Contents: 8 sections
Cambridge IGCSE Physics 0625 · Core and Extended
Syllabus points
- State that mass is a measure of the quantity of matter in an object.
- State that weight is a gravitational force acting on an object.
- Recall and use the equation W = mg.
- Understand that weights, and therefore masses, can be compared using a balance.
- Understand gravitational field strength as force per unit mass, and that it is equivalent to the acceleration of free fall.
Two different quantities
This subtopic exists because everyday speech merges two things that physics keeps apart.
| Mass | Weight | |
|---|---|---|
| What it is | Quantity of matter | Gravitational force on that matter |
| Unit | kilogram, kg | newton, N |
| Scalar or vector | Scalar | Vector, acting downwards |
| Changes with location? | No | Yes |
| Measured with | Balance | Newton meter (spring balance) |
A question asking for a mass is not answered in newtons, and a question asking for a weight is not answered in kilograms. Whole questions are built on nothing more than this, with all four options carrying the same number and only the units differing.
W = mg
weight = mass x gravitational field strength
- W in newtons
- m in kilograms
- g in N/kg, about 9.8 N/kg on Earth, and 10 N/kg is accepted in most questions
Worked example. A 6.0 kg object rests on a planet where g = 20 N/kg. Find its weight.
W = 6.0 x 20 = 120 N.
The commonest slip is to reach for Earth's g out of habit. If a question puts you on another planet, it is testing whether you read the value it gave you.
Why the same mass weighs different amounts
Mass is a property of the object. Move it and nothing about it changes: the same number of particles, the same amount of matter.
Weight depends on where the object is, because g depends on the body producing the field.
- On the Moon g is about one sixth of Earth's, so a 60 kg astronaut weighs about 100 N there instead of 600 N.
- On Mars g is smaller than Earth's, so a probe weighs less on arrival. Its mass is unchanged.
- In deep space, far from any large body, g is near zero, so the weight is near zero. The mass is still the same.
This is worth a moment. Asked what happens to a space probe taken to Mars, the answer is that the weight decreases and the mass is unchanged. Nothing about the journey removes matter.
Working the other way
If a spring stretches by the same amount, the force on it is the same, so the weight is the same.
On the Moon, where g is one sixth of Earth's, you need six times the mass to produce the same weight. A 3.0 kg mass on Earth is matched by an 18 kg mass on the Moon, not by 0.5 kg. Weaker gravity means more mass is needed for a given force, and getting that factor the right way up is the whole question.
Gravitational field strength
g is the force per unit mass, in N/kg:
g = W / m
It is also numerically equal to the acceleration of free fall, in m/s², and this is not a coincidence. An object in free fall has only its weight acting on it, so:
acceleration = force / mass = mg / m = g
The mass cancels, which is why every object falls at the same rate when air resistance is ignored, and why 9.8 N/kg and 9.8 m/s² are the same number written two ways.
Comparing masses with a balance
A beam balance compares the weight in one pan with the weight in the other. Because both pans sit in the same gravitational field, equal weights mean equal masses, and the comparison works anywhere. A beam balance taken to the Moon still balances correctly.
A spring balance measures force, so its reading changes with location. Taken to the Moon it reads about a sixth of what it read on Earth for the same object.
If a shopkeeper hangs rice in a dish from a spring balance and later hangs pasta that gives the same reading, the quantity that must be the same is the weight. Rice and pasta have different densities, so equal weights do not mean equal volumes.
Inertia
Mass also measures how strongly an object resists a change in motion. Loading a car makes it harder to accelerate and harder to stop, because both are changes in motion. Inertia works in both directions, which catches out anyone who expects extra mass to help with one of them.
Common mistakes
- Giving a mass in newtons or a weight in kilograms.
- Saying an object's mass decreases in space, or on the Moon.
- Using Earth's g when the question supplies a different value.
- Dividing by six instead of multiplying, when asked what mass gives the same weight under weaker gravity.
- Saying a beam balance would give a different reading on the Moon.
- Forgetting that extra mass makes stopping harder as well as starting.
- Treating g as if it had only one meaning; it is both a field strength in N/kg and an acceleration in m/s².