Class 9 Science Chapter 6: How Forces Affect Motion

A push or pull that can set a resting object going, change the speed or direction of a moving one, or change its shape. It needs a direction stated along with its magnitude.

The SI unit of force, written with a small letter and given the symbol N. The magnitude of a force expresses its strength.

Two forces equal in magnitude but opposite in direction. They leave the object as it was: a rope pulled equally hard from both ends does not move.

Forces that do not cancel, so a non-zero net force acts on the object and its state of motion changes.

The single force equivalent to all those acting. For two along the same line it is their sum if they point together, and their difference, in the direction of the larger, if they oppose.

A force can make an object move from rest, as when a ball lying still is kicked. It can change the speed and direction of a moving object, as when a cricket bat strikes the ball. And it can change the shape of an object, as when fingers squeeze a lemon.

Because force is a physical quantity for which direction has to be given alongside magnitude and unit, just as it is for position, displacement, velocity and acceleration. If either the magnitude or the direction changes, the effect of the force changes too.

The SI unit is the newton, written with a small letter and given the symbol N, and the magnitude of a force expresses its strength. A spring balance measures it: pulling on the free end gives the force with which the spring inside is being pulled.

Weight is the gravitational force with which the Earth pulls the object. Since a spring balance measures the magnitude of any force applied to it, and weight is simply one such force, the instrument reads it directly.

When both teams pull the rope with equal force, the two forces are equal in magnitude but opposite in direction, which makes them balanced forces, and the rope does not move. If one team pulls harder the forces are no longer balanced, a non-zero net force acts, and the rope travels towards the larger of the two forces.

If the two forces act in the same direction, the magnitude of the net force is the sum of their magnitudes and its direction is the same as theirs. If they act in opposite directions, the magnitude of the net force is the difference between their magnitudes and its direction is along the force of the larger magnitude.

With both acting towards the right, the net force is $10 + 6 = 16$ N towards the right. With 10 N right and 6 N left, it is $10 - 6 = 4$ N towards the right. With 10 N left and 6 N right, it is again $10 - 6 = 4$ N, but this time towards the left.

Along a single line they do cancel, which is what balanced forces means. Apply the pair at the two ends of something long, though, and what you get is a turn rather than a shift — which is exactly how a handlebar or a tap answers your hands. That case is taken up in higher grades.

What a force can do is start something that was standing still, alter how fast or which way something already travelling is going, or squash the thing out of its shape. Push a ball that is lying still and it sets off; meet a ball with a bat and it leaves in quite another direction than it arrived; close your fingers on a lemon and the lemon gives way.

Look back at how forces were described in earlier grades and one thing stands out: the direction was always specified. Friction pulls backwards along whatever path a body is taking. Magnets push apart at like poles and draw together at unlike ones. Like charges repel and unlike charges attract. The Earth attracts objects towards itself. A liquid exerts a buoyant force in an upward direction on anything placed in it.

So force is a physical quantity for which direction has to be specified along with magnitude and unit, exactly as it is for position, displacement, velocity and acceleration.

Force is measured in newtons in SI, the word spelt with a lower-case n and shortened to N; how large that number is says how strongly the force acts.

The reason direction matters is practical. If either the magnitude or the direction of a force changes, or both, the effect of the force changes too. Two forces of 10 N and 6 N can give a net force of 4 N pointing either left or right, depending only on which way round they are arranged.

In real life situations where only one force acts on an object are rare. Pushing a box across a surface brings friction into play in the direction opposite to the motion, and a ball floating on water has the Earth's gravitational force pulling it down while the liquid's buoyant force pushes it up.

The tug of war shows what happens when two forces meet. If both teams pull the rope with equal force it does not move. Two forces equal in magnitude, and opposite in their direction, are balanced forces, and both teams are still pulling hard even though nothing happens.

Let one side heave with more strength than the other and the balance is broken, so the rope travels the way the stronger side is pulling. So balanced pulls leave the rope where it is, and unbalanced pulls set it going.

Once the balance fails, what is left over acts on the body as a net force that is not zero. For two forces opposite in direction but unequal in magnitude, the magnitude of the net force equals the difference between the two magnitudes, and its direction is along the force of the larger magnitude.

Where two forces act in the same direction, as when two people push a stalled car, the magnitude of the net force is the sum of the two and its direction is the same as theirs.

Two forces of 10 N and 6 N act on a block lying on a table, and the question is the magnitude and direction of the net force in each of three arrangements.

In the first, both forces act towards the right. Since they point the same way their magnitudes add, giving a net force of $10 + 6 = 16$ N acting towards the right.

In the second, the 10 N force acts towards the right and the 6 N force towards the left. Opposing forces subtract, so the magnitude of the net force is $10 - 6 = 4$ N, and since the larger force points right, the net force acts towards the right.

In the third the arrangement is reversed, with 10 N towards the left and 6 N towards the right. The arithmetic is the same, giving 4 N, but the larger force now points left, so the net force acts towards the left.

Two lessons follow. The first is the pair of rules themselves: same direction add, opposite directions subtract with the larger setting the direction. The second is why direction has to be quoted at all, since the last two cases have net forces of identical magnitude that point opposite ways, and an answer of 4 N alone would not distinguish them.

The instrument is the spring balance, already familiar from measuring the weight of objects. Its wider use follows from one fact: weight is a force like any other, being the gravitational hold the Earth keeps on the body.

So the balance is not restricted to weighing. Take hold of a spring balance by its loose end and haul; the reading is the size of your own haul on the spring within. In that way the magnitude of a force in general can be read off.

The magnitude is expressed in the SI unit of force, the newton, which is written with a small letter and given the symbol N. What the magnitude tells you is the strength of the force.

As for how small a force can be, the smallest that a person can directly feel are of the order of millinewtons, which is $10^{-3}$ N, about what a light touch amounts to.

Scientists, however, can measure forces far smaller than anything a fingertip would notice. In specialised experiments they reach down to yoctonewtons, which is $10^{-24}$ N, twenty-one orders of magnitude below the threshold of human touch.

A force arising between two surfaces in contact, acting against the direction in which one is being pushed or is travelling. It is why a resting object often needs a larger push than expected.

The upward push exerted by a surface on an object resting on it, acting at right angles to that surface. It balances the object's weight.

The drag the surrounding air exerts on a moving object. In many everyday cases its size is so small that it can be neglected.

An experiment carried out in the mind, used when the conditions required are difficult or impossible to recreate in the real world, such as a surface with no friction at all.

That a body moving along a horizontal plane will continue to move indefinitely once all impediments to its motion are removed, overturning the older view that motion itself needs a force.

Because the force of friction arises between the bottom surface of the object and the floor, acting in the direction opposite to the applied force. The object only starts moving when the applied force is of larger magnitude than the friction, so that a net force acts in the direction of motion.

Four forces act: the applied push, the force of friction opposing it, the gravitational force which is the box's weight acting downwards, and the normal force exerted upward by the surface at right angles to it. The weight and the normal force are balanced, so the motion is decided by the applied force and friction alone.

A force must be applied continuously only to counter the force of friction. Leave friction unopposed and it works against the travel until the body stops. So the force is not maintaining the motion but cancelling what would destroy it.

Before release the stack is stationary, so the forces on it are balanced. On release your own force vanishes and the stretched band pushes the stack forward; since that push exceeds friction, a net force acts forward and accelerates the stack. Once the stack loses contact with the band, only friction acts, against the direction of motion, gradually decreasing the velocity until the stack comes to rest.

So that the launch is identical in every case and the only thing that differs is the surface. If the stretch varied, a difference in the distance travelled could not be attributed to a difference in friction.

The forces on the block are the spring's pull and friction. The reading is taken at the moment the block just starts moving, when its velocity is neither increasing nor decreasing, so the net force on it is zero. That means the pull and the friction are matched, and the reading therefore gives an approximate measure of the friction.

Weaker friction lets the stack's velocity die away more gradually, so it covers more ground before halting. The balance bears this out, reading lowest on whichever surface carried the coins furthest.

It is reasoning run in the mind, used where the setup wanted is hard or impossible to build, as a surface offering no friction at all would be. Arguing that way through a series of such experiments, Galileo Galilei reached a conclusion in the seventeenth century. A body travelling along a horizontal plane keeps going indefinitely once every impediment to its motion is taken away.

Suppose an object rests on the floor and a force is applied to it in the forward direction. Many a time the object does not move, and a larger force has to be applied before it does.

The reason is the force of friction, which arises between the bottom surface of the box and the floor and acts in the direction opposite to the applied force. Only when the push outweighs the friction does the box shift, because only then is there anything left over to act along the direction it goes.

Two further forces are present. One is the gravitational force, which is the object's weight, acting downwards. The second comes from whatever it is resting on, a push we call the normal force, directed straight up out of that surface at right angles. These two are balanced, which is why neither affects the sliding.

The air round the object exerts a force of friction too on it when it moves through the air, though in many cases the magnitude is so small that it can be neglected.

One rule covers the lot: however many forces are at work on a body, what its motion answers to is their sum and nothing else.

Four ten-rupee coins are stacked and secured with adhesive tape around the sides. A large strong rubber band is held slightly stretched between forefinger and thumb on a level wooden table top, with marks A and B made at its ends and a further mark C up to which the band will be stretched.

Holding the ends at A and B, the stack is placed near the middle and pushed back until the band is pulled to C. The stack is then released, and the distance it travels from C before coming to rest is measured and recorded, the step being repeated twice. The whole procedure is then repeated on a laminated table top and on a polished marble or tiled floor, with A, B and C kept at the same distances throughout.

Before release the stack is stationary, so the forces acting on it are balanced. On release, the force applied by your finger vanishes while the stretched band pushes the stack forward. That the stack moves shows the band's force is larger than friction, so a net force acts forward and provides an acceleration.

The moment the stack loses contact with the band, that forward force is gone, but friction continues to act against the motion, gradually decreasing the velocity until the stack stops. Since the stretch was identical each time and yet the distances differ, the friction offered by those surfaces must differ too.

A spring balance is placed horizontally on one of the surfaces used earlier and checked to read zero, and a wooden block is attached to its hook. The balance is then pulled with gradually increasing force, and the reading is noted at the moment the block just starts moving.

What that reading means follows from the forces at work. Only two act along the surface: the force applied by the spring and the force of friction. If the block's velocity is neither increasing nor decreasing, the net force on it must be zero, so the two are matched in magnitude. The reading therefore gives an approximate measure of the force of friction between the block's surface and the surface it moves on.

The step is repeated on the remaining three surfaces and the readings compared. A smaller reading indicates smaller friction and a larger reading larger friction.

The two activities can then be cross-checked. The reading should be smallest for the surface on which the coin stack travelled the largest distance, and largest for the surface on which it travelled the smallest.

Taken together they establish the conclusion: when friction is smaller, the velocity decreases more slowly and the object travels further before coming to rest.

A thought experiment is carried out when the conditions required for a real experiment are difficult to recreate in the world. Here the condition wanted is an object and a horizontal floor so smooth that the force of friction between them is zero, which cannot be built. The questions to ask of it are whether the object's velocity would decrease at all, and whether it would ever come to rest or continue moving forever.

That question mattered because of an old mistake. The ancients had no doubt that it took a force to start something standing or to halt something running, and in both they were right.

But it was also asked whether a force was required to keep an object moving with a constant velocity, and for ages it was mistakenly thought that one was. Everyday evidence seemed to agree, since moving things really do stop unless something keeps pushing them.

The hidden cause was friction, which is present in every real case and easily overlooked. Activity 6.1 makes it visible: the less friction a surface offers, the further the coins run and the more gently their velocity falls away.

Not until the 1600s did Galileo Galilei reason his way, by one thought experiment after another, to this: take a body travelling on a level surface, strip away everything that hinders it, and it will go on without end.

A body stays at rest, or keeps travelling at a constant velocity, for as long as no net force acts upon it.

Velocity whose magnitude and direction both stay the same. A non-zero constant velocity means straight-line travel one way at an unchanging speed.

The condition where all the forces on a body cancel. The body's acceleration is then nil, so it cannot start moving or change the velocity it has.

The name Newton gave to the tendency of objects to resist a change in their state of rest or of uniform motion. He built the first law around this idea.

Two cases only. At rest gives a level position-time line and a velocity-time line along the axis; constant velocity gives a sloping position-time line and a level velocity-time line.

A body stays at rest, or keeps travelling at a constant velocity, for as long as no net force acts upon it. The same thing said from the force's side: where the net force works out at zero, the body can neither set off nor alter the velocity it has, and its acceleration is nil.

Constant velocity means there is no change in either the magnitude or the direction of the velocity. So a non-zero constant velocity is motion in a straight line, in the same direction, with the magnitude unchanged. A vehicle rounding a bend at a fixed speedometer reading has a changing direction, so its velocity is not constant even though its speed is.

No. Friction acts on the box in the backward direction, so the two forces are equal and opposite and balance each other. The net force on the box is zero, and by Newton's first law of motion the box continues moving with constant velocity.

Its position does not change with time, so the position-time graph is a level line. Its velocity remains zero throughout, so the velocity-time graph is a line running along the time axis.

It continues moving with the same velocity, so the velocity-time graph is a level line at that value. Since equal intervals of time carry equal changes of position, the position-time graph is a straight sloping line.

Inertia is the name for an object's reluctance to have its state altered, whether that state is rest or steady travel, and Isaac Newton built his first law around the idea. He set out two further laws alongside it in 1687, and framing the three was a turning point in the story of science.

A net force would still be needed to set an object at rest moving, to change its velocity in magnitude or direction, and to stop it once it is moving. The one case needing no force at all is keeping a moving object going at constant velocity.

Nowhere in the world will you find a body that nothing at all acts upon. But by applying additional forces, a condition can be reached where the net force works out at zero. Pushing a moving box forward with exactly the force that friction exerts backward is such a case: friction is still acting, but it has been cancelled rather than removed.

By the law, whatever is still stays still and whatever is travelling keeps its velocity unaltered, until some force left over after cancellation acts on it.

Turn it round: let the forces on a body add to nothing and it can neither set itself going nor alter the velocity it has, which is to say its acceleration is nil. The two statements say the same thing.

The first half needs little unpacking: an object at rest simply means one whose velocity is zero.

The second half needs more. Constant velocity means nothing changes in either the magnitude or the direction of the velocity. Where that unchanging velocity is not itself zero, the travel is dead straight, always one way, and at a speed that never varies from start to finish.

That qualification matters in practice. A vehicle going round a bend at a fixed speedometer reading is not moving at constant velocity, since its direction is changing, so the law's condition is not met and a net force must be acting on it.

Notice too what the law covers. Rest and steady motion are, as far as it is concerned, the same situation, since neither involves a net force, which is why a single law handles both.

When no net force acts on an object there are exactly two possibilities: either the object is at rest, or it is moving with a constant velocity. Each has its own pair of graphs.

Take the object at rest first. Its position will not change with time, so its position-time graph is a level line. Its velocity will remain zero, so its velocity-time graph is a line running along the time axis.

Now take the object moving at constant velocity. Since no net force acts on it, it will continue moving with the same velocity, so its velocity-time graph is a level line drawn at that value. Equal intervals of time then carry equal changes of position, so its position-time graph is a straight sloping line.

One detail deserves attention. A level line appears in both cases, but it means opposite things. Level on a position-time graph shows an object that is not moving at all, while level on a velocity-time graph shows one moving steadily and not changing its velocity.

The habit that prevents the error is to check which quantity has been put up the vertical axis before reading any shape at all.

Nowhere in the world will you find a body that nothing acts upon. Gravity and friction are present almost everywhere. But a condition can still be reached where the net force works out at zero, by applying additional forces that cancel those already present.

The case worked through is a box already travelling, with someone pushing it forward by exactly as much as the friction under it resists.

Friction acts on the box in the backward direction. The two forces are therefore equal in magnitude and opposite in direction, so they balance each other and the net force acting on the box is zero.

By Newton's first law of motion it follows that the box will continue moving with constant velocity. It will not speed up, and it will not slow down, for as long as that balance is maintained.

The important point is what has and has not happened to the friction. It has not been removed, and it is still acting on the box every moment. It has simply been cancelled by an equal force the other way, which is how a zero net force is arranged in a world where forces cannot be switched off.

The name Isaac Newton gave to a body's unwillingness to have its rest or its steady travel interfered with was inertia, and on that notion he built the first of his laws. Two further laws came with it, published in 1687, and between them the three marked one of the great turning points science has had. It is his name the unit of force carries, and the convention for any unit named after a person is a small letter in the spelt-out word against a capital in the symbol: newton, but N.

What the first law settles is when a force is needed and when it is not. Suppose the force of friction were zero. A net force would still have to be applied to an object at rest in order to set it moving, since starting is a change.

Once it is under way, though, nothing more need be supplied for it to hold a steady velocity. Continuing is not a change, and the law says plainly that nothing is needed to sustain it.

A force is called for again only to change the velocity, in magnitude or in direction, or to stop the moving object altogether.

So of the four situations, three need a force and one does not, and the one that does not is the one everyday experience makes hardest to believe.

A net force accelerates an object along its own direction, by an amount proportional to that force and inversely proportional to the object's mass.

The law written in symbols, equivalently $a = \frac{F}{m}$. The acceleration always points the same way as the net force.

Whatever it takes to make a 1 kg mass gain speed at $1\ \text{m s}^{-2}$, which comes to $1\ \text{kg m s}^{-2}$.

The acceleration of an object falling under the Earth's pull, close to $9.8\ \text{m s}^{-2}$ near the surface. It does not depend on the object's mass, and the force on a mass $m$ is $F = mg$.

The product of an object's mass and its velocity, pointing the way the velocity does. The fuller form of the second law is stated as the rate of change of momentum.

First, that with one and the same object a bigger force yields a bigger gain of speed and a gentler one a smaller gain. Second, that with one and the same force a lighter object gains speed faster and a heavier one more slowly.

A thread attached to the front of the cart passes over a piece of pipe at the far end of the table and carries a paper cup. When the system is released, the cup moves down under the Earth's gravitational force on it, and the thread pulls the cart with a constant force. Loading the cup with different amounts supplies forces of different magnitudes.

Both runs start from rest and cover the same distance $s$, so $s = \frac{1}{2}a_1T_1^2$ and $s = \frac{1}{2}a_2T_2^2$. Equating the two right-hand sides gives $\frac{a_2}{a_1} = \frac{T_1^2}{T_2^2}$, so the two times are enough to compare the two accelerations.

When a net force acts upon an object, that object accelerates along the direction of that force, with a magnitude proportional to the force and inversely proportional to the mass. In symbols, $a = \frac{F}{m}$, or equivalently $F = ma$.

One newton is the force that produces an acceleration of $1\ \text{m s}^{-2}$ on an object of mass 1 kg, which works out as $1\ \text{kg m s}^{-2}$. For a feel of its size, the upward force your palm applies when holding a 100 g mass is around one newton.

The net force is $55 - 50 = 5$ N, so the acceleration is $a = \frac{5}{25} = 0.2\ \text{m s}^{-2}$. Starting from rest, $s = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2} \times 0.2 \times 4 = 0.4$ m in the forward direction.

Doing so increases the time over which the ball's high velocity is reduced to zero. Since the same change of velocity now takes longer, the magnitude of the acceleration is smaller, and by $F = ma$ a smaller force is needed to stop the ball. Applying a smaller force to the ball also minimises injury to the fielder.

By the equation, doubling the force should have doubled the acceleration and doubling the mass should have halved it. The measured values fall a little short of that, partly because of measurement errors and partly because of the friction between the cart's wheels and the surface, which the analysis does not allow for.

Both use the same apparatus. A cardboard box is fitted with two pencils pushed through its sides as axles, with a ball-bearing wheel on each free end. A thread from the front of the box passes over a piece of pipe at the far end of the table and carries a paper cup. As the system is released, the cup descends under the Earth's gravitational force and the thread pulls the cart with a constant force.

In the first activity the cart is released from a start line and filmed in slow motion until it reaches the pipe, and the difference between the release and arrival times is recorded as $T_1$. The load in the cup is then doubled and the run repeated to give $T_2$.

Since both runs start from rest and cover the same distance, $s = \frac{1}{2}a_1T_1^2$ and $s = \frac{1}{2}a_2T_2^2$, so $\frac{a_2}{a_1} = \frac{T_1^2}{T_2^2}$. Put the measured times in and the acceleration is seen to climb with the force: hold the mass fixed and the harder you push, the harder it accelerates.

The second activity keeps the cup's load constant and doubles the mass of the cart instead. The acceleration drops off: keep the push the same and what you get falls away as the mass rises.

Together the two results are exactly what Newton's second law states.

Whatever is left over after the forces cancel sends the body accelerating the way it points, and how big that acceleration is goes up with the force and down with the mass.

In symbols this is $a = \frac{F}{m}$, or equivalently $F = ma$, where $a$ is the acceleration, $F$ the net force and $m$ the mass. The direction of the acceleration is the same as that of the net force.

The unit of force follows directly. Taking mass in kilograms and acceleration in metres per second squared, put $m = 1$ kg and $a = 1\ \text{m s}^{-2}$ into the equation to get $F = 1\ \text{kg m s}^{-2} = 1$ N. So one newton is the force that produces an acceleration of $1\ \text{m s}^{-2}$ on an object of mass 1 kg.

Applying the law to a falling object gives another standard result. The acceleration of an object falling under the Earth's gravitational force is written $g$, measured in $\text{m s}^{-2}$ like any acceleration, so the gravitational force on a mass $m$ is $F = mg$.

Near the Earth's surface $g = 9.8\ \text{m s}^{-2}$ and may be treated as nearly constant, with $10\ \text{m s}^{-2}$ used for quick estimates. Importantly, $g$ itself does not depend on the mass of the object.

All three turn on the same relation. A given change of velocity spread over a longer time means a smaller acceleration, and by $F = ma$ a smaller force. Squeeze the same change into a shorter time and the force becomes large.

A fielder catching a fast-moving ball pulls their hands backwards with the ball just after catching it. That increases the time over which the ball's high velocity reduces to zero, reducing the magnitude of its acceleration, so a smaller force is needed to stop it. Applying a smaller force to the ball also minimises injury to the fielder.

Airbags work for the same reason. In a collision the vehicle comes to an abrupt halt, and the bag inflates quickly into a soft compressible cushion. Head and chest sink into the bag rather than meeting wheel or dashboard bare, which stretches out the time the stopping takes. A gentler acceleration means a gentler force on the body, and less chance of grave injury, more so again when the belt is worn.

The coconut is the same principle in reverse. Sent fast onto something hard, it is brought to a standstill almost at once. A velocity killed that abruptly calls for an enormous push from the ground, and the shell is not built to take it.

Each interval is read from the shape of the graph and then turned into a force with $F = ma$.

Between 0 and 5 s the graph is a straight line inclined to the time axis, which indicates constant acceleration, with $u = 0$, $v = 10\ \text{m s}^{-1}$ and $t = 5$ s. Using $v = u + at$ gives $10 = 0 + 5a$, so $a = 2\ \text{m s}^{-2}$. Then $F = ma = 1500 \times 2 = 3000$ N, acting towards the east.

Between 5 and 10 s the graph is a straight line parallel to the time axis, which indicates constant velocity. With no acceleration there is no net force, so no force is acting on the car.

Between 10 and 15 s the graph is inclined again, with $u = 10\ \text{m s}^{-1}$, $v = 0$ and $t = 5$ s. Using $v = u + at$ gives $0 = 10 + 5a$, so $a = -2\ \text{m s}^{-2}$, and $F = 1500 \times (-2) = -3000$ N.

The negative sign is not an error. It shows the force acts in the direction opposite to the motion, which for a car travelling east means the force points west.

Whenever one object pushes or pulls on another, the second pushes or pulls back on the first at that very moment, equally hard and in exactly the opposite direction.

The two forces of a third-law pair act on two different objects. Only two equal opposite forces acting on the same object would balance each other.

The equal and opposite pull that two connected boxes exert on each other through the string joining them. Within a system it counts as an internal force.

Two or more connected objects treated as one. Internal forces may then be ignored entirely, and only the external forces need be considered.

The paired forces are always equal in magnitude, but the accelerations they produce need not be, since the two objects may have very different masses.

Sitting on a wheeled chair with the legs raised off the floor, a person pushes a heavy table away. The chair rolls backwards; pulling the table towards them sends the chair the other way. The conclusion is that each time a force was applied on the table, the table applied an equal force back on the person in the opposite direction.

You push the ground backwards with your feet, and the ground applies an opposite force on your feet that moves you forward. The force the ground applies comes in the form of friction, so here friction helps you move rather than opposing you. With no friction the foot would slip backwards as it pushed and you would fall.

Whenever one object exerts a force on a second, the second simultaneously exerts an equal and opposite force on the first. The two forces always occur in pairs, but they act on two different objects, which is why neither cancels the other. Only two equal and opposite forces acting on the same object would balance.

Two identical spring balances are laid horizontally and connected by their hooks, with one free end fixed and the other pulled. The two readings come out the same every time, and repeating with different pulls gives the same result, which indicates that the forces the balances apply on each other in opposite directions are equal in magnitude.

The engine makes gas and hurls it downward, and by the pairing rule that gas presses back up on the rocket just as hard. Since that upward press outweighs what the rocket weighs, something is left over acting upward, and the rocket climbs.

Because acceleration is the force divided by the mass. The forces are equal in magnitude, but the mass of the Earth is so large compared with the fruit that the acceleration the Earth gains from that force is extremely small, far too small to be noticed.

By the third law the recoil force on the gun is also 2 N. The gun's acceleration is $\frac{2}{5} = 0.4\ \text{m s}^{-2}$ and the bullet's is $\frac{2}{0.1} = 20\ \text{m s}^{-2}$. Even though the paired forces are equal in magnitude, the accelerations differ because the masses differ.

Box 1 and Box 2 pull on each other through the string with equal and opposite forces called the tension. If the two boxes and the string are treated as a single system, that tension becomes an internal force and need not be considered at all, leaving only the external force $F$. The acceleration is then $a = \frac{F}{m_1 + m_2}$, so the pair behaves just like a single object of the combined mass.

The law holds that whenever one object exerts a force on a second object, the second simultaneously exerts an equal and opposite force on the first.

The first activity shows the pairing. Sitting on a wheeled chair with the legs raised clear of the floor, a person pushes a heavy table away and the chair rolls backwards; pulling the table instead sends the chair forwards. Each time a force went onto the table, the table put one back the opposite way. Raising the legs matters, since it leaves the table as the only thing being interacted with.

The second activity shows the equality. Two identical spring balances are laid flat and hooked together, one end held fixed and the other pulled. The readings match every time, however hard the pull, which indicates that the forces they apply on each other in opposite directions are equal in magnitude.

The crucial point is stated as a note: the forces always occur in pairs, but the two act on two different objects. That is why they do not cancel and why anything is able to move at all.

Only two equal and opposite forces acting on the same object balance each other. A canoeist's paddle pushing water and the water pushing the paddle are not such a case, since one acts on the water and the other on the paddle.

All three work the same way: push something backwards and it pushes you forwards.

When you walk or run you push the ground backwards with your feet, and the ground applies an opposite force on your feet that carries you forward. What is notable is the form that return force takes: it comes as friction, so here friction helps you move rather than opposing you. Without friction the push of your foot would send it sliding backwards and drop you where you stood. That is why soles are moulded with grooves and tyres cut with treads, and why a wet polished floor, ice, or a road under snow is treacherous.

The paddle drives water astern and the water drives the paddle ahead by the same amount. Equal as they are, the two land on separate bodies, one on the water and one on the paddle, so there is no question of their cancelling. The force on the paddle drives the paddle and the canoe forward, and pushing harder makes that forward force larger, so the canoe speeds up.

A rocket's engine produces gas and expels it downwards, and the gas exerts an equal and opposite force upward on the rocket. That upward force exceeds the rocket's weight, so the net force is upward and the rocket lifts off. Fired in the direction of motion instead, the same arrangement slows a craft down, which is how the Vikram lander of Chandrayaan-3 reached the velocity it needed for a soft landing.

The third law fixes the forces but says nothing about what those forces do. That is settled by the second law, in which the acceleration is the force divided by the mass. So equal forces on unequal masses give unequal accelerations.

The first example is a falling fruit. Fruit and Earth pull on one another gravitationally, and by precisely the same amount each way, yet it is only the fruit anyone sees move. The reason is that the mass of the Earth is so large compared with the fruit that the acceleration it gains from that force is extremely small, too small to be noticed. The Earth does move; the effect is simply invisible.

The second example is a gun. A gun of 5 kg fires a bullet of 0.1 kg under a force of 2 N. By the third law the recoil force on the gun is also 2 N, so both objects feel exactly the same force.

For the gun, the acceleration is $\frac{2\ \text{N}}{5\ \text{kg}} = 0.4\ \text{m s}^{-2}$. For the bullet, it is $\frac{2\ \text{N}}{0.1\ \text{kg}} = 20\ \text{m s}^{-2}$, fifty times as large.

The general point follows: the pair are matched in size every time, but the accelerations they produce usually are not, for the plain reason that the two bodies rarely weigh the same.

Newton's laws have so far been applied to a single object. The question is whether they can handle two or more objects connected together.

Put two boxes, $m_1$ and $m_2$, on a level frictionless surface with a string between them, and haul Box 1 rightward with a force $F$. Through the string Box 1 acts on Box 2, and by the third law Box 2 acts back along the string on Box 1 with as much force the other way. That force is called the tension, $T$. On Box 1 the force $F$ acts right while $T$ acts left; on Box 2, $T$ acts right.

One approach is to work out the net force on each box separately and apply the second law to each. A simpler way is to treat the two boxes and the string as a single system. Then the forces within the system, the internal ones, need not be considered at all, and only the forces acting from outside matter. Here the tension is internal and $F$ is external.

So the acceleration of the system is $a = \frac{F}{m_1 + m_2}$, and the pair accelerates just like a single object of the combined mass. Analysing the boxes individually gives the same answer.

Besides $F$, the external forces are the combined weight $(m_1g + m_2g)$ downwards, balanced by the combined normal force $(N_1 + N_2)$ from the ground.

A force can make an object move from rest, as when a ball lying still is kicked. It can change the speed and direction of a moving object, as when a cricket bat strikes the ball. And it can change the shape of an object, as when fingers squeeze a lemon.

Because force is a physical quantity for which direction has to be given alongside magnitude and unit, just as it is for position, displacement, velocity and acceleration. If either the magnitude or the direction changes, the effect of the force changes too.

The SI unit is the newton, written with a small letter and given the symbol N, and the magnitude of a force expresses its strength. A spring balance measures it: pulling on the free end gives the force with which the spring inside is being pulled.

Because the force of friction arises between the bottom surface of the object and the floor, acting in the direction opposite to the applied force. The object only starts moving when the applied force is of larger magnitude than the friction, so that a net force acts in the direction of motion.

Four forces act: the applied push, the force of friction opposing it, the gravitational force which is the box's weight acting downwards, and the normal force exerted upward by the surface at right angles to it. The weight and the normal force are balanced, so the motion is decided by the applied force and friction alone.

A force must be applied continuously only to counter the force of friction. Leave friction unopposed and it works against the travel until the body stops. So the force is not maintaining the motion but cancelling what would destroy it.

A body stays at rest, or keeps travelling at a constant velocity, for as long as no net force acts upon it. The same thing said from the force's side: where the net force works out at zero, the body can neither set off nor alter the velocity it has, and its acceleration is nil.

Constant velocity means there is no change in either the magnitude or the direction of the velocity. So a non-zero constant velocity is motion in a straight line, in the same direction, with the magnitude unchanged. A vehicle rounding a bend at a fixed speedometer reading has a changing direction, so its velocity is not constant even though its speed is.

No. Friction acts on the box in the backward direction, so the two forces are equal and opposite and balance each other. The net force on the box is zero, and by Newton's first law of motion the box continues moving with constant velocity.

First, that with one and the same object a bigger force yields a bigger gain of speed and a gentler one a smaller gain. Second, that with one and the same force a lighter object gains speed faster and a heavier one more slowly.