Mass, Weight, Newton and Kilogram Weight മാസ് · ഭാരം
The whole chapter is about two forces: the Earth pulling an object down, and a liquid or gas pushing it up. Before you can compare them, you need to be sure what mass and weight are, why the weight of 1 kg is 9.8 newtons, what “kilogram weight” (kgwt) means, how a spring balance shows a force, and how to draw forces as arrows. This page builds all of that from the start.
- Multiplying and dividing decimals, such as 0.25 × 9.8.
- Nothing else – everything is built here.
1. Mass – how much matter
The mass (മാസ്) of an object is the amount of matter in it. A full sack of rice has more matter than a half-full one, so it has more mass. Mass is measured in kilograms (kg) and grams (g):
Mass does not depend on where the object is. A coconut taken to the Moon still has exactly the same coconut in it, so its mass is the same. In physics formulas we always use mass in kilograms.
2. Weight – the Earth's pull
Drop a key and it falls: the Earth pulls everything towards its centre. The force with which the Earth pulls an object is its weight (ഭാരം). Your textbook calls this pull the force of gravity (ഭൂഗുരുത്വാകർഷണ ബലം), and it always acts downwards. Weight is a force, so it is measured in newtons (N).
Near the Earth's surface, the Earth pulls with 9.8 N on every kilogram. This number is called g, the acceleration due to gravity, g = 9.8 m/s². So:
Change the place but keep the mass: the mass number does not change, but the weight arrow does. On the Moon the pull is only about one-sixth of the Earth's pull. Mass is “how much stuff”; weight is “how hard it is pulled”.
Worked example 1 · A packet of tea
Q. A packet of Munnar tea has a mass of 250 g. Find its weight. (g = 9.8 m/s²)
First change 250 g into kilograms (divide by 1000). Then use W = m × g.
3. The newton and the kilogram weight (kgwt)
The SI unit of force is the newton (N). One newton is a small force: a 100 g chocolate bar weighs 0.1 × 9.8 = 0.98 N, so about 1 N. Your textbook also uses an older, everyday unit: the kilogram weight (കിലോഗ്രാം ഭാരം, kgwt). 1 kgwt is the weight of a 1 kg mass – the force with which the Earth pulls 1 kg:
Both scales show the same force. Every 1 kgwt on the top scale lines up with 9.8 N below. Try 0.45, 0.31 and 0.14 kgwt – you will meet these numbers in the chapter (page 8).
Mass: amount of matter, in kg; the same everywhere. Weight: the Earth's pull, a force, in N (or kgwt); W = m × g. 1 kgwt = 9.8 N. A 1 kg mass has a weight of 1 kgwt = 9.8 N.
The hanging scale at a Kochi fish market says “kg”. Strictly, a spring scale measures the pull on its hook, so “2 kg of sardines” on that scale really means a weight of 2 kgwt = 19.6 N. Because 1 kg always weighs 1 kgwt on Earth, the shopkeeper's number is also the mass in kg – which is why everyday life mixes the two words.
Worked example 2 · From kgwt to newtons
Q. An object weighs 0.45 kgwt in air. Express its weight in newtons.
1 kgwt = 9.8 N, so multiply the kgwt value by 9.8.
4. The spring balance – a force meter
Pull a spring gently and it stretches a little; pull twice as hard and it stretches twice as much. A spring balance (സ്പ്രിങ് ബാലൻസ്) has a pointer fixed to a spring, moving along a scale marked in newtons (or kgwt). Its reading is the force pulling down on the hook. When an object just hangs from it, the reading is the object's weight.
Now the important idea for this chapter. Suppose you push the object up from below with your hand while it hangs. Your hand now carries part of the weight, so the spring has to pull less, and the reading drops:
Choose the stone (W = 0.3 × 9.8 = 2.94 N) and push up with 1.13 N: the reading falls to 1.81 N. Push with 2.94 N or more and the reading becomes 0 – your hand holds all the weight and the spring goes slack. In this chapter, water will play the part of the hand.
On page 5 you will hang the same stone from a spring balance and lower it into water. The reading drops exactly as if a hand were pushing up. That invisible upward push of the water is the buoyant force (പ്ലവക്ഷമബലം), and the drop in the reading is the apparent loss of weight (ഭാരക്കുറവ്).
Worked example 3 · A push from below
Q. A stone of mass 300 g hangs from a spring balance. A friend pushes it gently upwards with a force of 1.13 N. What does the spring balance read now?
First find the weight: W = m × g with m = 0.3 kg. The spring only has to pull with whatever the hand does not supply: reading = W − push.
5. Forces as arrows
A force has a size and a direction, so we draw it as an arrow. The arrow points the way the force acts, and a longer arrow means a bigger force. When several forces act on one object, we add them up. Forces in the same direction add; forces in opposite directions take away. What is left over is the net force:
- Upward push = weight → net force 0 → the forces are balanced. An object at rest stays at rest.
- Upward push > weight → net force upwards → the object starts moving up.
- Upward push < weight → net force downwards → the object starts moving down.
Make the two arrows equal and press Let go: the ball does not move. Make the push bigger than the weight: up it goes – just like an empty bottle pushed under water (page 5).
6. Balanced forces everywhere
Whenever something stays still, the forces on it are balanced: something is pushing or pulling it up with a force exactly equal to its weight. Step through these five pictures. The last two are unbalanced, and they are the two questions this chapter answers.
An object that stays still, or floats without rising or sinking, has net force zero: the upward force on it equals its weight. A boat floating on Vembanad lake is held up by the water with a force equal to its weight.