Weight, mass and quick revision

4.1 Weight is a force

An object's weight is the pull that the Earth exerts on it. Weight tells us how strongly the Earth pulls the object. Because it is a force, weight is measured in newtons (N).

Not every object is pulled with the same force. Hang a pencil case, a lunch box and a stone from a spring in turn. The spring stretches, and the amount of stretch is different for different objects. So the pull differs from object to object, and so does the weight.

4.2 Measuring weight with a spring balance

A spring balance is a device used to measure weight, and therefore force. A spring is fixed inside it, and a hook hangs from its free end. Hanging an object on the hook stretches the spring, and the amount of stretch gives the weight of the object. A scale on the balance shows the weight in newtons; usually a second scale shows the corresponding mass in grams.

Reading a spring balance takes care. Look at the largest mark on the scale to find its range. In the chapter's example, the balance can measure up to 10 N, so its range is 0 to 10 N. Then look at the small divisions between two large marks. If the difference between 0 and 1 N is divided into five small parts, one small division stands for 0.2 N, so the smallest readable weight is 0.2 N. Never hang an object heavier than the maximum the balance can measure, because the spring may be damaged.

4.3 Mass is not weight

Mass and weight are often confused because everyday language mixes them. Mass measures how much matter an object contains, in grams or kilograms. Its value stays the same everywhere. Weight is the gravitational force on the object, measured in newtons, and it can change from place to place because gravity can change.

The difference becomes large on other worlds. An object with a mass of 1 kg has a weight of about 10 N on the Earth, about 1.6 N on the Moon, 3.8 N on Mars, 9 N on Venus and 25.4 N on Jupiter. The mass stays 1 kg everywhere; only the weight changes. Everyday speech says a bag of wheat weighs 10 kg, but in science the correct statement is that its mass is 10 kg; its weight would be about 100 N.

4.4 Floating and sinking

Lift a mug of water while it is still inside a bucket; the mug feels lighter than it does in air. A liquid pushes upward on objects placed in it. Push an empty, tightly closed bottle into a bucket of water and you feel an upward push; release it and the bottle rises back to the top. The upward force a liquid exerts on an object is called upthrust or buoyant force.

Two forces act on an object in water: gravity pulls it down and buoyant force pushes it up. When gravity wins, the object goes down to the bottom; when the upward push matches gravity, the object stays on the surface. One factor that decides the buoyant force is the density of the liquid. Archimedes' principle puts it this way: an object fully or partly immersed in a liquid feels an upward push matching the weight of the fluid it pushes aside. A pumice rock floats because it is full of gas bubbles and is less dense than water.

4.5 Common mistakes to avoid

• Thinking a force needs contact: magnetic, electrostatic and gravitational forces act from a distance.
• Believing an object at rest has no forces on it: the forces may be balanced.
• Mixing up mass and weight: mass is measured in grams or kilograms and stays the same, while weight is a force measured in newtons and can change.
• Using kilograms for weight in science: the correct unit of weight is the newton.
• Saying like charges attract: like charges repel, while unlike charges attract.
• Forgetting that friction opposes motion: it acts against the direction of motion or attempted motion.
• Treating all forms of friction as a nuisance: friction between surfaces has real effects that engineers design around.