Mechanics

Universal gravitation

Newton’s law of universal gravitation and weight vs mass.

CAPS

Grade 11 · Physical Sciences (Physics) · Mechanics

Physics is Physical Sciences Paper 1.

The paper
Grade 11 Paper 1 builds Newton’s laws, momentum in one dimension, electrostatics, electric circuits and geometrical optics.
Working
Write the formula as it appears on the data sheet, substitute with units, then the answer with the unit and the direction if it is a vector. A positive direction you chose must be stated when the sign matters.
The relation
F=G m₁ m₂r². Gravitational force
How a marker reads it
r is centre-to-centre distance, never the gap between surfaces only.

Paper 1 is 150 marks. The data sheet is allowed. A formula copied wrong cannot be saved by a tidy final number.

Diagram

Worked example

Two 80 kg learners stand 2 m apart. Find the gravitational force between them. G = 6.67 × 10⁻¹¹ N·m²·kg⁻².

Before any working — hunt first

Given

Numbers and units already in the sentence: 80 kg · 2 m · 6.67 · 10⁻¹¹. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: the gravitational force between them. Circle that word — that is the missing variable.

Find

We are required to find: the gravitational force between them. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write F = G m₁ m₂ / r² with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives the gravitational force between them.

Simplified approach

Plug into F = G m mr². The force is tiny — gravity is weak between people.

Culture note

Two teammates standing on a Polokwane pitch feel a real but unnoticeable gravitational pull.

Formulas

F=G m₁ m₂r²

Gravitational force

How to hunt the missing letter

Do not start by naming the letters. First hunt the missing one: copy every number you can see (Given). The letter with no number is Missing. The asking word is Find. The formula that still contains that letter is what you Calculate.

How to hunt: (1) Underline every number and its unit — those are Given. (2) Circle the asking word — find, calculate, how far, what is. That word names Find. (3) The letter the asking word names, which has no number yet, is Missing. (4) Write the formula with empty letters. Cross out every given letter. The letter still standing is what you Calculate.

G
universal constant G
How you spot this in the sentence
When the sentence names the universal constant G, that letter is G. Copy the number next to it into Given. If the sentence never names it, G is Missing. G = 6,67 × 10⁻¹¹ N·m²/kg². Do not mix it up with g.
Example:F=G m₁ m₂r².
m₁, m₂
the two masses
How you spot this in the sentence
When the sentence names the the two masses, that letter is m₁, m₂. Copy the number next to it into Given. If the sentence never names it, m₁, m₂ is Missing. Both in kilograms. Attractive force on each is the same size.
Example:Earth M and a 1 kg apple: F is tiny because G is tiny.
r
centre-to-centre distance
How you spot this in the sentence
When the sentence names the centre-to-centre distance, that letter is r. Copy the number next to it into Given. If the sentence never names it, r is Missing. From the centre of one mass to the centre of the other, in metres. Not surface-to-surface.
Example:On Earth’s surface r ≈ R_earth, not zero.

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

Use g = 9,8 unless the paper says take g = 10
How:Copy g from the data sheet onto your given column first. If the instruction line says “take g = 10”, write that. Otherwise 9,8 m·s⁻². Using 10 when the paper did not say so loses the accuracy mark even if the method is right.
When to use it:Free fall, projectiles, weight, and gravitational potential energy.
List the five, then pick the equation that still has the missing letter
How:Write a column: v_i, v_f, a, Δt, Δx. Tick every one that has a number. The unticked letter is Missing. Choose the SUVAT line that does not need a letter you do not have — do not start from the formula you remember first.
When to use it:Any constant-acceleration question that names times, speeds or distances.
State “mechanical energy is conserved” in words before you substitute
How:The method mark sits in the sentence, not in the algebra. Write: mechanical energy conserved because no non-conservative work (or friction is neglected). Then E_k + E_p at A = E_k + E_p at B. Then substitute.
When to use it:Any conservation question, rollers, pendulums, or falling masses.

Step 1 / 8

Step A — Read the question twice

Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

4. Step-by-step working

01
Substitute
F=(6.67 × 10⁻¹¹)(80)(80)4=1.07×10⁻⁷ N.
1.07×10⁻⁷ N
02
Step F — Box the answer with its unit
1.07 × 10⁻⁷ N

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

Two masses. Distance doubles. New F compared with old?

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Two masses. Distance doubles. New F compared with old?

Before any working — hunt first

Given

Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: New F compared with old. Circle that word — that is the missing variable.

Find

We are required to find: New F compared with old. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write F4 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives New F compared with old.

In other words — as if you have never seen this before

If you have never seen this before: Newton’s law of universal gravitation: F = Gm₁m₂/r², so F ∝ m₁m₂ and F ∝ 1r². We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

F ∝ 1r².

3. Which method — and why this one?

Newton’s law of universal gravitation: F = Gm₁m₂/r², so F ∝ m₁m₂ and F ∝ 1r².

4. Step-by-step working

01 / 05
Write the formula
r→2r ⇒ F→F4.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Calculate
F4
F4
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
F4
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

Copy onto your answer sheet — in this order

Formula: F4

Answer: F4

6. Check it like a marker

Square the distance factor: doubling r quarters F, it does not halve it.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

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