Units, Powers of Ten and Conversions
Work and energy questions are full of units: joules and kilojoules, watts, kilowatts and megawatts, calories and kilocalories, horsepower, grams, minutes and km/h. Almost every mistake in this chapter's numericals is a unit mistake. This page shows you how to write very big numbers with powers of ten, how to change any unit into the one the formula needs, and how the joule and the watt are built from the kilogram, the metre and the second.
- Multiplying and dividing by 10, 100 and 1000 (move the decimal point).
- Force in newtons and W = m g (page 1).
1. The three units everything is built from
In physics we use the SI system of units. Every quantity in this chapter can be built from just three base units:
| Quantity | SI unit | Symbol | Common other units → change to SI |
|---|---|---|---|
| mass | kilogram | kg | gram: 1 g = 0.001 kg (÷ 1000) · tonne: 1 t = 1000 kg |
| length, height, displacement | metre | m | cm: 1 cm = 0.01 m (÷ 100) · km: 1 km = 1000 m |
| time | second | s | minute: 1 min = 60 s · hour: 1 h = 3600 s |
Before you put numbers into W = F s, Ep = m g h, Ek = ½ m v² or P = W/t, change every quantity to kg, m, s, N and J. Then the answer comes out in J or W automatically.
2. Powers of ten
Energy numbers get big very fast: a hammer of a pile driver has about 98 000 J; one KSEB “unit” of electricity is 3 600 000 J. Instead of writing many zeros we use powers of ten: 10³ means 10 × 10 × 10 = 1000 (a 1 followed by three zeros), and 10⁶ means a 1 followed by six zeros = 10,00,000 (ten lakh, or one million). A number like 3 600 000 is written 3.6 × 10⁶: move the decimal point six places to the right.
Each step of n moves the decimal point one place to the right (multiplies by 10). India groups digits as lakh and crore (10,00,000); most of the world groups them in threes (1,000,000). Physics books often just leave a small space: 1 000 000.
10³ = 1000 (one thousand) · 10⁵ = 1,00,000 (one lakh) · 10⁶ = 10,00,000 (ten lakh = one million) · 10⁷ = 1,00,00,000 (one crore).
3. Kilo and mega: bigger units
A prefix in front of a unit multiplies it by a power of ten. You will meet two of them all through the chapter:
So 1 kJ (kilojoule) = 1000 J, 1 MJ = 10⁶ J, 1 kW (kilowatt) = 1000 W, 1 MW (megawatt) = 1000 kW = 10⁶ W, and 1 kg = 1000 g. The Idukki project's Moolamattom power house can produce about 780 MW – that is 780 000 kW, or 7.8 × 10⁸ W.
- Going to a smaller unit (kJ → J): the number gets bigger – multiply by 1000.
- Going to a bigger unit (J → kJ, g → kg): the number gets smaller – divide by 1000.
Every step down the staircase multiplies by 1000; every step up divides by 1000. The amount is the same on every step – only the unit changes.
Worked example 1 · Kilojoules to joules
Q. A mixer grinder does 2.5 kJ of work in crushing a handful of rice for dosa batter. Express this in joules.
1 kJ = 1000 J. Going to a smaller unit, so the number gets bigger: multiply by 1000.
4. Time and speed: minutes, hours and km/h
Power is work per second, so times must be in seconds: 1 min = 60 s, 1 h = 60 × 60 = 3600 s. Kinetic energy needs speeds in m/s, but speedometers show km/h:
The slider moves in steps of 9 km/h; each step adds exactly 2.5 m/s (9 × 5/18 = 2.5). A motorcycle at 54 km/h covers 15 m – about three autorickshaw lengths – every second.
Worked example 2 · A motorcycle's speed
Q. A motorcycle moves at 54 km/h. Express its speed in m/s.
Multiply by 5/18. Divide 54 by 18 first – it goes exactly.
5. Food energy: calories and joules
The SI unit of energy is the joule (ജൂൾ), but food packets and diet charts use the calorie (കലോറി) and the kilocalorie (കിലോകലോറി). Your textbook uses these values:
To change calories into joules, multiply by 4.2; to change joules into calories, divide by 4.2. (A more exact value is 4.186 J, but use 4.2 J in the exam.) When a food label says “Energy 90 kcal”, it means 90 kilocalories.
Typical values (approx.): one idli ≈ 40 kcal, a banana ≈ 90 kcal, a cup of cooked rice ≈ 200 kcal. The last line uses the work against gravity, m g h (page 6): if all of that energy could lift a 40 kg student, how high would she go? (Real muscles turn only about a quarter of food energy into work – the rest becomes body heat.)
6. Power units: watt, kilowatt, megawatt and horsepower
Power (പവർ) is measured in watts (വാട്ട്, W): 1 W = 1 joule every second. Bigger units are the kilowatt (1 kW = 1000 W) and the megawatt (1 MW = 10⁶ W). Water pumps, motors and vehicles are often rated in horsepower (കുതിരശക്തി, HP). Your textbook uses
A “1 HP” pump that fills an overhead tank in a Kerala home uses 746 W. Every red tick on the watt scale is one more horsepower.
Worked example 3 · A pump motor
Q. The motor of a well pump is rated 2 HP. Express its power in watts and in kilowatts. (1 HP = 746 W)
Multiply by 746 to get watts. Then divide by 1000 to get kilowatts.
7. How the joule and the watt are built
The newton, the joule and the watt are derived units: each one is made from kg, m and s through a formula. Step through the chain – it is exactly what the textbook's “Let us assess” question 3 asks.
Newton: 1 N = 1 kg m/s². Joule (work and energy): 1 J = 1 N m = 1 kg m²/s². Watt (power): 1 W = 1 J/s = 1 kg m²/s³. And the electricity “unit” on a KSEB bill is 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.