction you try to move. When you push the box forward, friction pushes it backward. The box stays still until your push becomes larger than friction. Only then is there a net force forward, and the box moves.

A box being pushed has more than two forces on it. Figure 6.4 shows all four.

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Two of these forces are new names worth knowing:

• Weight: the gravitational force pulling the box straight down.
• Normal force: the push the surface gives back, straight up, perpendicular to the surface. (“Normal” here means perpendicular, not “ordinary”.)

The weight (down) and the normal force (up) are equal and balanced, so they cancel. That is why the box does not sink into the floor or fly up. The only forces that decide side-to-side motion are the applied force and friction.

Why a moving object slows down and stops

Now push the box and let go. It slides a little, then stops. Stop pedalling a cycle and it slows and stops too. Why?

Because friction never switches off. Once you stop pushing, friction is the only horizontal force left. It acts against the motion and keeps slowing the object until it stops. This is the key insight: a moving object does not stop on its own. A hidden force — friction — stops it.

This also answers a common confusion. People think you must keep pushing to keep something moving. Not true! You keep pushing only to cancel friction. If friction vanished, one push would keep the object moving forever.

We can test that friction depends on the surface. The smoother the surface, the smaller the friction, and the farther an object slides before stopping.

A thought experiment. Imagine a surface so perfectly smooth that friction is exactly zero. Push an object on it and let go. With no friction to slow it, the object would never stop. It would keep moving at the same speed forever. We cannot build such a perfect surface, but imagining it reveals the truth: motion does not need a force to continue — only to change.

This was a huge discovery. For thousands of years, people wrongly believed a force was needed just to keep something moving. In the 1600s, Galileo argued through thought experiments that a moving object, with all obstacles removed, would keep moving on its own. Newton later named the object’s tendency to resist a change in its motion inertia, and built his first law around it.

Newton’s First Law of Motion

Newton’s first law of motion states:

Newton’s First Law: An object at rest stays at rest, and an object in motion keeps moving with constant velocity, unless a net force acts on it.

In plain words: if the net force is zero, the object cannot start moving or change its velocity by itself. Its acceleration is zero.

Let us be careful about “constant velocity”. An object at rest has zero velocity, and that is constant too. If the velocity is constant and non-zero, the object moves in a straight line, in the same direction, at the same speed. Nothing about the motion changes.

This tendency to keep doing the same thing — staying still or moving steadily — is called inertia. A heavier object has more inertia and is harder to start or stop. This is why pushing a loaded truck is much harder than pushing an empty trolley.

When no net force acts, an object either stays at rest or moves at constant velocity. Figure 6.5 shows what the position-time and velocity-time graphs look like in both cases.

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Newton’s Second Law of Motion

The first law tells us what happens when the net force is zero. But what happens when the net force is not zero? That is what the second law answers.

You already know a force produces acceleration (a change in velocity). The question is: how big? Two everyday observations point the way.

First, push the same ball gently and it accelerates slowly; push it hard and it accelerates fast. So for the same object, more force gives more acceleration.

Second, with the same push it is easier to get a light object moving than a heavy one. So for the same force, more mass gives less acceleration.

Figure 6.6 puts both patterns together.

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Newton combined both into his second law:

Newton’s Second Law: When a net force acts on an object, it accelerates in the direction of that net force. The acceleration is proportional to the net force, and inversely proportional to the mass of the object.

As a formula:

a = F / m

or, rearranged, F = ma

Here F is the net force, m is the mass, and a is the acceleration. The acceleration points the same way as the net force.

Why a heavier object needs more force for the same acceleration

This is one of those “givens” that deserves a real explanation. The formula a = F / m holds the key.

Look at the division. The same force F is, in a sense, shared across all the matter in the object. A heavier object has more mass — more matter to get moving. So the same force, spread over more mass, produces a smaller acceleration. To push a heavy object to the same acceleration as a light one, you must apply a bigger force to make up for the bigger mass. That is exactly what dividing by m captures: bigger m on the bottom means smaller a, unless you raise F to match.

Defining the newton

The formula also gives us a clean definition of the unit of force. Put m = 1 kg and a = 1 m s⁻² into F = ma:

F = 1 kg × 1 m s⁻² = 1 kg m s⁻² = 1 N

So one newton is the force that gives a 1 kg object an acceleration of 1 m s⁻². That is what a newton is.

Weight as a force

When an object falls, the Earth’s gravity gives it an acceleration called g (the acceleration due to gravity). Near the Earth’s surface g = 9.8 m s⁻² (often rounded to 10 m s⁻² for quick sums). Using F = ma with a = g, the gravitational force on a mass m — its weight — is:

F = mg

Note that g does not depend on the object’s mass. A heavy stone and a light pebble both fall with the same g.

Newton’s second law explains everyday safety

Many tricks for staying safe are really the second law in disguise. The key idea: stretching out the time over which a velocity changes makes the acceleration smaller, and so makes the force smaller.

Figure 6.7 shows this for a cricket catch.

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• A cricket fielder pulls their hands back while catching a fast ball. This makes the ball take longer to stop, lowering the acceleration and so the force on their hands — less sting, less injury.
• A car airbag inflates into a soft cushion in a crash. The passenger’s head pushes into the bag over a longer time, so the force on the body is much smaller.
• Cracking a coconut works the opposite way. You bring it down fast onto a hard floor so it stops in a tiny time. A tiny stopping time means a huge acceleration, which needs a huge force — and that big force cracks the shell.

Newton’s Third Law of Motion

So far we looked at one object at a time. But a force always needs two objects. When you kick a ball, do you ever feel the ball push back on your foot? You do. The third law is about this two-sided nature of every force.

Try this: sit on a chair with wheels, raise your feet, and push a heavy table away from you. The table moves one way — and your chair rolls the opposite way. You pushed the table, and the table pushed you back.

This happens everywhere. Figure 6.8 shows three examples.

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Newton’s third law states:

Newton’s Third Law: Whenever one object exerts a force on a second object, the second object at the same time exerts an equal and opposite force on the first.

These two forces are often called action and reaction. The most important point about them is in the box below.

The action and reaction forces are equal in size and opposite in direction. But they always act on two different objects — never on the same one. That is why they do not cancel each other out.

Why action and reaction don’t cancel

This is the part students find tricky, so let us go slowly. You might think: “If the two forces are equal and opposite, shouldn’t they cancel and nothing should move?”

The answer is no, and the reason is simple. Forces cancel only when they act on the same object. Action and reaction act on two different objects. Each object feels only one of the pair, so each can move.

Kick a ball. Your foot pushes the ball (this force acts on the ball). The ball pushes your foot back (this force acts on your foot). The force on the ball sends the ball flying. The force on your foot you feel as a tap. They never meet on the same object, so they cannot cancel.

Even though the two forces are equal, their effects are usually very different — because the two objects usually have very different masses. A small mass gets a big acceleration; a large mass barely moves. Figure 6.9 shows this clearly with a gun firing a bullet.

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Third-law examples around you

Once you spot the pattern, it is everywhere:

• Walking and running. You push the ground backwards with your foot. The ground pushes you forwards. This forward push is friction — so here friction helps you, it does not oppose you. With no friction (wet tiles, ice) your foot slips back and you can fall. Grooves on shoe soles and treads on tyres add friction to stop this.
• Rowing a canoe. The paddle pushes water backwards; the water pushes the paddle (and canoe) forwards. Push the water harder, and the forward push is bigger, so the canoe speeds up.
• A rocket and a balloon. Let go of an inflated balloon and air rushes out one way while the balloon shoots the other way. A rocket does the same: it pushes hot gas down, the gas pushes the rocket up. When this upward push beats the rocket’s weight, the rocket lifts off — no air or ground needed. The Vikram lander of Chandrayaan-3 even fired its engine forwards to slow down for a soft landing on the Moon.
• Climbing a tree. Your legs push down against the trunk; friction pushes you up. A smooth trunk has little friction, so it is harder to climb.

Newton’s third law works for all forces — pushes you can touch, and forces that act across a gap like magnetism, electric charge and gravity. Even the Earth and a falling fruit pull each other with equal force.

Forces on a System of Objects

So far we used Newton’s laws on a single object. But what about two or more objects joined together — like a tractor pulling a trolley, or train coaches linked by couplings?

Consider two boxes on a smooth (frictionless) surface, joined by a string. You pull the front box with a force F. The string passes a force between the boxes called tension (T). Figure 6.10 shows the setup.

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Here is the clever shortcut. Instead of studying each box separately, treat the two boxes plus the string as one single system. Now the tension T is an internal force — it acts inside the system, as an equal-and-opposite pair (Box 1 pulls Box 2, Box 2 pulls Box 1). Internal forces always come in such pairs, so they cancel within the system. Only the external force F is left over.

So we apply the second law to the whole system, using the total mass:

a = F / (m₁ + m₂)

The system speeds up just like a single object of mass m₁ + m₂. (The downward weight of both boxes is balanced by the upward normal force from the ground, so those do not affect the side-to-side motion.) This trick — looking at the whole instead of the parts — makes even complicated problems simple, and shows the real power of Newton’s laws.

Common Mistakes

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Practice Problems

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Summary

You can now explain:

• That a force is a push or a pull, has both magnitude and direction, is measured in newton (N) with a spring balance, and can start motion, change speed, change direction, or change shape.
• The difference between balanced forces (equal and opposite, net force zero, motion unchanged) and unbalanced forces (a leftover net force that changes motion), and how to add or subtract forces to find the net force.
• Why a moving object slows and stops because of friction, not on its own — and why, with no friction, it would move forever (the idea behind inertia).
• Newton’s first law: with zero net force, an object stays at rest or keeps moving at constant velocity, because of its inertia.
• Newton’s second law, F = ma, including why a heavier object needs a bigger force for the same acceleration, how the newton is defined, weight as F = mg, and why stretching the stopping time (catching, airbags) reduces the force.
• Newton’s third law: forces come in equal and opposite pairs on two different objects — which is why action and reaction never cancel — and how it explains walking, rowing, rockets and recoil.
• How to treat connected objects as one system, where internal forces cancel and only external forces matter, so a = F / (total mass).

What’s Next

You now know what forces do to motion. Next, you will learn what happens when a force makes an object move through a distance — that is, when a force does work. You will meet energy, the ability to do work, and discover how machines let a small effort move a big load. Continue to Chapter 7 — Work, Energy, and Simple Machines.