Why Does a Rolling Ball Stop?

Roll the same ball, just as hard, on three different floors.

• On long grass, it stops after a few meters.
• On a concrete yard, it rolls much farther.
• On a smooth tiled floor, it goes farther still.

The ball is the same, and you gave it the same start. So the difference must come from the ground. Grass blades bend under the ball and drag on it. Concrete is rough, and the ball and the ground squash a little where they touch. A smooth tile drags much less. You met this rubbing force in Grade 7: friction. The air also pushes back a little on anything moving through it: air resistance.

You know this from carrom, too. Players sprinkle fine powder on the board so the striker and coins slide farther. The powder doesn’t push the coins along. It just makes the friction smaller.

So here is a question. What if you could take friction away completely? Make the floor smoother and smoother, and the ball rolls farther and farther. On a floor with no friction and no air, how far would it roll?

So a rolling ball doesn’t stop because it “runs out of push”. It stops because forces act against its motion: friction from the ground and resistance from the air. Take those away, and it would go on for ever at the same speed, in the same direction.

That isn’t just an idea. Spacecraft show it every day. Far out in space, with no ground and almost no air, a spacecraft with its engines off keeps moving for years. Nothing rubs on it or pushes back, so it doesn’t slow down by itself: only the pull of the Sun or a planet changes its motion.

You learned in Grade 6 that a force is a push or a pull, and that it can start a thing moving, stop it, speed it up, slow it down, or turn it. Forces are measured in newtons (N), with a spring balance. A 100 g packet of biscuits weighs about 1 N.

A force has a size (how many newtons) and a direction (which way it pushes). So we draw a force as an arrow: it points the way the force pushes or pulls, and the longer the arrow, the bigger the force. A drawing of all the forces on one thing, as arrows, is a force diagram.

Adding up forces

Usually more than one force acts on a thing at once. What happens to it depends on all of them together.

In Bisket Jatra, people from the upper part of Bhaktapur and from the lower part pull the great chariot of Bhairab in opposite directions, each side trying to drag it to their own part of town. Which way does it go?

Forces along one line add up like this:

• Forces in the same direction add together. Two friends each pushing a cart forward with 50 N push it with 100 N.
• Forces in opposite directions take away from each other. The bigger one wins, by the difference.

The one force that has the same effect as all the forces together is the net force (also called the resultant force): the sum of the forces, counting their directions.

To add forces in opposite directions without getting muddled, pick one direction to call positive, say to the right (or east, or forward). A force that way is +, and a force the other way is −. Then just add the numbers. The answer’s sign tells you the net force’s direction.

When the forces on a thing add up to zero, they are balanced. When they don’t, they are unbalanced, and the net force has a size and a direction.

Here is the big idea of this topic:

• Balanced forces don’t change a thing’s motion. If it was still, it stays still. If it was moving, it keeps moving at the same speed in the same direction.
• Unbalanced forces change its motion. It speeds up, slows down, or changes direction, in the direction of the net force. A net force forwards speeds it up; a net force backwards slows it down.

Think about riding a bicycle. When you start, you pedal hard: the forward push is bigger than the forces holding you back, so you speed up. As you go faster, the air pushes back harder. Soon the backward forces grow until they are as big as your forward push. Now the forces balance, and you go on at a steady speed. Stop pedaling, and only the backward forces are left: you slow down.

A fruit seller pushes his cart (a thela) to the market each morning. Empty, it is easy to get moving. Loaded with 150 kg of oranges, it is hard work to start, and just as hard to stop once it is rolling. The push is the same; what changed is how much stuff it has to move.

How much matter a thing has is its mass, measured in kilograms (kg). The more mass a thing has, the more force it takes to change its motion by the same amount: to start it, stop it, speed it up or turn it. Every grown-up who has push-started a car with a flat battery knows this. It takes two or three people to get the car rolling, but once it is rolling at a walking pace, one person can keep it going: now the push only has to balance the friction.

How much change?

Scientists measured exactly how a thing’s motion changes. You met acceleration in Grade 8: how much the speed changes every second Grade 8: Acceleration. Experiments like the one you will plan below show two simple rules:

• With the same mass, twice the net force gives twice the acceleration. Three times the force, three times the acceleration.
• With the same net force, twice the mass gives half the acceleration. Three times the mass, a third.

Both rules fit into one sentence:

$$\text{acceleration} = \frac{\text{net force}}{\text{mass}}$$

with the net force in newtons, the mass in kilograms, and the acceleration in m/s² (the change in speed, in m/s, every second). In fact, that is how the newton was chosen: 1 N is the force that makes 1 kg speed up by 1 m/s every second.

This is a preview: in Grade 9 you will meet the same rule as Newton’s second law, written F = ma Grade 9: Newton’s second law. For now, a few short calculations are enough to see how it works.

If the net force is backwards, against the motion, the same rule tells you how fast the thing slows down.

The rules above are claims. How could you test them yourself? Scientists answer a question like this with an investigation, planned before anything is measured. Here is how to plan one.

The question: does the change in a trolley’s motion depend on the force pulling it, and on its mass?

1. What will you change? This is the independent variable. Change only one thing at a time (you met the fair test in Testing fairly). First, change the pulling force and keep the mass the same. Then, in a second set of runs, change the mass and keep the force the same.
2. What will you measure? This is the dependent variable: something that shows the change in motion. The easiest is the time the trolley takes to cover 1 m from rest. A shorter time means a bigger change in motion.
3. What will you keep the same? These are the controlled variables: the same trolley, the same floor (so friction stays the same), the same 1 m, starting from rest every time, the same way of pulling.
4. What tools do you need? A trolley (or a toy truck that rolls easily), rubber bands for the pull, a ruler, a tape measure, a stopwatch (a phone has one), and loads of known mass.
5. How will you record it? A table with a column for what you changed and a column for each time you measured.
6. How many data? At least three different values of what you change, and three runs of each, to find an average. If one run is very different from the other two, do it again.

Try it first on the screen. The trolley here has 1 kg packets to load it with, and each rubber band, stretched to the mark, pulls with 1 N. A speed gate at the 1 m mark measures how fast it is going, and from the time and the speed you get its acceleration (from rest, the acceleration is the speed ÷ the time).

What you should find:

• With the mass kept the same, more force gives a bigger change in motion. The points lie on a straight line through zero: twice the force, twice the acceleration.
• With the force kept the same, more mass gives a smaller change in motion: twice the mass, half the acceleration.

That is the evidence for the rule. A real trolley gives slightly smaller numbers than the screen, because a little friction always pulls back on it (the screen’s trolley has none). That doesn’t spoil the test, as long as the friction is the same in every run.

You learned in Grade 8 that whether something is moving depends on what you compare it with, your reference point Grade 8: Rest, motion and the reference point. This matters for forces too.

A ball lies on the floor of a bus driving at a steady speed. The driver brakes hard. The ball rolls towards the front of the bus. Did a force push it forwards?

No. Watch from the roadside. Before the braking, the ball was moving along with the bus. When the bus slows, the floor can drag back on the ball only a little, because the ball rolls freely. So the ball keeps going at nearly the same speed, slowing only a little, while the bus slows down a lot under it. The ball doesn’t speed up at all; the bus falls behind.

So the rules of this topic work when you measure motion compared with the ground (or with anything moving steadily in a straight line, like a bus at a steady speed). Inside a bus that is speeding up, slowing down or turning, things seem to start moving with no force on them. They aren’t really: the bus is changing its motion around them.

• Who Feels the Bigger Push in a Crash? When two things collide, they push on each other equally hard, but the one with less mass has its motion changed more.
• How Can Something Push Without Touching? Magnets, electric charges and gravity push and pull across empty space.
• Why Is Speeding So Dangerous? The faster a thing moves, the more energy it carries, and the farther it goes before friction can stop it.