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Mass and weight

🌍 1.3: Mass and Weight

1️⃣ What is Mass?​

Definition:
Mass is a measure of the quantity of matter in an object.

  • It tells us how much “stuff” (matter) an object contains.

  • It does not change wherever the object is in the universe (on Earth, the Moon, or in space).

  • It is a scalar quantity – it only has magnitude (size), not direction.

  • SI Unit: kilogram (kg)

  • Other common units: gram (g), tonne (t)

    1 kg = 1000 g
    1 tonne = 1000 kg

Example:
A rock has a mass of 2 kg whether it is on Earth, on the Moon, or floating in space.

2️⃣ What is Weight?​

Definition:
Weight is the gravitational force acting on an object with mass.

  • It depends on gravitational field strength (g) — how strong gravity is at a place.

  • It is a vector quantity — it has both magnitude and direction (always acts downward, towards the center of the Earth).

  • SI Unit: newton (N)

  • Weight changes depending on where the object is (Earth, Moon, etc.).

Formula:

W = m x g

Where:

  • ( W ) = weight (N)

  • ( m ) = mass (kg)

  • ( g ) = gravitational field strength (N/kg)

3️⃣ Gravitational Field Strength (g)​

Definition:
Gravitational field strength is the force per unit mass experienced by an object in a gravitational field.

g = W/m

  • On Earth, ( g = 9.8 N/kg ) (often approximated as 10 N/kg in IGCSE).

  • On the Moon, ( g = 1.6 N/kg ).

  • It tells us how strong gravity is — it shows how much force acts on each kilogram of mass.

Example:
If an object has a mass of 3 kg:

W = m x g = 3 x 10 = 30 N

That means the Earth pulls the object downward with a force of 30 N.

4️⃣ Comparing Weights and Masses Using a Balance​

  • A beam balance or electronic balance compares mass, not weight.

  • It works by comparing the force of gravity on an unknown object with that on known masses.

  • Since gravity acts equally on both sides, it gives a true comparison of mass, even if the gravitational field strength changes.

Example:
If you use a balance to compare a rock to a 1 kg standard mass, and the balance is level, both have the same mass — even on the Moon.

5️⃣ Weight as the Effect of a Gravitational Field​

  • Every massive object (like Earth or the Moon) has a gravitational field that pulls other objects toward it.

  • The weight of an object is the effect of that field on its mass.

  • In space (far from planets), where there’s no significant gravitational field, an object becomes weightless, but its mass remains the same.

Example:
An astronaut’s mass is 70 kg:

  • On Earth: W = 70 x 10 = 700 N

  • On Moon: W = 70 x 1.6 = 112 N

  • In space (zero gravity): W = 70 x 0 = 0 N

But in all cases, mass = 70 kg (unchanged).

🧠 Exam Tips​

✅ Tip 1: Always use the correct units.

  • Mass → kg

  • Weight → N

  • ( g ) → N/kg

✅ Tip 2: Remember that mass never changes, but weight does.

✅ Tip 3: If you see “find the weight,” use the formula W = m g
If you see “find the mass,” rearrange the formula to m = W g.

✅ Tip 4: Questions often test understanding with situations like:

“A person has a mass of 60 kg on Earth. What is their weight on the Moon?”
→ 60 1.6 = 96 N

✅ Tip 5: Be careful with direction — weight always acts downward (towards the center of the planet).

🌌 Real-World Example​

  • A 10 kg bag of flour has the same mass everywhere.

  • But its weight:

    • On Earth = 10 9.8 = 98 N

    • On the Moon = 10 1.6 = 16 N

    • In space = 10 0 = 0 N

You could push it easily on the Moon or in space, but it still contains the same amount of flour!