CBSE Class 6 Science Advanced Physics Motion and Measurement of Distances Notes Set 01

Motion and Measurement of Distances

Transportation

Carrying people or goods from one place to another is called transportation. Trade cannot take place without it, because goods must reach buyers. Very early humans simply walked and carried their things. Around 5000 BC they began to make animals pull and carry loads. Wagons and sailing ships came later. Loads were first dragged along the ground, then placed on sledges made of logs and poles. On water, people tied logs or reeds into rafts, then hollowed logs into canoes that were moved with hands or poles, and these slowly developed into boats. Early boats were weak and could be used only on rivers and lakes.

Examples of modes of transport: on land (cart, cycle, car, train), on water (raft, canoe, boat, ship) and in air (aeroplane, helicopter).

Physical Quantities and Units

A physical quantity is anything studied in physics that can be measured, for example length, mass and time. To measure it, we compare it with a known quantity of the same kind. This known quantity is called a unit. Kilogram, second and metre are units of mass, time and length.

History of Length Measurement

In ancient times people used parts of their own body as measuring units: the hand span (from the tip of the thumb to the tip of the little finger of a fully opened hand), the cubit (from the tip of the middle finger to the elbow), the foot, the stride, the fathom and the yard. Because body sizes differ from person to person, such units gave different values for the same object, so they were not dependable.

Standard Units

A standard unit has a fixed value that does not depend on the person or the place. The metric system, created in France in 1790, is a set of standard units. Even so, different countries used different standard units (for example gram and pound for mass). To solve this, the General Conference on Weights and Measures adopted the SI system in 1960. SI stands for Système International d'Unités (International System of Units). Its base units of length, mass and time are the metre (m), the kilogram (kg) and the second (s). Other familiar units of length are the inch, millimetre, centimetre and kilometre.

Choosing a Suitable Unit and Converting

The unit should suit the size of the object: metre for a piece of cloth, kilometre for the distance between places, millimetre for the thickness of a hair. Converting between units of length means multiplying or dividing by 10, 100, 1000 and so on.

1 km = 1000 m; 1 m = 100 cm; 1 m = 1000 mm. Units smaller than a metre are its sub-multiples, and units bigger than a metre are its multiples.

Ladder of conversions: 10 mm = 1 cm, 10 cm = 1 dm, 10 dm = 1 m, 10 m = 1 dam, 10 dam = 1 hm, 10 hm = 1 km.

Measurement of Length

The length of an object is the distance between its two ends. A ruler, a measuring tape or a metre rod can be used, whichever suits the job.

Using a Ruler: Precautions

1. Place the ruler along the length of the object, in line with it.
2. If the end of the ruler is broken or worn, start from some other clear mark, and subtract that starting reading from the final reading.
3. Keep the eye exactly above the point where the reading is taken, so that the reading is not tilted.

Activity: measuring the height of a person. Make your friend stand straight, without shoes, with the back against a wall. Hold a thick flat book on the head and mark the wall at the lower edge of the book. Measure from the mark down to the floor with a measuring tape. This is the height.

Using a Divider

A divider is a two-legged pointed instrument for measuring the distance between two points quite accurately. Put its two points on the two ends of the length, lift it without changing the gap, and measure the gap on a ruler.

Length of a Curved Line

Lay a thread carefully along the curve, mark the two end positions on the thread, straighten it and measure the marked part with a ruler. Activity: draw a curve on paper, fix one end of the thread at the start of the line, press the thread along the line a little at a time, and finally measure the thread against a ruler.

Activity: thickness of a thin wire. Wind the wire closely around a pencil to make a coil of side-by-side turns, then measure the length of the coil with a scale. Dividing that length by the number of turns gives the thickness of a single wire.

Very small lengths, such as the thickness of a wire, can be measured directly with laboratory instruments called the vernier calliper and the screw gauge.

Measurement of Area

The surface covered by an object is its area; it involves two dimensions. The SI unit is the square metre (m²), the area of a square of side 1 m. For regular shapes: area of a square = side × side, and area of a rectangle = length × breadth.

Example. How many m² make 1 cm²? 1 cm² = 1 cm × 1 cm = (1/100) m × (1/100) m = 1/10000 m² = 10⁻⁴ m².

Measurement of Volume

The space occupied by an object is its volume. The SI unit is the cubic metre (m³). In daily life the litre (l) is a popular unit of volume.

1 litre = 1000 ml; 1 m³ = 1000 litres; 1 litre = 1000 cm³ because 1 litre = (100 cm)³ ÷ 1000 = 1000 cm³. Hence 1 cm³ = 1 ml. The volume of a liquid is usually given in millilitres.

For solids with regular shapes the volume comes from a formula: cube = l³ (l is the side), cuboid = l × b × h, cylinder = πr²h (r is the radius, h is the height).

Worked values: a cube of side 1 m has volume 1 m³; of side 1 cm has volume 1 cm³; of side 10 cm has volume 10 × 10 × 10 = 1000 cm³; of side 1 dm has volume 1 dm³. So 1000 cm³ = 1 dm³ = 1 litre = 1000 ml.

In the laboratory the volume of a liquid is measured with a measuring cylinder, a glass cylinder marked with graduations. Sizes range from 10 ml (10 cm³) to 1000 ml (1000 cm³).

Rest and Motion

Rest: an object is at rest if its position does not change with time with respect to its surroundings.

Motion: an object is in motion if its position keeps changing with time with respect to its surroundings (or an observer).

Rest and Motion Are Relative

An object can be moving with respect to one thing and at rest with respect to another. When you sit in a moving train, a person standing outside sees you moving, but the person sitting beside you sees you at rest. Even while you sit reading, you are moving along with the spinning earth, which also goes round the sun, and the sun with its planets moves within the galaxy.

Types of Motion

1. Linear (Translatory) Motion

Motion along a straight line. Examples: a moving car on a straight road, a runner on a straight track, a stone falling down, a train on a straight track.

2. Random Motion

Motion with no fixed direction or pattern. Examples: a flying bird, a hockey player chasing the ball, an ant crawling on paper, a child playing in a ground.

3. Periodic Motion

A motion that repeats its path after equal intervals of time. It has two kinds:

(A) Circular motion: a periodic motion in which a body goes round a fixed point along a circle. Examples: the tip of a clock hand, the earth going round the sun.
(B) Oscillatory motion: a periodic motion in which a body moves to and fro about a fixed point. Examples: a simple pendulum, a body hung from a spring, a swing.

4. Combined Motion

A body may have two types of motion at the same time. The wheel of a moving car spins and also moves forward; a coin rolled on a table spins and also travels ahead.

Distance and Speed

Distance is the real length of the path a body travels between two places. If a body goes from A to B along path (1) or via C along path (2), the distances are different, because the paths are different lengths. For the path A-C-B the distance is the length of ACB.

Speed is the distance travelled in one unit of time.

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}}, \quad s = \frac{d}{t} \]

The SI unit of speed (average speed) is m/s. Here d is distance, t is time and s is speed.

Uniform motion: equal distances are covered in equal intervals of time, however small the intervals. A car running steadily at 10 m/s covers 10 m every second.

Non-uniform motion: unequal distances are covered in equal intervals of time. A ball dropped from the top of a building covers 4.9 m in the first second, 14.7 m in the second second and 24.5 m in the third second, and so on.

Distance and Displacement (Add to Your Knowledge)

Displacement is the change in position, measured in a straight line from the starting point to the end point, with a sign for direction. A body starts from A, moves 4 m to B, then 6 m to C, then returns back along the same line past A and reaches D, which lies 5 m to the left of A.

Summary

1. Transportation is the movement of people or goods from one place to another.
2. A physical quantity is a quantity that can be measured, such as length, mass and time.
3. The SI unit of length is the metre.
4. Area is the surface covered by an object; its SI unit is m².
5. Volume is the space occupied by an object; its SI unit is m³.
6. A body is at rest if its position does not change with time with respect to its surroundings, and it is in motion if its position changes.
7. The types of motion are linear, random, circular, periodic, oscillatory and combined motion.
8. Linear motion is along a straight line, and random motion has no fixed direction.
9. Periodic motion repeats after a fixed interval of time.
10. Distance is the length of the actual path travelled, and speed is the distance travelled in unit time.

Concept Map

1. Measurement leads to physical quantities, which are of two kinds: fundamental quantities and derived quantities.
2. Motion has two states: rest and motion. For a moving body we study the nature of the motion (translatory, rotatory and vibratory), the distance covered and the speed.