Forces, mass and weight
A force is a push or a pull that comes from an interaction between two objects. Weight is the force of gravity on an object, and it is not the same thing as mass, which is why you would weigh less on the Moon but have the same mass.
Part 1 of 3: Learn it
In short
- Scalars have size only; vectors have size and direction. Force is a vector.
- Weight W = mg: mass in kg times gravitational field strength in N/kg gives newtons.
- Mass stays the same everywhere; weight depends on the gravitational field.
Where this is in your specification
Spec points: AQA 4.5.1.1 to 4.5.1.3 (Combined Trilogy 6.5.1.1 to 6.5.1.3), Edexcel Topics 8 and 9, OCR P2.3
| Board | Topic: Forces, work, elasticity, moments and pressure |
|---|---|
| AQA 8463 | 4.5.1 to 4.5.5 (8463); 6.5.1 to 6.5.3 (8464) |
| Edexcel 1PH0 | Topics 8, 9 and 15 |
| OCR J249 | P2.3 |
| Eduqas C420 | 3.1 to 3.3 |
| Cambridge IGCSE 0625 | 1.3, 1.5, 1.8 |
| National 5 C857 75 | Dynamics: Newton's laws |
Scalars and vectors
| Scalars (size only) | Vectors (size and direction) |
|---|---|
| distance | displacement |
| speed | velocity |
| mass | force, including weight |
| energy, time, temperature | acceleration, momentum |
A vector can be drawn as an arrow: its length shows the size and it points in the direction of the quantity.
Contact and non-contact forces
- Contact forces need the objects to touch: friction, air resistance, tension, normal contact force.
- Some forces act without the objects touching: gravitational, electrostatic and magnetic forces.
Mass and weight
W is weight in newtons (N), m is mass in kilograms (kg) and g is gravitational field strength in newtons per kilogram (N/kg). On Earth g is about 9.8 N/kg; on the Moon it is about 1.6 N/kg.
Weight is proportional to mass, and it is measured with a calibrated spring balance called a newtonmeter. Mass is measured with a balance and does not change from place to place.
Centre of mass
The weight of an object can be treated as acting at a single point, its centre of mass. For a symmetrical object of even density it is at the centre. A hanging object comes to rest with its centre of mass directly below the point it hangs from.
Is velocity a scalar or a vector?
Show the answer
A vector. Velocity includes which way the object is going as well as how fast.
Part 2 of 3: See it worked
Worked examples
Example 1
A person has a mass of 65 kg. Find their weight on Earth (g = 9.8 N/kg) and on the Moon (g = 1.6 N/kg).
- Earth: W = 65 × 9.8 = 637 N
- Moon: W = 65 × 1.6 = 104 N
- The mass is 65 kg in both places
Answer: 637 N on Earth and 104 N on the Moon.
Example 2
A bag has a weight of 24.5 N on Earth. What is its mass? (g = 9.8 N/kg)
- m = W ÷ g
- m = 24.5 ÷ 9.8
Answer: 2.5 kg.
Common mistakes
- Giving weight in kilograms. Weight is a force, measured in newtons.
- Saying mass changes on the Moon. Only the weight changes.
- Using grams in W = mg.
- Calling speed a vector. Velocity is the vector; speed has no direction.
Find the weight of a 3.2 kg rock on a planet where g = 3.7 N/kg.
Show the answer
W = 3.2 × 3.7 = 11.84 N.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
Is velocity a scalar or a vector?
A vector. Velocity includes which way the object is going as well as how fast.
Find the weight of a 3.2 kg rock on a planet where g = 3.7 N/kg.
W = 3.2 × 3.7 = 11.84 N.
Name two non-contact forces.
Any two of: gravitational, magnetic, electrostatic.
Jobs that use this
- Mechanical engineer (se abre en otra pestaña)
- Aerospace engineer (se abre en otra pestaña)
- Structural engineer (se abre en otra pestaña)
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Estos apuntes están en inglés porque siguen los programas de examen del Reino Unido.
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