Force and Motion

Ramesh’s house is at point A. His school is at point B, straight to the east. There are two paths. Path Y goes straight across the river, but its bridge has collapsed, so Ramesh walks the long, winding path X, round by the hill.

On path X, Ramesh keeps changing direction: north-east, then south, then east again. Path Y goes in one direction only, east, and it is the shortest way between the house and the school. However he gets there, Ramesh ends up in the same place: at the school, due east of his house.

So we have two different ways of saying “how far”:

• Distance is the total length of the path an object really travels, whatever its shape. Ramesh’s distance is the whole length of path X.
• Displacement is the shortest, straight-line distance from the starting point to the end point, in a particular direction. Ramesh’s displacement is the length of the straight line AB, towards the east.

Scalars and vectors

To tell someone a distance, a number with its unit is enough: “I walked 300 m.” A quantity that is complete with only its size (its magnitude) is called a scalar quantity, or a scalar. Distance is a scalar. Mass, time and speed are scalars too.

A displacement needs more: “300 m” is not enough, you must also say “towards the east”. A quantity that needs both a magnitude and a direction is called a vector quantity, or a vector. Displacement is a vector. Velocity and weight (a force) are vectors too.

	Distance	Displacement
Symbol	d	s
SI unit	meter (m)	meter (m)
Scalar or vector?	scalar	vector
Formula	distance = speed × time	displacement = velocity × time

Activity 6.2: Roshani walks round a rectangle

Roshani starts at corner A of a rectangle 3 m wide and 5 m long. She walks from A to B (3 m north), B to C (5 m east), C to D (3 m south), and D back to A (5 m west).

Answer the activity’s three questions:

Activity 6.3: distance and displacement side by side

Dolma walks from her house to her uncle’s house along the road (path A). The road is 1800 m long, and the walk takes her 30 minutes. In a straight line, her uncle’s house is 1200 m to the east (path B).

How fast did she walk? Divide the distance she covered by the time she took.

$$\text{speed} = \frac{\text{distance}}{\text{time}}$$

The time is 30 min = 30 × 60 s = 1800 s. So

$$\text{speed} = \frac{1800\ \text{m}}{1800\ \text{s}} = 1\ \text{m/s}$$

Dolma walked at 1 m/s: on average she covered 1 meter every second. The distance covered by an object in unit time (in one second) is called its speed. Speed is a scalar, and its SI unit is the meter per second (m/s).

Now use the straight line instead. Her displacement is 1200 m east, so

$$\text{velocity} = \frac{\text{displacement}}{\text{time}} = \frac{1200\ \text{m}}{1800\ \text{s}} = 0.67\ \text{m/s}$$

Her velocity is 0.67 m/s towards the east. The displacement of an object in unit time is called its velocity; it is the rate of displacement. Velocity is a vector, so it always has a direction. Its SI unit is also m/s.

A motorbike going round a roundabout at a steady 20 km/h has a constant speed, but its velocity keeps changing, because its direction keeps changing. That is why velocity needs its own name.

6.2.1 Numerical problems

Look at a waterfall. The water pours down. Drop a stone from a rooftop: it falls down too. Throw a ball up, and it slows, stops, and comes back down. Why does everything go the same way?

Isaac Newton, an English scientist, wondered about this around 1666. The story says he saw an apple fall from a tree. He realized that the Earth pulls the apple towards itself. The force of attraction with which the Earth pulls objects towards its center is called gravity.

Newton went further. He found that it is not only the Earth: every object in the universe pulls every other object towards it. This pull between any two objects is called the gravitational force, and it acts along the line joining their centers. The Earth pulls the Moon; the Sun pulls the Earth; even you and your friend pull on each other, but so weakly that you can never feel it. Only a huge object, like the Earth, pulls hard enough to notice.

What gravity does for us

• It holds the air (the atmosphere) around the Earth. Without gravity, the air would drift away into space.
• It makes rain, snow and hail fall to the ground, and makes rivers flow downhill.
• It keeps the Moon going round the Earth, and the Earth round the Sun.
• It gives every object its weight (next section).

Acceleration due to gravity

Drop a stone from a high window. It doesn’t fall at a steady speed: it goes faster and faster as it falls. The change in velocity of an object in unit time (one second) is called its acceleration. The acceleration produced in a falling object by the Earth’s gravity is called the acceleration due to gravity, written g.

Near the Earth’s surface, g is about 9.8 m/s². This means that a falling object (with no air to slow it) gets 9.8 m/s faster every second: 9.8 m/s after 1 second, 19.6 m/s after 2 seconds, 29.4 m/s after 3 seconds.

The force with which the Earth pulls an object towards its center is called the weight of the object. The more mass an object has, the harder the Earth pulls it, so the more it weighs.

Weight is a force, so its SI unit is the newton (N), and we measure it with a spring balance: the heavier the object, the more the spring stretches. Numerically, weight is the product of the object’s mass and the acceleration due to gravity:

$$\text{weight} = \text{mass} \times \text{acceleration due to gravity}, \qquad W = m \times g$$

A 1 kg bag of sugar weighs 1 × 9.8 = 9.8 N, about 10 N.

Numerical problems

Have you ever slipped while walking? Think of the place. Was the ground wet or dry? Smooth or rough? Did you step on something that rolled, like a pebble or a marble?

You slip most easily on surfaces that are wet, smooth, or covered in things that roll. On dry, rough surfaces, where nothing rolls, your feet grip. The force that grips, or holds you back, is friction.

Friction is the force that opposes (acts against) the motion when one surface moves, or tries to move, over another. It always acts in the direction opposite to the motion.

Why is there friction?

No surface is perfectly smooth. Even a surface that looks smooth, like a polished table, has tiny bumps (projections, raised parts) and dips (depressions, pressed-in parts). You can see them with a hand lens, and much better with a microscope. When one surface slides over another, their bumps catch on each other and hold back the motion. That is friction.

The amount of friction depends on:

1. the nature of the surfaces: friction is more between rough surfaces than between smooth ones;
2. the pressing force: the harder the surfaces are pressed together (a heavier load), the more the friction.

6.5.1 Advantages and disadvantages of friction

Why do you slip more when the pattern on the soles of your shoes or chappals has worn away? Could people and animals walk, or vehicles drive, if there were no friction?

Friction helps us.

• Walking: your feet push back on the ground, and friction stops them sliding. On smooth ice or a wet marble floor, there is too little friction, and you slip.
• Tyres: vehicle tyres have a pattern of grooves (the tread) to increase friction with the road, so they don’t skid.
• Brakes: when you brake a bicycle, the rubber brake pads rub on the wheel rim. Friction stops the bicycle. With no friction, nothing could ever be stopped.
• Holding things together: nails hammered into wood, and nuts and bolts, stay in place because of friction.
• Holding and writing: you can hold a glass, tie a knot, and write with a pencil on paper only because of friction.

Friction also causes problems.

• It turns energy of motion into heat. Rub your hands together hard and feel them warm up. In a machine, this heat is wasted energy, so the machine needs more effort to do the same job, and its efficiency goes down.
• It causes wear and tear: the moving parts of machines, the soles of shoes and the tyres of vehicles wear out by rubbing.

Because we can’t live without it, but it also wastes energy and wears things out, friction is called a necessary evil.

6.5.2 Measures of minimizing friction

Why do we put oil or grease on the hinges of a door and on the chain of a bicycle? Friction lowers the efficiency of a machine, so we reduce friction to make machines work better and last longer.

From these activities, the ways to reduce friction are:

1. Lubricants: oil, grease and mobil (engine oil) form a thin, slippery layer between moving parts, so the surfaces don’t grind against each other. Hinges, bicycle chains and engines are oiled.
2. Polishing: making the surfaces smoother.
3. Wheels and ball bearings: rolling causes far less friction than sliding. A ball bearing has small, hard steel balls between two rings; one ring turns over the balls with very little friction. Ball bearings are used in electric fans, electric motors, bicycle wheels and almost every machine that turns.
4. Streamlining: things that move fast through air or water are given a narrow, rounded front and a tapering back, so the air or water flows smoothly round them. This shape is called streamlined. Airplanes, rockets, ships, boats and fast trains are streamlined to reduce the friction of the air or water (called drag).

6.6.1 Work

Think of four people: a security guard standing at a gate all day, a girl reading a book, a man playing the madal, and a woman walking in a park. All of them may feel tired by evening. Which of them are doing work in the language of science?

In science, work has a special meaning. Work is done when a force moves an object in the direction of the force. Two things are needed:

1. a force must act on the object, and
2. the object must move in the direction of the force.

If either is missing, no work is done. The guard stands at his post for hours, and the girl sits reading, but nothing is moved by a force, so in science they do no work (thinking hard is not “work” in this sense, though it uses energy). The man playing the madal pushes the drumheads with his hands and moves them, and the woman in the park moves her own body forward, so they are doing work.

Work is measured as the product of the force and the distance moved in the direction of the force:

$$\text{work} = \text{force} \times \text{displacement}, \qquad W = F \times d$$

The SI unit of work is the joule (J), named after the English scientist James Prescott Joule. One joule of work is done when a force of 1 newton moves an object 1 meter in the direction of the force:

$$1\ \text{J} = 1\ \text{N} \times 1\ \text{m}$$

Lifting a 100 g apple (weight about 1 N) up 1 m takes about 1 J of work.

Work against friction

When we slide or roll an object along the ground, friction acts against the motion. To keep it moving, we must push or pull in the opposite direction to the friction. The work done is called work against friction. Pushing a cart, dragging a sack along the floor, sliding a box, and cycling along a road are examples.

work against friction = the force needed to overcome friction × the distance moved

Work against gravity

When we lift an object up, we must pull it upwards, against the downward pull of gravity. The work done is called work against gravity. Lifting a load, throwing a ball upwards, pulling up a bucket of water from a well, and climbing stairs or a hill (lifting your own body) are examples. The force needed is the object’s weight, and the distance that counts is the height it is lifted:

work against gravity = weight × height = m × g × h

6.6.2 Power

Suppose you have to go to a market far from your house. Which gets you there faster, a bicycle or a motorbike? Both can do the job, but the motorbike does it faster: it can do work at a faster rate.

Dataram digs a field in 3 hours. Sohan digs the same field in 2 hours. They have done the same amount of work, but Sohan did it in less time, so he did more work in each hour. We say Sohan has more power: a greater capacity to do work quickly.

The work done in unit time (in one second) by a person or a machine is called its power. Power is the rate of doing work:

$$\text{power} = \frac{\text{work}}{\text{time}}, \qquad P = \frac{W}{t}$$

The SI unit of power is the watt (W), named after James Watt, who improved the steam engine. Since work is in joules and time in seconds, power is in joules per second:

$$1\ \text{watt} = 1\ \text{joule per second}, \qquad 1\ \text{W} = 1\ \text{J/s}$$

A machine with a power of 1 W does 1 J of work in 1 s. If you know a machine’s power, you know how fast it can do a job: a 1000 W water pump fills a tank faster than a 500 W one.

Bigger units of power, and an old one:

Unit	In watts
1 kilowatt (kW)	1000 W = 10³ W
1 megawatt (MW)	1,000,000 W = 10⁶ W = 1000 kW
1 horsepower (hp)	about 746 W

1. Choose the correct answer

2. Fill in the blanks

Use these words: power, gravity, velocity, speed, friction, watt. (Two words are not needed.)

3. Answer the following questions

4. Solve these numerical problems

5. Write the differences

6. Give reasons