---
title: "Weight vs Mass: Measuring Forces"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 64
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/64-weight-vs-mass-measuring-forces
---

# Chapter 64 — Weight vs Mass: Measuring Forces

Five years ago, on a paper [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon), you split “heavy” in two: [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) for the stuff, [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) for the pull. The split was wisdom; now it becomes arithmetic. [Forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) get their [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) — named for the man of the falling apple — [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) gets its formula, and the rubber-band scale of your childhood returns in professional dress.

## 64.1 The newton

**Definition 64.1 (The newton).**

[Forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) — pushes, pulls, [weights](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight), [gravitation](https://one-course.com/books/physics/1/en/chapter/63-gravitation#def-g9-gravitation-gravitation)’s grip — are measured in *newtons* ($\mathrm{N}$), honoring the author of the law of [gravitation](https://one-course.com/books/physics/1/en/chapter/63-gravitation#def-g9-gravitation-gravitation). Handy anchors: one newton is about the [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) of a small apple (history smiles); your schoolbag weighs some $50\,\mathrm{N}$; a solid handshake squeezes with around $100\,\mathrm{N}$; last chapter’s Moon-lease ran to $10^{20}$.

**Definition 64.2 (Dynamometer).**

A *dynamometer* is the force-meter: a calibrated spring in a case, stretching in proportion to the [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) applied, its pointer reading [newtons](#def-g9-weight-vs-mass-newton) directly. It is your rubber-band scale grown up — and like the [voltmeter](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltmeter) and [ammeter](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-ammeter) before it, it retires another patch of “feels strong” into honest numbers.

**Method 64.3 (Measuring a force).**

1. choose a [dynamometer](#def-g9-weight-vs-mass-dynamometer) whose range suits the job — a $2\,\mathrm{N}$ instrument for pencil cases, a $100\,\mathrm{N}$ one for schoolbags;
2. zero it in the position of use (hanging, if the load will hang — the spring’s own [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) shifts the zero);
3. apply the [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) steadily, along the instrument’s axis, and read at eye level;
4. record with the [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) — and, since [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) have directions, note the direction too when it matters.

On diagrams, a measured [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) becomes an arrow drawn to a declared scale — “one [centimetre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) per ten [newtons](#def-g9-weight-vs-mass-newton)” — pointing as the [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) points: the childhood force-arrows, now quantitative.

## 64.2 The weight formula

**Proposition 64.4 (Weight is proportional to mass).**

At any given place, an object’s [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) $P$ (in $\mathrm{N}$) is proportional to its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) $m$ (in $\mathrm{kg}$):

$$
P = m \times g ,
$$

where $g$, the *gravitational strength* of the place, gives the [newtons](#def-g9-weight-vs-mass-newton) of pull per [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) of stuff. Near the Earth’s surface,

$$
g \approx 9.8\,\mathrm{N}/\mathrm{kg}:
$$

each [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) is pulled with just under ten [newtons](#def-g9-weight-vs-mass-newton). The formula is last chapter’s law in local dress: $g$ bundles the Earth’s [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) and radius into one number for “here”.

![Weight against mass, measured with a dynamometer and a set of marked masses: a straight line through the origin whose steepness is the place’s g.](https://one-course.com/images/onecourse/chapters/physics-1/g9-weight-vs-mass/fig-0e4084431006.svg)

*[Weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) against [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass), measured with a [dynamometer](#def-g9-weight-vs-mass-dynamometer) and a set of marked masses: a straight line through the origin whose steepness *is* the place’s $g$.*

**Example 64.5 (The formula at work).**

A $60\,\mathrm{kg}$ pupil: $P = 60 \times 9.8 = 588\,\mathrm{N}$. A $450\,\mathrm{g}$ football: $P = 0.45 \times 9.8 \approx
4.4\,\mathrm{N}$ — mind the [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units). Backward: a crate weighing $343\,\mathrm{N}$ has [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) $m = P/g = 343 \div 9.8 =
35\,\mathrm{kg}$. And upside down: on a mountain where a $10\,\mathrm{kg}$ pack weighs $97.7\,\mathrm{N}$, the local $g$ is $97.7 \div 10 = 9.77\,\mathrm{N}/\mathrm{kg}$ — $g$ thins slightly with altitude, exactly as the inverse square promised.

**Example 64.6 (One suitcase, many weights).**

Each world sets its own $g$, and the old astronaut story becomes a table. Your faithful $10\,\mathrm{kg}$ suitcase:

| place | $g$ ($\mathrm{N}/\mathrm{kg}$) | suitcase [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) |
| --- | --- | --- |
| Earth | $9.8$ | $98\,\mathrm{N}$ |
| [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) | $1.6$ | $16\,\mathrm{N}$ |
| Mars | $3.7$ | $37\,\mathrm{N}$ |
| Jupiter’s cloud-tops | $24.8$ | $248\,\mathrm{N}$ |

Ten [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) of stuff everywhere — and a different [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) on every world: the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) is unchanged, while the [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) follows the local $g$.

**Remark 64.7 (The two scales, judged for good).**

Now the childhood verdicts close with formulas. The balance compares $m_1 g$ against $m_2 g$: the local $g$ multiplies both pans and cancels — balances [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) *[mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)*, truthful on any world. The [spring scale](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-springscale) reads $P = m g$ directly: it [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) *[weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight)*, loyal to its location. The bathroom scale is a [spring scale](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-springscale) in disguise, factory-marked in [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) by dividing your [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) by the *Earth’s* $g$ — honest at home, a flatterer 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) ($10\,\mathrm{kg}$ read for every $60\,\mathrm{kg}$ of you), and a slanderer on Jupiter.

## 64.3 Forces on paper

**Example 64.8 (The book on the table, in newtons).**

The oldest [equilibrium](https://one-course.com/books/physics/1/en/chapter/13-balance-and-equilibrium#def-g2-balance-equilibrium-equilibrium) in this book, at last with numbers: a $2\,\mathrm{kg}$ dictionary rests on a desk. Its [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight): $P = 2
\times 9.8 = 19.6\,\mathrm{N}$, drawn as an arrow $2\,\mathrm{cm}$ long at a scale of ten [newtons](#def-g9-weight-vs-mass-newton) per [centimetre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units), pointing straight down from the book. The desk’s supporting push: $19.6\,\mathrm{N}$ straight up — an equal arrow, opposite way. The tie is exact, and stillness is its proof: the childhood picture, now a measured budget.

**Remark 64.9 (What forces do — the missing law).**

This chapter [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force); it does not yet say what a *surplus* of [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) does to motion. The four childhood jobs — start, stop, turn, deform — await their exact law, and it is one of the greatest in all physics: the High School volume opens its mechanics with it. This year finishes the groundwork: [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) in [newtons](#def-g9-weight-vs-mass-newton), [weights](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) by formula, arrows to scale — the grammar of the sentence to come.

## 64.4 Exercises

**Exercise 64.1 ★.**

Name the [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) and its instrument. Give two everyday anchors for one [newton](#def-g9-weight-vs-mass-newton) and for a hundred.

**Solution of Exercise 64.1.**

The [newton](#def-g9-weight-vs-mass-newton) ($\mathrm{N}$), measured with the [dynamometer](#def-g9-weight-vs-mass-dynamometer). Anchors: one [newton](#def-g9-weight-vs-mass-newton) — a small apple’s [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight); a hundred — a solid handshake (or a $10\,\mathrm{kg}$ suitcase’s [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight)).

**Exercise 64.2 ★.**

Write the [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) formula with [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring), and the meaning of $g$ in words.

**Solution of Exercise 64.2.**

$P = m \times g$: [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) in [newtons](#def-g9-weight-vs-mass-newton), [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) in [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units), and $g$ — the place’s [gravitational strength](#prop-g9-weight-vs-mass-formula) — the [newtons](#def-g9-weight-vs-mass-newton) of pull each [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) receives there ($9.8\,\mathrm{N}/\mathrm{kg}$ on Earth).

**Exercise 64.3 ★.**

Compute Earth [weights](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight): a $25\,\mathrm{kg}$ dog; a $700\,\mathrm{g}$ loaf; yourself (pick your [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)).

**Solution of Exercise 64.3.**

Dog: $25 \times 9.8 = 245\,\mathrm{N}$. Loaf: $0.7 \times 9.8
\approx 6.9\,\mathrm{N}$. A $55\,\mathrm{kg}$ reader: about $539\,\mathrm{N}$.

**Exercise 64.4 ★.**

A hanging melon stretches the [dynamometer](#def-g9-weight-vs-mass-dynamometer) to $14.7\,\mathrm{N}$. Its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)?

**Solution of Exercise 64.4.**

$m = 14.7 \div 9.8 = 1.5\,\mathrm{kg}$.

**Exercise 64.5 ★.**

Read the chapter’s graph: what does its slope mean, and what would the line do 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)?

**Solution of Exercise 64.5.**

The slope is the local $g$ — [newtons](#def-g9-weight-vs-mass-newton) per [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units). 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) the line stays straight through the origin but slumps to a gentle $1.6$ slope: same proportionality, weaker world.

**Exercise 64.6 ★.**

The $10\,\mathrm{kg}$ suitcase tours Earth, [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon), Mars, Jupiter. Which numbers in the table never change, and which change — and why?

**Solution of Exercise 64.6.**

The [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) column never changes — $10\,\mathrm{kg}$ of stuff travels intact. The $g$ and [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) columns change with the world: [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) is the local toll, $m \times g$.

**Exercise 64.7 ★.**

Why does a balance tell the truth on every world while the bathroom scale flatters 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)? Formulas, not feelings.

**Solution of Exercise 64.7.**

The balance compares $m_1 g$ with $m_2 g$: $g$ multiplies both pans and cancels — [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass), truthfully, anywhere. The bathroom scale [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) $P = m g_{\text{here}}$ but divides by $g_{\text{Earth}}$ to print [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units): 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) it prints $m \times 1.6/9.8$ — one sixth of the truth.

**Exercise 64.8 ★.**

Draw (or describe) the $2\,\mathrm{kg}$ dictionary’s two [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) arrows at one [centimetre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) per five [newtons](#def-g9-weight-vs-mass-newton): lengths, directions, and the budget’s verdict.

**Solution of Exercise 64.8.**

[Weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight): $19.6\,\mathrm{N}$ down — an arrow about $3.9\,\mathrm{cm}$ long at five [newtons](#def-g9-weight-vs-mass-newton) per [centimetre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units), from the book downward. Support: an equal $3.9\,\mathrm{cm}$ arrow upward. Equal lengths, opposite ways: budget balanced, book still.

**Exercise 64.9 ★★.**

An airline allows $23\,\mathrm{kg}$ per bag. A passenger argues: “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) it would only weigh a few [newtons](#def-g9-weight-vs-mass-newton)!” Why does the airline’s limit — fuel and floor-strength aside — properly concern [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass), and what instrument should check it at a lunar airport?

**Solution of Exercise 64.9.**

The plane must carry, lift and brake the bag’s *stuff* — its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) — and $23\,\mathrm{kg}$ of stuff is $23\,\mathrm{kg}$ on any world. The lunar desk needs a balance with marked masses: the only scale that survives the change of $g$.

**Exercise 64.10 ★★.**

On Mars, a rover’s arm weighs $111\,\mathrm{N}$. Its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)? What would the same arm weigh back in the assembly hall on Earth?

**Solution of Exercise 64.10.**

$m = 111 \div 3.7 = 30\,\mathrm{kg}$; on Earth it weighs $30
\times 9.8 = 294\,\mathrm{N}$.

**Exercise 64.11 ★★.**

A [dynamometer](#def-g9-weight-vs-mass-dynamometer) zeroed lying flat, then used hanging, lies by a little — which way, and why? (What extra [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) joins the load’s?)

**Solution of Exercise 64.11.**

It reads too high: hanging, the spring also carries its own (and its hook’s) [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight), which the flat zero never included — the instrument adds a constant surplus. Zero it hanging, and the surplus is subtracted before the load arrives.

**Exercise 64.12 ★★★.**

Design the experiment that draws the chapter’s graph and extracts $g$: equipment, table of measurements, the plot, and how the slope is read out. Then explain what the same protocol, run in a [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) laboratory, would deliver — which numbers change, which method survives untouched.

**Solution of Exercise 64.12.**

Equipment: [dynamometer](#def-g9-weight-vs-mass-dynamometer), set of marked masses ($1$ to $5\,\mathrm{kg}$), hook. Hang each [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass), record ($m$, $P$) pairs, plot $P$ against $m$: the points align through the origin, and the slope — rise in [newtons](#def-g9-weight-vs-mass-newton) over run in [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) — is $g \approx 9.8\,\mathrm{N}/\mathrm{kg}$. 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): identical protocol, identical straightness, new slope $1.6$ — the method [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) whatever world it stands on; only the number is local.

## 64.5 Problem: The Interplanetary Outfitters

**Problem 64.1.**

Weekend problem — the interplanetary outfitters’ fitting room; one body, four worlds; scales, dynamometers and the luggage desk

The outfitters equip travelers for the [Solar System](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-family)’s ports ($g$, in $\mathrm{N}/\mathrm{kg}$: Earth $9.8$; [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) $1.6$; Mars $3.7$; Jupiter cloud-deck $24.8$). You staff the fitting room.

**Part I — The fitting.** A traveler of [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) $70\,\mathrm{kg}$ steps up.

1. Their [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) at each of the four ports?
2. At which port does the classic bathroom scale (marked in [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) , calibrated for Earth) read their [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) correctly — and what does it read at the other three? (Divide each [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) by Earth’s $g$ .)
3. The outfitters’ honest scale is a balance with marked masses. What does it report at each port, and why?
4. The traveler’s boots must never press the ground with more than $2000\,\mathrm{N}$ (thin station floors). Any port where boots-plus-body ( $70\,\mathrm{kg}$ total) break the rule?

**Part II — The luggage desk.**

5. The Mars-bound trunk masses $40\,\mathrm{kg}$ . Compute its [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) at departure (Earth) and at arrival (Mars).
6. The porters’ union caps hand-carried *[weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight)* at $200\,\mathrm{N}$ at every port. What maximum *[mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)* may a porter carry at each?
7. A crate labeled “ $150\,\mathrm{N}$ 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) ” must clear Earth customs by [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) . Do the conversion.
8. The desk’s [dynamometer](#def-g9-weight-vs-mass-dynamometer) reads a hanging duffel at $294\,\mathrm{N}$ on Earth. [Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) , and its [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) for the manifest?

**Part III — Complaints and curiosities.**

9. A bodybuilder returns from the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) furious: “Six-fold strength gains, gone overnight!” Console them with the formula: what actually changed at each port, and what never did?
10. A Jupiter-deck chef complains that whisking feels like lifting anvils, though the whisk “masses a mere $200\,\mathrm{g}$ ”. Compute the whisk’s deck [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) and adjudicate.
11. The gift shop sells “a [newton](#def-g9-weight-vs-mass-newton) of chocolate, anywhere”. At which port does the buyer get the most chocolate *stuff* , and how much [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) at each of Earth, [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) , Jupiter?
12. Write the outfitters’ motto: one sentence separating what travels with you from what each world charges.

**Solution of Problem 64.1.**

**1.** Earth $70 \times 9.8 = 686\,\mathrm{N}$; [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) $112\,\mathrm{N}$; Mars $259\,\mathrm{N}$; Jupiter deck $1736\,\mathrm{N}$. **2.** Correct on Earth: $70\,\mathrm{kg}$. [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon): $112 \div
9.8 \approx 11.4\,\mathrm{kg}$; Mars: $259 \div 9.8 \approx
26.4\,\mathrm{kg}$; Jupiter: $1736 \div 9.8 \approx
177\,\mathrm{kg}$ — flattery and slander by formula. **3.** $70\,\mathrm{kg}$ at every port: the balance’s comparison cancels the local $g$. **4.** Only Jupiter’s deck: $1736\,\mathrm{N}$ approaches the limit but stays under — no port breaks $2000\,\mathrm{N}$ for this traveler (a heavier colleague of $90\,\mathrm{kg}$ would break it there: $90 \times 24.8 = 2232\,\mathrm{N}$). **5.** Departure: $40 \times 9.8 = 392\,\mathrm{N}$; arrival: $40 \times 3.7 = 148\,\mathrm{N}$. **6.** $m = 200/g$: Earth $20.4\,\mathrm{kg}$; [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) $125\,\mathrm{kg}$; Mars $54\,\mathrm{kg}$; Jupiter $8.1\,\mathrm{kg}$ — the union’s fixed [newtons](#def-g9-weight-vs-mass-newton) buy very different masses. **7.** $m = 150 \div 1.6 = 93.75\,\mathrm{kg}$ — about $94\,\mathrm{kg}$ of crate for customs. **8.** $m = 294 \div 9.8 = 30\,\mathrm{kg}$; [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) $30 \times 1.6 = 48\,\mathrm{N}$. **9.** Muscles and [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) came home unchanged; only the opponent did. 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) each [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) cost $1.6\,\mathrm{N}$ to lift; home charges $9.8\,\mathrm{N}$ again. The gains were 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 discount, not the body’s growth — $P = m g$, with $m$ loyal and $g$ fickle. **10.** $0.2 \times 24.8 \approx 5\,\mathrm{N}$ — an anvil it is not: on Earth the whisk weighed $2\,\mathrm{N}$, so deck whisking is two-and-a-half-fold heavier, wearying for a wrist but hardly foundry work. Complaint: sustained, partially. **11.** A [newton](#def-g9-weight-vs-mass-newton) of chocolate is $m = 1/g$: Earth about $102\,\mathrm{g}$; [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) $625\,\mathrm{g}$; Jupiter $40\,\mathrm{g}$. Buy your [newtons](#def-g9-weight-vs-mass-newton) 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). **12.** For example: “[Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) travels with you; [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) is each world’s toll on it — pack [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units), and let the ports charge their [newtons](#def-g9-weight-vs-mass-newton).”