Mass, Vectors and Friction മാസ് · സദിശ അളവ് · ഘർഷണം
Four last tools before the chapter starts. Mass appears in inertia, momentum and F = ma, and it must always be in kilograms. Vectors are quantities with a direction, such as velocity, force and momentum, and their signs matter. Friction is the force that makes moving things stop. And the chapter's numericals need decimals and minus signs handled without mistakes.
- Forces as arrows with + and − (page 1); velocity and acceleration (page 2); v² = u² + 2as (page 3).
1. Mass and its unit
Mass (മാസ്) is the quantity of matter in an object. Its SI unit is the kilogram (kg). A mass stays the same wherever the object is taken. (Weight is different: it is the force with which the Earth pulls the object, measured in newtons. You saw on page 1 that 100 g weighs about 1 N.)
Textbook questions often give masses in grams: a 200 g ball, a 60 g bullet, a 250 g block. Every formula in this chapter (p = mv, F = ma) needs kg, so convert first:
Dividing by 1000 moves the decimal point three places to the left: 250 g = 0.250 kg = 0.25 kg; 60 g = 0.060 kg = 0.06 kg; 20 g = 0.020 kg = 0.02 kg. Lengths work the same way with 100: 4 cm = 4 ÷ 100 m = 0.04 m.
Try 200 g (a hockey ball), 60 g (a bullet), 20 g, 500 g and 1000 g. Fill in zeros in front when the number has fewer than three digits: 20 g = 0.020 kg.
| In the textbook | In SI units |
|---|---|
| 200 g | 0.2 kg |
| 250 g | 0.25 kg |
| 500 g | 0.5 kg |
| 60 g | 0.06 kg |
| 20 g | 0.02 kg |
| 10,000 kg (a loaded lorry) | 10 000 kg = 1 × 10⁴ kg (already in kg) |
| 4 cm | 0.04 m |
Worked example 1 · Into SI units
Q. Express in SI units: (a) a ball of mass 160 g, (b) a bullet of mass 20 g, (c) a distance of 4 cm.
g → kg: ÷ 1000 (decimal point 3 places left). cm → m: ÷ 100 (2 places left).
2. Scalars and vectors
Some quantities are fully described by a number and a unit: a mass of 5 kg, a time of 4 s, a speed of 20 m/s. These are scalar quantities. Others also need a direction: a force of 50 N to the left, a velocity of 20 m/s towards the east. These are vector quantities (സദിശ അളവ്).
Scalar (size only)
mass, time, distance, speed (വേഗം), temperature
Vector (size + direction)
displacement, velocity (പ്രവേഗം), acceleration, force (ബലം), momentum (മൊമെന്റം, page 8)
Ask yourself: does it make sense to say “… towards the east”? “5 kg towards the east” is nonsense, so mass is a scalar. “50 N towards the east” makes sense, so force is a vector.
For vectors along a line we use + and − for the two directions, as you did for forces. This matters most when something turns back. A ball that hits a wall at 20 m/s and bounces straight back at 20 m/s has the same speed, but its velocity changed from +20 m/s to −20 m/s.
Towards the wall (right) is +. Set both speeds to 20: the speed did not change, but the change in velocity is −20 − (+20) = −40 m/s. Set the speed after to 0 (a ball of clay that sticks): the change is only −20 m/s.
Worked example 2 · The rebounding ball
Q. A ball moving at 20 m/s hits a wall and returns along the same path at 20 m/s. Find the change in its velocity.
Velocity is a vector. Take the original direction as +; the returning velocity is then −20 m/s. Change = final − initial.
“Same speed before and after, so no change” is wrong for a rebound. Velocity and momentum are vectors; the change in direction is a change. You will meet this again with a hockey ball in “Let us assess”.
3. Friction: the force that stops things
Friction (ഘർഷണം) is the force between two surfaces in contact that opposes motion (or an attempt to move). It always acts against the direction in which the object moves, or tries to move.
- Rough surfaces (a mud road, a coir mat, sand) give more friction; smooth surfaces (polished tiles, ice, a carrom board with powder) give less.
- A ball rolled on the ground slows down and stops because of friction (and some air resistance), not because it “runs out of force”.
- A heavy box does not move when you push it gently: friction pushes back with an equal force, and the forces are balanced. Only when your push is bigger than the largest friction the surfaces can give does the box start to move.
Arrows are drawn to scale. While your push is less than the largest friction (rough floor ≈ 98 N, tiles ≈ 39 N, ice ≈ 6 N for this box), friction exactly matches your push: balanced, no motion. Push harder than that and the box accelerates with a = (push − friction) ÷ mass. (For simplicity the friction while sliding is taken equal to the largest friction at rest.)
Friction gives a retardation (rough ≈ 4.9 m/s², tiles ≈ 2 m/s², ice ≈ 0.3 m/s²). Less friction → it slides much further. With no friction nothing slows it down: it would keep going at the same speed in a straight line forever. That is exactly Galileo's idea on page 6!
Carrom players sprinkle powder on the board to reduce friction so the coins glide. On a wet, muddy road during the monsoon, tyres can lose grip because there is less friction, so vehicles need a longer distance to stop. Sand is spread on oily patches to increase friction.
4. Decimals and minus signs in calculations
The chapter's answers often look like −0.125 N, −2.8 N or −7500 kg m/s². Two skills make these easy.
Multiplying and dividing decimals
- Multiply: ignore the decimal points, multiply the whole numbers, then put back as many decimal places as the two numbers had together. 0.25 × 0.5: 25 × 5 = 125; places 2 + 1 = 3 → 0.125.
- Divide by 10, 100, 1000: move the point 1, 2, 3 places left. Multiply by 10, 100, 1000: move it right. 0.02 × 125000 = 2 × 1250 = 2500.
- Divide a decimal by a whole number: 0.2 × 30 = 6, and 6 ÷ 0.3 = 60 ÷ 3 = 20 (multiply top and bottom by 10 first).
Rules for signs
| Multiply or divide | Result | Example |
|---|---|---|
| (+) and (+) | + | 1000 × 5 = 5000 |
| (+) and (−) | − | 1000 × (−5) = −5000 |
| (−) and (+) | − | (−25) ÷ 5 = −5 |
| (−) and (−) | + | (−6) ÷ (−3) = 2 |
And for subtracting: 0 − 25 = −25, and (−20) − 20 = −40 (going further in the negative direction).
Like signs give +, unlike signs give −. Dividing by 0 is not allowed, so the machine refuses it.
Worked example 3 · A force with a minus sign
Q. A 400 g toy car rolling on the floor has an acceleration of −0.5 m/s² because of friction. Using F = m × a (you will meet it on page 9), find the force on the car and say what the sign means.
Change 400 g into kg first. Then multiply: a positive number × a negative number is negative.
5. Check yourself
You now have every tool the chapter needs: forces as arrows with signs, velocity and acceleration, the three equations and graphs, mass in kg, vectors and friction. Time to start the chapter itself.
Next: The chapter begins: resultant, balanced and unbalanced forces ▶