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The Earth pulls every object toward its center; weight is that pull in newtons, and mass stays the same everywhere.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will say which way gravity pulls anywhere on Earth, explain why things fall, work out weights in newtons on Earth and the Moon, and keep mass and weight apart.
From the first lesson you know every force has two ends, and that some forces reach across a gap, like a magnet's. From the balanced-forces lesson you know that an unbalanced force changes how something moves. And you can measure a force in newtons with a spring scale.
Gravity uses all of those ideas. It is a non-contact pull between the Earth and every object, and when nothing balances it, things fall.
| Term | What it means |
|---|---|
| Gravity | The pull between the Earth and every object, reaching across any gap. |
| Weight | The pull of gravity on an object, measured in newtons. |
| Mass | How much stuff an object has, measured in kilograms. |
| Down | Toward the center of the Earth. |
| Newton (N) | The unit of force; on Earth about 10 N pull on each kilogram. |
| Free fall | Falling with nothing but gravity acting. |
Gravity is a pull between the Earth and every object near it. Like a magnet's pull, it reaches across a gap; unlike a magnet, it pulls on everything: rocks, water, air, people and paper.
The Earth pulls toward its center. That is what down means. The Earth is round, so down points a different way in different places: in Alaska and in Australia, people's feet point toward the same center, and nobody falls off.
The size of the pull on an object is its weight, measured in newtons. On Earth gravity pulls about $10$ N on every kilogram, so a $3$ kg bag weighs about $30$ N. The Moon pulls much less, about $1.6$ N on each kilogram, so the same bag weighs about $4.8$ N there. The bag's mass, $3$ kg, is the same in both places.
Another way: action
Hang a bag of books from a spring scale and read its weight in newtons. Then look at the label on a bag of flour in kilograms and multiply by ten.
Another way: steps
A book on a table does not fall, because the table pushes up just as hard as the Earth pulls down. The forces are balanced. Slide the book off the edge and the table's push is gone. Now only gravity acts, the forces are unbalanced, and the book speeds up toward the floor.
So falling is not what happens when a force stops. It is what happens when gravity, which was pulling all along, is left without anything to balance it. The apple on a tree is pulled down the whole time; the stem was pulling it back up. When the stem snaps, the apple falls.
People often use weight to mean mass, as in I weigh 30 kilograms. In science they are two different things.
| Mass | Weight | |
|---|---|---|
| what it is | how much stuff | the pull of gravity |
| unit | kilogram (kg) | newton (N) |
| on the Moon | the same | about a sixth |
A $20$ kg child has a mass of $20$ kg on Earth, on the Moon, and floating in a space station. Their weight is about $200$ N on Earth, about $32$ N on the Moon, and almost nothing when floating far out in space.
Draw the Earth as a circle and draw people standing on it all the way around, with their feet on the circle and their heads pointing out. Every person's down points toward the middle of the circle.
That is why the Earth is round in the first place. Gravity pulls every bit of it toward the middle, squeezing it into a ball. It is also why oceans do not pour off the bottom of the planet: there is no bottom, only a center that everything is pulled toward.
A dropped ball in New York falls toward the same center as a dropped ball in Sydney, Australia, even though the two balls fall in almost opposite directions through space.
Gravity pulls on every kilogram the same amount. A heavy bowling ball has more kilograms than a tennis ball, so it has a bigger weight. But each kilogram of it is pulled just the same as each kilogram of the tennis ball.
That leads to a surprise. Dropped together from the same height, a bowling ball and a baseball land at almost the same moment. Only air pushing on the falling things makes any difference, which is why a feather falls slowly. On the Moon, where there is no air, an astronaut dropped a hammer and a feather together in 1971, and they landed at exactly the same time.
Run three checks.
The second check catches the most common slip: saying an astronaut's mass drops on the Moon. Only her weight drops.
Gravity is a pull between any two objects, and it is stronger when the objects have more mass. The Earth has an enormous mass, so its pull on you is strong enough to notice. The Moon has much less mass than the Earth, about one eightieth as much, so its pull on each kilogram is weaker.
You might expect the Moon's pull to be one eightieth of the Earth's, but it is about one sixth. That is because the Moon is also much smaller, and standing on its surface puts you much closer to its center. Being closer makes gravity stronger, just as a magnet's pull is stronger up close. The two effects together give about $1.6$ N on each kilogram instead of $10$.
Every planet has its own pull. On Mars it is about $3.7$ N for each kilogram, and on Jupiter, a giant planet, about $25$ N. A $30$ kg child would weigh about $111$ N on Mars and about $750$ N on Jupiter, while their mass stayed $30$ kg the whole trip.
Every force has two ends, and gravity is no exception. The Earth pulls you down, and you pull the Earth up toward you, just as hard. So why does the Earth not move?
It does, but by an amount far too tiny to notice. The Earth has so much mass that your pull hardly changes its motion at all, while its pull on your small mass makes you fall quickly. It is like a small child and a truck pushing each other: the push is the same size both ways, but only the child goes anywhere.
This is also why the ocean has tides. The Moon's gravity pulls on the whole Earth, and it pulls a little harder on the side facing it. The water there bulges toward the Moon, and as the Earth turns, beaches around the world see the sea rise and fall about twice a day.
A spring scale measures weight directly. Hang an object from the hook, and gravity pulls it down, stretching the spring until the spring's pull up balances the weight. The pointer then shows the weight in newtons.
Read it exactly like any other scale: find two printed numbers, count the spaces, work out what one mark is worth, and count along. A bag of apples that stretches the spring to $15$ N has a mass of about $15 \div 10 = 1.5$ kg.
Take the same spring scale and apples to the Moon, and the pointer would stop at only about $2.4$ N. The spring is the same and the apples are the same. The pull on them is weaker, so the spring stretches less, and the reading tells you so honestly, without any trick at all, on any world.
NASA plans missions to the Moon carefully by mass, because every kilogram must be launched off the Earth. A moon rover might have a mass of $200$ kg. On Earth it weighs about $2{,}000$ N, far too heavy for two astronauts to lift. On the Moon it weighs about $200 \times 1.6 = 320$ N, which two astronauts could lift together.
But its mass is still $200$ kg. Once it is rolling, it is just as hard to stop as on Earth, because stopping it depends on how much stuff it has, not on how hard the Moon pulls on it. Astronauts have to remember both: the rover is light to lift but heavy to stop.
Engineers write the mass on every piece of equipment, and work out its weight for whichever world it is going to.
At a checkup, a nurse weighs you on a scale. Most scales actually measure the push of your feet, which is your weight, and then divide by ten to show kilograms or convert to pounds. That works because on Earth every kilogram is pulled about the same amount.
A child with a mass of $30$ kg presses down with about $300$ N. The scale shows $30$ kg. If the same scale were taken to the Moon, the child would press down with only about $48$ N, and the scale, still dividing by ten, would wrongly show about $5$ kg.
The child would not have lost any mass. The scale would simply be using the wrong pull. A balance that compares the child with known masses would still read $30$ kg on the Moon, because it compares mass with mass.
Many people explain falling as what happens when support is taken away, as if gravity only started then. Gravity pulls all the time. Support balances it; take the support away and the pull, now unbalanced, makes the thing speed up.
A second mistake is thinking down is one fixed direction in space, so people on the other side of the world ought to fall off. Down is toward the Earth's center, wherever you stand.
A third is mixing up mass and weight. Mass is how much stuff, in kilograms, and it does not change on the Moon. Weight is the pull of gravity, in newtons, and it does.
Read the mass.
$4\ \text{kg}$
From a kitchen scale.
Recall the Earth's pull.
$10\ \text{N per kg}$
About ten newtons on each kilogram.
Multiply the mass by the pull.
$4 \times 10 = 40\ \text{N}$
The weight on Earth.
Check with a spring scale.
$\text{reads about } 40\ \text{N}$
Measured and worked out agree.
Name what you found.
$\text{weight} = 40\ \text{N}, \ \text{mass} = 4\ \text{kg}$
Two different quantities with different units.
Keep the mass.
$4\ \text{kg}$
The same amount of stuff.
Recall the Moon's pull.
$1.6\ \text{N per kg}$
Much weaker than Earth's.
Multiply the mass by the pull.
$4 \times 1.6 = 6.4\ \text{N}$
The weight on the Moon.
Compare with Earth.
$40 - 6.4 = 33.6\ \text{N lighter}$
Easy to carry on the Moon.
Check the fraction.
$6.4 \approx 40 \div 6$
About a sixth, as expected.
State what did not change.
$\text{mass: still } 4\ \text{kg}$
Only the pull changed.
Name the forces on the hanging apple.
$\text{Earth pulls down; stem pulls up}$
Two forces, two ends each.
Compare the two forces.
$\text{equal and opposite}$
The apple hangs still.
Break the apple stem.
$\text{the stem's pull is gone}$
Only one force remains.
Find the resultant.
$\text{gravity alone, downward}$
Unbalanced.
Say what happens.
$\text{the apple speeds up toward the ground}$
An unbalanced force changes motion.
Name the direction.
$\text{toward the Earth's center}$
That is what down means.
Check the misconception.
$\text{gravity was pulling all along}$
It did not switch on when the stem broke.
Recall the Earth's pull.
$10\ \text{N per kg}$
About ten newtons each.
Multiply the mass by the pull.
Name the mass too.
A child in Alaska and a child in Australia each drop a ball. Which way does each ball fall?
Complete the worked solution: a toy moon rover has a mass of $35$ kg, on Earth and on the Moon alike. Find its weight on Earth, its weight on the Moon, and how much lighter it is there.
Find the weight on Earth.
$35 \times 10 =$ a N
Ten newtons for every kilogram.
Find the weight on the Moon.
$35 \times 1.6 =$ b N
The same mass, pulled more weakly on each kilogram.
Find how much lighter it is.
$\text{Earth weight} - \text{Moon weight} =$ c N
Its mass did not change; only the pull did.
Match each statement to mass or to weight.
| mass | weight | |
|---|---|---|
| measured in kilograms | ||
| measured in newtons | ||
| the same on the Moon as on Earth | ||
| smaller on the Moon than on Earth |
An apple hangs on a tree, then its stem snaps. Why does it fall?
A rock has a mass of $5$ kg. Fill in its mass and its weight on Earth and on the Moon.
| mass (kg) | weight (N) | |
|---|---|---|
| on Earth | ||
| on the Moon |
A dog has a mass of $26$ kg. About how much does it weigh on Earth, in newtons?
Answer: unit: N / kN
An astronaut's tool bag has a mass of $5$ kg. On Earth gravity pulls about $10$ N on every kilogram; on the Moon, about $1.6$ N. How many newtons lighter does the bag feel on the Moon than on Earth?
Answer: unit: N / kN
An astronaut stands on a bathroom scale that measures the push of her feet in newtons, first on Earth and then on the Moon. What happens to the reading, and to her mass?
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A rock has a mass of $20$ kg. Fill in its mass and its weight on Earth and on the Moon.
| mass (kg) | weight (N) | |
|---|---|---|
| on Earth | ||
| on the Moon |
You can work out an object's weight on Earth and on the Moon. Tell someone why an astronaut's mass stays the same on the Moon even though her weight drops.
19. Your turn: a 12 kg suitcase. What does it weigh on Earth?, step 2
$12 \times 10 = 120\ \text{N}$
The weight.
19. Your turn: a 12 kg suitcase. What does it weigh on Earth?, step 3
$\text{still } 12\ \text{kg}$
Mass and weight are different.