---
title: "Weight and Mass"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 24
exercises: 11
source: https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass
---

# Chapter 24 — Weight and Mass

Astronauts on the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) bounced like children on a trampoline, though they carried heavy packs. Were their packs heavy or [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) up there? To answer properly, we must split an everyday word in two: what a thing *is made of* — its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) — and how hard the Earth *pulls on it* — its [weight](#def-g4-weight-and-mass-weight). They are close cousins, but not twins.

## 24.1 Two ideas hiding in “heavy”

You know [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass): how much stuff, in [grams](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) and [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units), judged by the [balance scale](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-scale). And you know the Earth’s pull: the no-touch [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) that brings every dropped thing down. [Weight](#def-g4-weight-and-mass-weight) is where the two meet.

**Definition 24.1 (Weight).**

The *weight* of a thing is the [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) with which the Earth pulls it downward. Weight is what your arm fights when you hold a bucket, and what stretches the spring when the bucket hangs from it. Like every [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force), weight has a direction: straight down, always.

**Proposition 24.2 (More stuff, stronger pull).**

The Earth pulls harder on things that contain more stuff: at the same place, more [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) always means more [weight](#def-g4-weight-and-mass-weight) — two identical bricks weigh twice what one does. That is why the [balance scale](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-scale), which compares the *pulls* on its two pans, manages to compare *masses*: at one place, equal pulls mean equal stuff.

**Example 24.3 (Cousins, not twins).**

[Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) answers: *how much stuff?* It is a property of the thing alone — the same in your hand, underwater, or on the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon). [Weight](#def-g4-weight-and-mass-weight) answers: *how hard is it pulled down here?* It depends on the thing *and* on where it is. Change nothing but the place, and the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) stays; the [weight](#def-g4-weight-and-mass-weight) can change.

## 24.2 The spring scale

**Definition 24.4 (Spring scale).**

A *spring scale* [measures](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-measure) [weight](#def-g4-weight-and-mass-weight) by letting it stretch a spring: the harder the pull, the longer the stretch. A pointer beside the stretched spring shows the reading. Fishermen’s scales, luggage scales and the kitchen scale’s insides all work this way — they feel the *pull*, not the stuff.

![A spring feels weight: one brick stretches it; two identical bricks stretch it twice as far.](https://one-course.com/images/onecourse/chapters/physics-1/g4-weight-and-mass/fig-51993884d06d.svg)

*A spring feels [weight](#def-g4-weight-and-mass-weight): one brick stretches it; two identical bricks stretch it twice as far.*

**Method 24.5 (A rubber-band scale).**

Build a weight-feeler of your own:

1. hang a rubber band from a hook, with a light paper cup taped to its bottom;
2. with the cup empty, mark where the cup’s rim stands and [measure](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-measure) nothing yet: this is the zero mark;
3. load the cup — $10$ marbles, say — and [measure](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-measure) with your ruler how far the rim sank below the zero mark;
4. load $20$ marbles and [measure](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-measure) again.

Twice the marbles, about twice the stretch: your rubber band confirms the proposition — more stuff, stronger pull.

![A spring scale at work: the load’s weight stretches the spring, and the pointer turns that stretch into a reading.](https://one-course.com/images/onecourse/chapters/physics-1/g4-weight-and-mass/img-71459ec54c60.jpg)

*A [spring scale](#def-g4-weight-and-mass-springscale) at work: the load’s [weight](#def-g4-weight-and-mass-weight) stretches the spring, and the pointer turns that stretch into a reading.*

## 24.3 A trip to the Moon

**Example 24.6 (The Moon is a weaker puller).**

The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is much smaller than the Earth, and it pulls things far more weakly — about six times more weakly. An astronaut’s pack keeps every [gram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) of its *[mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)* on the trip, but its *[weight](#def-g4-weight-and-mass-weight)* up there shrinks to a sixth. That is the whole secret of the bouncing: legs trained to fight Earth-pull suddenly fight a gentle Moon-pull, and every step becomes a leap.

![The same pack — same mass — in two worlds. Only the pull-arrow changes: weight belongs to the place as much as to the thing.](https://one-course.com/images/onecourse/chapters/physics-1/g4-weight-and-mass/fig-59490458e32c.svg)

*The same pack — same [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) — in two worlds. Only the pull-arrow changes: [weight](#def-g4-weight-and-mass-weight) belongs to the place as much as to the thing.*

**Example 24.7 (Two scales on the Moon).**

Take both scales to the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) and weigh the same pack. The *spring* scale tells the truth about the place: it reads six times less — the pull really is weaker. The *balance* scale notices nothing: the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) pulls the pack and the reference blocks weakly *alike*, the pans still tie, and it reports the same [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) as on Earth. Springs feel the place; balances compare the stuff.

**Remark 24.8 (Everyday words, physics words).**

In the shop, “the melon weighs one [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units)” is harmless talk — on Earth, [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) and [weight](#def-g4-weight-and-mass-weight) travel everywhere together, so nobody is confused. Physics splits the words because it plans farther than the shop: for astronauts, for falling things, and — in a later year — for measuring [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) in their own proper [unit](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-measure), which will be named after the scientist who first wrote the law of the Earth’s pull.

## 24.4 Exercises

**Exercise 24.1 ★.**

What question does [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) answer? What question does [weight](#def-g4-weight-and-mass-weight) answer? Which one is a [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force)?

**Solution of Exercise 24.1.**

[Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass): how much stuff? [Weight](#def-g4-weight-and-mass-weight): how hard is it pulled down here? [Weight](#def-g4-weight-and-mass-weight) is the [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) — the Earth’s downward pull.

**Exercise 24.2 ★.**

Which way does [weight](#def-g4-weight-and-mass-weight) always pull? What instrument feels [weight](#def-g4-weight-and-mass-weight) by stretching?

**Solution of Exercise 24.2.**

Straight down, always. The [spring scale](#def-g4-weight-and-mass-springscale) — [weight](#def-g4-weight-and-mass-weight) stretches its spring, and the pointer reports the stretch.

**Exercise 24.3 ★.**

One brick stretches the [spring scale](#def-g4-weight-and-mass-springscale)’s spring by two finger-widths. How far will two identical bricks stretch it? Which proposition says so?

**Solution of Exercise 24.3.**

About four finger-widths — double the stuff, double the pull, double the stretch: the proposition “more stuff, stronger pull”.

**Exercise 24.4 ★.**

In the rubber-band scale of [Method 24.5](#met-g4-weight-and-mass-rubberband), why must you mark the empty cup’s position before loading it?

**Solution of Exercise 24.4.**

The stretch must be measured *from the empty position*: the band already hangs somewhat under the cup’s own [weight](#def-g4-weight-and-mass-weight), and only the extra sinking below the zero mark [measures](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-measure) the load.

**Exercise 24.5 ★.**

An astronaut carries a pack of $20\,\mathrm{kg}$ of stuff to the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon). Up there, is its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) still $20\,\mathrm{kg}$? Is it as hard to hold up as on Earth?

**Solution of Exercise 24.5.**

Yes — [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) travels unchanged: still $20\,\mathrm{kg}$ of stuff. But it is far easier to hold up: the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) pulls it about six times more weakly, so its [weight](#def-g4-weight-and-mass-weight) is about a sixth of the Earth value.

**Exercise 24.6 ★.**

Why could the astronauts leap so high on the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon), in spite of their heavy packs?

**Solution of Exercise 24.6.**

Their legs push as hard as Earth-trained legs always do, but the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s pull-back is six times weaker — so every ordinary step turns into a leap.

**Exercise 24.7 ★.**

On the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon), which scale changes its report — the [spring scale](#def-g4-weight-and-mass-springscale) or the [balance scale](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-scale)? Explain what each one really compares or feels.

**Solution of Exercise 24.7.**

The [spring scale](#def-g4-weight-and-mass-springscale): it feels the local pull, and reads six times less. The [balance scale](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-scale) compares the pack’s pull with the blocks’ pull, and the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) weakens both alike — the pans still tie at the same [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass).

**Exercise 24.8 ★.**

True or not: “A thing with no stuff at all would have no [weight](#def-g4-weight-and-mass-weight) anywhere.” Defend your answer with [Proposition 24.2](#prop-g4-weight-and-mass-morestuff).

**Solution of Exercise 24.8.**

True. [Weight](#def-g4-weight-and-mass-weight) is the Earth’s pull on a thing’s stuff, and the pull grows with the amount of stuff — no stuff, nothing to pull: [weight](#def-g4-weight-and-mass-weight) zero everywhere.

**Exercise 24.9 ★.**

The greengrocer’s hanging scale dips as she loads apples into its pan. Which of the two cousins is her scale feeling? Why does her trick still sell fair [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) of apples — on Earth?

**Solution of Exercise 24.9.**

The spring inside feels *[weight](#def-g4-weight-and-mass-weight)* — the apples’ pull on the pan. On Earth the pull and the stuff travel strictly together (more pull exactly when more stuff), so a scale marked in [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) of stuff still tells the truth — here.

**Exercise 24.10 ★★.**

A space agency must check that a probe’s parts have exactly the right masses — but the finished probe will work near a small far planet whose pull is feeble. An engineer worries: “Our Earth weighings will all be wrong out there!” Reassure him: which measurements travel unchanged, and which instrument made them?

**Solution of Exercise 24.10.**

[Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) measurements travel unchanged: they describe the stuff itself, not the place. Any weighing done by *comparison* — the [balance scale](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-scale) against reference blocks — reports [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) and remains exactly right near the far planet. Only spring-style readings of [weight](#def-g4-weight-and-mass-weight) will shrink out there, and those were never what the parts list recorded.

**Exercise 24.11 ★★.**

Deep in space, far from Earth, [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) and Sun alike, an astronaut lets go of a wrench: it [floats](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words) beside her hand, weightless. Has the wrench lost its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)? Give two everyday-style clues she could still notice showing the stuff is all there. (Hint: try to shake it, or to throw it.)

**Solution of Exercise 24.11.**

The [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) is all there. Clues: shaking the wrench still takes real effort — her hand feels the stuff resisting the back-and-forth; and thrown, it flies off no faster than her muscles can manage — a hammer of stuff is still a hammer to throw. [Weight](#def-g4-weight-and-mass-weight) is gone; stuff, never.