Weight
Step onto a weighing machine, or hang a bag of rice from a spring balance, and the number that appears is not really telling you "how heavy" something feels in some vague sense — it is measuring an actual force, the pull the entire Earth exerts on that object. Physicists call this force weight, and it is one of the simplest, most everyday forces you will study, yet it is also one of the most commonly muddled with a completely different idea: mass. This article builds weight up from the gravitational force you already know, shows how a spring balance turns that pull into a number in newton, gives you the rounded 1 kilogram equals 10 newton rule this chapter works with, and connects weight to why some things float while others sink.
Weight is the force with which the Earth pulls an object towards itself, it is measured in newton using a spring balance, and on Earth every 1 kilogram of mass corresponds to about 10 newton of weight.
The core idea
Weight is a force, not an amount of matter. The Earth's gravitational force acts on every object near it, pulling that object towards the Earth's centre. The size of that pull, for a particular object, is called the object's weight. Because weight is a force like any other force in this chapter — a push or a pull — its SI unit is the same as the unit for all forces: the newton (N).
Weight comes directly from gravitational force. An object has weight precisely because the Earth's gravity is pulling on it. If that pull could somehow be switched off, the object would still contain exactly the same amount of matter, but it would have no weight at all — the seed of a key distinction: weight can change with location, while the amount of matter making up the object does not.
A spring balance measures weight, not mass. Hang an object from the hook of a spring balance and its weight stretches the spring inside; the amount of stretch is shown against a scale marked in newton, so the reading you take is a force. Reading it correctly means noticing the balance's least count — the smallest division marked on the scale — and lining up the pointer against those markings as precisely as that least count allows. Many spring balances also print a second scale in gram or kilogram purely as a convenience, built on a fixed conversion, not because the spring is somehow sensing "amount of matter" directly.
The rounded conversion used in this chapter. To move between an object's mass and its weight without needing exact gravitational data, this chapter adopts a simple rounded rule:
where: the left side is the object's mass, measured in kilogram, and the right side is the corresponding weight, the force with which Earth pulls that mass, measured in newton. This rule is only used at this level as a rounded, working convention — it is not derived from any deeper formula here, and you do not need or any acceleration value to use it.
Weight decides floating and sinking. When an object is lowered into a liquid, the liquid pushes back on it with an upward force called the buoyant force, or upthrust. Whether the object floats or sinks is entirely a competition between this upthrust and the object's own weight pulling it down.
If the object's weight is greater than the buoyant force the liquid can exert on it, the object sinks. If the weight is balanced by (equal to) the buoyant force, the object floats. This qualitative rule is summed up by Archimedes' Principle: an object fully or partially immersed in a liquid experiences an upward force equal to the weight of the liquid it displaces.
The goal is to turn the chapter's rounded convention — that 1 kilogram of mass corresponds to about 10 newton of weight on Earth — into a working rule you can apply to any mass or any spring-balance reading, so that a mass in kilogram and a weight in newton can be converted into each other in one step, in either direction, without needing any value of gravitational acceleration.
Step 1. Start from the given convention as a ratio. Every 1 kg of mass produces about 10 N of weight, so the "exchange rate" between mass and weight, on Earth, is 10 newton for every kilogram. Writing mass as (in kg) and weight as (in N), one kilogram of mass corresponds to ten units of weight, which we can scale up for any mass: if kilogram of mass each contribute 10 N, the total weight is lots of 10 N added together.
Step 2. Express this as a general working rule. Adding copies of "10 N" gives , with in newton and in kilogram. This is exactly the rounded convention scaled up — not a new law, just the same 1 kg to 10 N ratio applied repeatedly, so it stays consistent with everything already stated about weight being the Earth's pull.
Step 3. Check the rule both ways. Going from mass to weight, a 5 kg object gives N, matching the chapter's own example. Going from weight to mass, a spring balance reading of 20 N means kg, again matching the chapter's own example. The rule works in both directions because it is just the ratio "10 N per kilogram" used either as a multiplier (mass to weight) or a divider (weight to mass).
Step 4. Note the limits of this rule. It is a rounded, Earth-specific convention for this level, not a universal law — it does not involve or the formula , and it should not be extrapolated to other planets or to precise scientific work. Within this chapter, it is only meant to let you move quickly between a mass in kilogram and the corresponding weight in newton.
Worked example
Question. A shopkeeper hangs a bag of rice from a spring balance and the pointer settles at the 30 N mark. Using the working rule from the derivation above, find the approximate mass of the bag of rice. Then, if a second, identical spring balance shows a different bag reading 45 N, find that bag's mass too, and say which bag is heavier.
Step 1. The spring balance reading of 30 N is the bag's weight, , since a spring balance measures weight directly in newton, not mass.
Step 2. Apply the working rule in the weight-to-mass direction: kg. So the first bag of rice has a mass of about 3 kg.
Step 3. For the second bag, the reading is N, so kg.
Step 4. Compare the two: 45 N is greater than 30 N, so the second bag, with a mass of 4.5 kg, is heavier than the first bag, with a mass of 3 kg. The first bag has a mass of about 3 kg, the second bag has a mass of about 4.5 kg, and the second bag is heavier.
Common traps
- Confusing weight with mass — weight is a force, measured in newton, caused by Earth's pull, while mass is the amount of matter in an object, measured in kilogram or gram; the two are related by the 10 N per kg rule but are never the same quantity.
- Assuming the spring balance's needle directly shows mass — it is really measuring the stretch of the spring due to weight in newton; any mass scale printed alongside it is only a convenience built on the 1 kg to 10 N convention.
- Thinking an object floats simply because it is "light" — floating depends on how the object's weight compares with the buoyant force the liquid can actually exert on it, not on the object's weight alone.
- Reading the spring balance without checking its least count — the smallest marked division limits how precisely the weight, and hence the mass calculated from it, can be known.
Ask the tutor: Want to work through whether a particular object of a given mass would float or sink in water, using its weight and the idea of buoyant force?
If I travel to a place with weaker gravity, does my weight change or does my mass change?
Your weight would change, but your mass would stay the same. Weight is the force of gravitational pull on you, so it depends on how strongly gravity is acting on you where you are. Mass is the amount of matter you are made of, and moving to a different place does not add or remove any matter from your body, so mass stays fixed. This chapter's 1 kg to 10 N rule is specifically an Earth convention; it is a reminder that weight is location-dependent even though this article does not work through weight on other planets in detail.
Why do some spring balances show both a newton scale and a gram or kilogram scale?
The newton scale is the one actually being measured — the spring genuinely stretches in response to a force, and that force is the object's weight. The gram or kilogram scale is added purely for convenience, using the same 1 kg to 10 N convention this chapter gives you: the manufacturer has pre-calculated, for each newton mark, what mass would produce that much weight on Earth, and printed that number alongside it. If you used that same balance somewhere gravity were different, the mass scale would no longer be accurate even though the newton scale would still be correctly measuring the force being applied.
Does a heavier object always sink and a lighter object always float?
No — what matters is not how heavy an object is by itself, but how its weight compares with the buoyant force the liquid can exert on it. A large ship made of steel is far heavier than a small pebble, yet the ship floats and the pebble can sink, because the ship's shape lets it displace a huge amount of water, and Archimedes' Principle says the buoyant force equals the weight of the liquid displaced. So a heavy object can still float if it displaces enough liquid for the upthrust to balance its weight, and a light object can sink if it displaces too little liquid for the upthrust to match its weight.