How Forces Affect Motion: Class 9 Science · Chapter 6

In Chapter 4 you described motion with position, velocity and acceleration, but you never asked what makes an object start, stop, speed up or turn. Free-wheel a bicycle down a slope and it gains speed without any pedalling. On a flat road it slowly loses speed and stops. Turn the handle and it changes direction. Each time, something is acting on it.

That something is a force. In this chapter we look closely at forces, see how several of them combine, and meet the three laws of motion with which Isaac Newton connected force to motion.

6.1 The Concept of Force

In earlier classes you met a force as a push or a pull. A force can do four kinds of things to an object. It can set the object moving from rest, change its speed, change its direction, or change its shape. Flick a carrom striker and a coin at rest shoots off. Squeeze the brakes of a bicycle and it slows down. A goalkeeper's palm sends a football off at a new angle. A rolling pin flattens a ball of dough into a roti. Fig. 6.1 shows all four effects on one rubber ball.

Suppose a friend tells you, 'I pushed the box with 50 N.' Can you say where the box went? Not yet: you also need to know which way the push pointed. Every force you know has a direction built into it. The Earth's pull points down. Water pushes a floating bottle up. Friction always points against sliding. So a force is described fully only by its magnitude (how strong it is) together with its direction, just like displacement, velocity and acceleration in Chapter 4.

Forces are measured in newtons (symbol N), the SI unit named after Isaac Newton. Written out in full, the unit begins with a small letter: newton, not Newton.

6.1.1 Measuring the magnitude of a force

How strong is a push or a pull? To measure it we use a spring balance. Pull on its hook and the spring inside stretches: the harder the pull, the longer the stretch. A pointer moving along a scale marked in newtons shows how strong the pull is. Hang a bag of vegetables from the hook, and the pull being measured is the Earth's pull on the bag, its weight. Pull the hook with your hand, a rubber band or a toy car instead, and the balance reads that pull just as happily (Fig. 6.2).

6.2 Balanced and Unbalanced Forces

Look at a bicycle standing on its stand. The Earth pulls it down, yet it does not sink into the ground, because the ground pushes up on its tyres and stand. Two forces act on it at once, and they cancel out. Most objects around you are like this, with several forces acting on them together. What, then, decides how such an object moves?

Picture a supermarket trolley with one friend pushing it from the front and another from the back. If both push equally hard, the trolley stays where it is. Two forces that are equal in size but opposite in direction cancel each other: they are balanced forces (संतुलित बल). If one friend pushes harder, the forces become unbalanced, and the trolley rolls the way the bigger push points (Fig. 6.3).

The single force that has the same effect as all the forces together is the net force (परिणामी बल). For forces along one straight line, there are two cases. When two forces act in opposite directions, the net force equals the difference of their magnitudes and points along the bigger force. When they act in the same direction, the net force is their sum. Think of one person pulling a loaded handcart from the front while another pushes it from behind: their efforts add up.

6.3 The Force of Friction: Often Overlooked but Always Present

Why does a heavy sack of rice refuse to budge when you give it a gentle push? Where the sack rests on the floor, tiny bumps on the two surfaces catch on each other. This gives rise to friction (घर्षण), a force that always points against sliding. Push gently and friction pushes back just as hard, so nothing happens. Push harder and friction grows too, but only up to a limit. Beyond that limit your push wins, a net force acts forwards, and the sack starts to slide.

Draw every force on a crate being pulled along the floor and you find four, not two (Fig. 6.4). Two act along the floor: the rope's pull and friction. The other two act up and down. The crate's weight points down, and the floor answers with an upward push at right angles to its surface, the normal force (अभिलंब बल). The crate neither sinks into the floor nor jumps off it, so these two must balance. Air drag is a fifth force, but on a slow-moving crate it is tiny, so we leave it out.

A carrom coin after a good strike, a toy car you let go of, a football rolling over grass: each one slows down and stops on its own. It is tempting to conclude that motion needs a force to keep it going. In fact, each of them is being slowed by friction. To keep something moving steadily on Earth, you must push just hard enough to cancel friction. Take the push away, and friction is left alone to bring the object to rest.

Why does the eraser first speed up and then slow down? Count the horizontal forces at each stage (Fig. 6.5). Held at the mark, it feels the band pulling it forwards and your finger pushing it back, and these cancel. Lift your finger and only the band and friction remain; the band is stronger, so the net force points forwards and the eraser speeds up. A moment later the band straightens and loses touch with the eraser. Friction is now the only horizontal force. It points backwards, so the eraser's speed falls to zero.

6.4 Newton’s First Law of Motion

Galileo's idea became the first of Newton's three laws.

Read the law backwards and it gives a quick test. Whenever an object's velocity is not changing, whether it is parked or cruising straight and steady, the net force on it is zero, and so is its acceleration. A parked scooter stays parked. A train coasting on a perfectly straight, level and frictionless track would keep the same speed in the same direction for ever. Because it describes inertia, the first law is also called the law of inertia.

6.5 Newton’s Second Law of Motion

Starting, stopping, speeding up, slowing down and turning are all changes in velocity, and every change in velocity is an acceleration. So forces cause accelerations. But how exactly are the net force and the acceleration linked?

Both activities point to one rule: the second of Newton's laws, and one of the most useful ideas in all of physics.

Here $F$ is always the net force, not any single force, and the acceleration points the same way as the net force. With mass in kilograms and acceleration in $\mathrm{m}{\mathrm{s}}^{-2}$, the force comes out in newtons. Put $m=1\mathrm{k}\mathrm{g}$ and $a=1\mathrm{m}{\mathrm{s}}^{-2}$ into Eq. (6.2):

Let go of a stone and it falls faster and faster: the Earth's pull gives it an acceleration. This particular acceleration has its own name, the acceleration due to gravity, and its own symbol, $g$ (unit $\mathrm{m}{\mathrm{s}}^{-2}$). Put $a=g$ into Eq. (6.2) and you get the size of the Earth's pull on any mass $m$, which is its weight:

Measured anywhere near the ground, $g$ is about $9.8\mathrm{m}{\mathrm{s}}^{-2}$; it changes only slightly from place to place. In rough calculations, $10\mathrm{m}{\mathrm{s}}^{-2}$ is close enough.

The second law also explains why soft landings hurt less. To stop a moving object, you must bring its velocity down to zero. Doing that in a very short time means a large deceleration and so, by $F=ma$, a large force. Stretching out the stopping time makes the deceleration, and the force, much smaller (Fig. 6.9).

Check the numbers: each egg ($0.06\mathrm{k}\mathrm{g}$) loses $4\mathrm{m}{\mathrm{s}}^{-1}$. Over $0.004\mathrm{s}$ the deceleration is $1000\mathrm{m}{\mathrm{s}}^{-2}$, which needs about $0.06\times 1000=60\mathrm{N}$. Over $0.1\mathrm{s}$ it is only $40\mathrm{m}{\mathrm{s}}^{-2}$, about $2.4\mathrm{N}$. (These are average forces, ignoring the egg's small weight.)

This is why you pull your hands back as you catch a fast throw. Catch a water balloon at Holi with stiff arms and it bursts. Let your hands move back with it, and the same balloon slows down over a longer time, needs a smaller force, and survives. A fielder's 'giving' hands work the same way and also protect the fingers.

Sometimes we want a large force. A hammer head striking a nail stops in a tiny fraction of a second, so it presses on the nail with a very large force and drives it into the wood. The quicker the stop, the bigger the force.

6.6 Newton’s Third Law of Motion

So far we have followed one object at a time. But a force always comes from an interaction between two objects. Slap a table and your palm stings: while your hand pushes the table, the table pushes back on your hand. What happens to both objects in such an interaction?

A skateboarder kicks the road backwards with one foot and shoots forwards. Your own walking is the same trick, done more gently (Fig. 6.12). At each step your sole presses back against the ground. The ground presses forwards on your sole with an equal force, and that forward force is what carries you along. Notice what kind of force it is: friction. We usually think of friction as the force that stops things; in walking, it is the force that gets you going.

Experiments like these, repeated in endless variations, lead to Newton's third law.

Climbing a rope in a gym uses the same pairing: your hands and feet press down on the rope, and the rope presses you up. And now the shikara puzzle has an answer. The boatman's paddle shoves water towards the stern; the water shoves back on the paddle towards the bow, and the paddle is held by the boatman sitting in the boat. One force acts on the water, the other on the paddle, so there is nothing to cancel. Sweep harder, and the water's push on the paddle grows, so the boat gains speed faster. Load four tourists, and the same push must accelerate a much larger mass, so the speed rises more slowly (Section 6.5).

A rocket uses the same idea (Fig. 6.13). Its engines burn fuel and force huge amounts of hot gas downwards out of the nozzles. The gas pushes the rocket upwards with an equal force. When this upward push is bigger than the rocket's weight, the net force points up and the rocket lifts off the launch pad, as in the launches you may have watched from Sriharikota.

Must the two objects touch? No: the third law holds for non-contact forces too. Two magnets pull, or push, each other equally. A comb charged by rubbing it in dry hair attracts a scrap of paper, and the paper attracts the comb just as strongly. A coconut dropping from a palm is pulled down by the Earth, while the coconut pulls the Earth up with exactly the same force. Explore the magnets in Fig. 6.14.

6.7 Forces Acting on a System of Objects

At an airport, a porter hitches two luggage trolleys together with a short rope and pulls the front one. How quickly will the pair speed up? Call the mass of the front trolley $m_1$ and of the rear one $m_2$, and the porter's horizontal pull $F$. The floor is smooth enough for friction to be ignored (Fig. 6.15).

The rope is stretched, and a stretched rope pulls on whatever is tied to its ends. It tugs the rear trolley forwards and the front trolley backwards with equal forces. This pull is called tension, $T$; the two tugs are a third-law pair passed along the rope.

Now step back and look at both trolleys and the rope as one object, a system. Ask which forces come from outside it. Along the floor, only the porter's pull does: it is an external force. The two tension forces are exchanged between parts of the system, so they are internal; being equal and opposite, they add up to zero for the system. The whole pair, of total mass $m_1+m_2$, is therefore accelerated by $F$ alone:

Working with each trolley separately gives the same answer, only with more steps; the example below checks this. Up and down there are external forces too, but they cancel: the total weight $(m_1+m_2)g$ acting down is balanced by the floor's normal forces $N_1+N_2$ acting up.