Mechanics

Friction

Static friction f_s ≤ μ_s N can prevent motion. Kinetic friction f_k = μ_k N opposes sliding. Always parallel to the surface, opposite the attempted motion.

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_s ≤ μ_s N. Static friction (maximum at the point of slipping)
How a marker reads it
Friction is NOT always μN. Static can be any value up to μ_s N. Only kinetic is exactly μ_k N.

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

A 20 kg crate on a warehouse floor in Isando. μ_s = 0.40, μ_k = 0.30, g = 9.8. (a) Max pull before it moves? (b) Friction once it slides?

Before any working — hunt first

Given

Numbers and units already in the sentence: 20 kg · 0.40 · 0.30 · 9.8. 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: (b) Friction once it slides. Circle that word — that is the missing variable.

Find

We are required to find: (b) Friction once it slides. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write f_s ≤ μ_s N with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives (b) Friction once it slides.

Simplified approach

N = mg on a horizontal floor. Max static = μ_s N. Once moving, use μ_k — it is smaller, so it is easier to keep it sliding than to start it.

Culture note

Pushing a crate of mielie-meal at a Limpopo spaza — the first shove is the hard one (static). Once it slides, you ease off (kinetic).

Formulas

f_s ≤ μ_s N

Static friction (maximum at the point of slipping)

f_k=μ_k N

Kinetic friction

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.

μ_s
static coefficient
How you spot this in the sentence
When the sentence names the static coefficient, that letter is μ_s. Copy the number next to it into Given. If the sentence never names it, μ_s is Missing. f_s ≤ μ_s N. The biggest friction before the object starts sliding.
Example:μ_s=0,4, N=50 N→f_s max=20 N.
μ_k
kinetic coefficient
How you spot this in the sentence
When the sentence names the kinetic coefficient, that letter is μ_k. Copy the number next to it into Given. If the sentence never names it, μ_k is Missing. f_k = μ_k N while it is already sliding. Usually μ_k < μ_s.
Example:N is the normal force, perpendicular to the surface — often mg on a flat floor.

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.

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.
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.
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 / 6

Normal force

N=mg=20×9.8=196 N.

N=196 N

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.

4. Step-by-step working

01
Normal force
N=mg=20×9.8=196 N.
N=196 N
02
Max static
f_s(max)=0.40×196=78.4 N.
78.4 N
03
Kinetic
f_k=0.30×196=58.8 N.
58.8 N

More worked examples

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

Example 1 / 20

A 10 kg crate, μ = 0.3, on level ground. Maximum static friction? g = 9.8.

4. Step-by-step working

01
Free-body diagram
N=mg=10×9.8=98 N.
N=98 N
02
Friction
f_max=0.3×98=29.4 N.
29.4 N

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: A 10 kg crate, μ = 0.3, on level ground. Maximum static friction? g = 9.8.

Before any working — hunt first

Given

Numbers and units already in the sentence: 10 kg · 0.3 · 9.8. 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: 8. Circle that word — that is the missing variable.

Find

We are required to find: 8. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write N = 98 N with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 8.

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

If you have never seen this before: Draw a free-body diagram, find N, then use f = μN. 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?

m=10 kg, μ=0.3, level so N=mg.

3. Which method — and why this one?

Draw a free-body diagram, find N, then use f=μN.

4. Step-by-step working

01 / 05
Free-body diagram
N=mg=10×9.8=98 N.
N=98 N
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
Friction
f_max=0.3×98=29.4 N.
29.4 N
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
29.4 N
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

29.4 N

Copy onto your answer sheet — in this order

Formula: N=98 N

Answer: 29.4 N

6. Check it like a marker

On level ground N = mg, not μ mg. Friction is μ times N.

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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Physical Sciences — Physics

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