Grade 11 Physical Sciences · Mechanics · Paper 1 (Physics)

Vectors in Two Dimensions Grade 11

Real Vectors in Two Dimensions past paper questions and answers from 2024 to 2026, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

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Question 1.1 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

Various options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in the ANSWER BOOK, e.g. 1.11 E.

1.1 Three forces act on an object so that the resultant force is zero.

Which ONE of the following vector diagrams is the CORRECT representation of the three forces?(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

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4. Question 2.3.1 · November 2025 · Paper 1 · National (DBE) · 2 marks
A block of mass $5$ kg is at rest on a rough horizontal surface. When a constant force F of magnitude $18$ N acts on the block at an angle $θ$ to the horizontal, the block experiences maximum static friction. See the diagram below.
2.3 The horizontal component of force F is $15$ N.

Calculate:
2.3.1 $θ$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $F_{x} = F cos θ$
  $15 = 18 cos θ$
  1 mark · Resolve a vector into components
2. ✓
  Answer $θ = 33, 56°$
  1 mark · Resolve a vector into components
5. Question 7.2.3 · May/June 2025 · Paper 1 · National (DBE) · 5 marks
7.2 Sphere S is attached to the ceiling at point P by a light inextensible string. When sphere R, on an insulated stand, is brought close to sphere S they repel and sphere S comes to rest with the horizontal distance between the centres of the spheres equal to $0, 03$ m.

Sphere R is directly below point P. The string makes an angle θ with the vertical, as shown in the diagram below.

Answer the questions that follow.
Sphere R has a charge of $+ 6$ nC. Sphere S has a charge $+ 3$ nC and a mass of $0, 15$ g.
7.2.3 Calculate angle θ.(5)
Show the memo (5 ticks)Memo
1. ✓
  Formula $F = \frac{k Q _{1} Q _{2}}{r ^{2}}$
  1 mark · Apply Coulomb's law
2. ✓
  Substitution $F = \frac{( 9 \times 1 0 ^{9} ) ( 6 \times 1 0 ^{- 9} ) ( 3 \times 1 0 ^{- 9} )}{( 0 , 03 ) ^{2}}$
  $= 1, 8 \times 1 0^{- 4}$ N
  1 mark · Apply Coulomb's law
3. ✓
  Weight of S $w = m g = (1, 5 \times 1 0^{- 4}) (9, 8) = 1, 47 \times 1 0^{- 3}$ N
  1 mark · Calculate weight
4. ✓
  Trig ratio $tan θ = \frac{F _{E}}{m g} = \frac{1 , 8 \times 1 0 ^{- 4}}{1 , 47 \times 1 0 ^{- 3}}$
  1 mark · Find resultant of perpendicular vectors
5. ✓
  Answer $θ = 6, 98°$
  1 mark · Find resultant of perpendicular vectors
6. Question 7.2.2 · May/June 2024 · Paper 1 · National (DBE) · 6 marks
7.2 Two identical neutral polystyrene balls A and B are suspended from a ceiling by insulated, light inextensible strings of equal length, as shown in the diagram below.

Ball B is then given an initial negative charge, $Q_{B}$ , of unknown magnitude. The balls attract each other, touch and then repel each other. The balls come to rest with their centres $10$ cm apart so that each string makes an angle of $9°$ with the vertical. See the diagrams below.

Answer the questions that follow.
7.2.2 Calculate the magnitude of the initial charge $Q_{B}$ given to ball B if the mass of each ball was $0, 012$ kg.(6)
Show the memo (6 ticks)Memo
1. ✓
  Correct trig expression equated to $F_{E}$ $F_{E} = w tan θ$
  
  Any one: $F_{E} = m g tan θ$ or $F_{E} = \frac{w}{t a n ( 90° - θ )}$
  1 mark · Find resultant of perpendicular vectors
2. ✓
  Substitution of mg with angle $9°$ $F_{E} = (0, 012) (9, 8) (tan 9°)$
  $= 0, 0186$ N
  1 mark · Find resultant of perpendicular vectors
3. ✓
  Coulomb's formula $F_{E} = \frac{k Q _{A} Q _{B}}{r ^{2}}$
  1 mark · Apply Coulomb's law
4. ✓
  Substitution into Coulomb's formula $0, 0186 = \frac{( 9 \times 1 0 ^{9} ) ( Q ^{2} )}{0 , 1 ^{2}}$
  $Q = 1, 44 \times 1 0^{- 7}$ C
  1 mark · Apply Coulomb's law
5. ✓
  Calculating 2Q $Q_{B} = 2 (1, 44 \times 1 0^{- 7})$
  1 mark · Calculate shared charge and electrons transferred
6. ✓
  Final answer $Q_{B} = 2, 88 \times 1 0^{- 7}$ C
  1 mark · Calculate shared charge and electrons transferred
7. Question 7.1.3 · September 2026 · Paper 1 · Provincial · 5 marks
7.1 A sphere, M, carrying a charge of $+ 20 \times 1 0^{- 7}$ C, is suspended at the end of a light inextensible string which is attached to a fixed point. Another sphere, N, carrying a charge of $+ 12 \times 1 0^{- 7}$ C, on an insulated stand, is brought closer to sphere M. Sphere M experiences an electrostatic force and comes to rest when the string makes an angle of $20°$ with the vertical, as shown in the diagram below.

Answer the questions that follow.
7.1.3 Calculate the mass of sphere M.(5)
Show the memo (5 ticks)Memo
1. ✓
  Formula $F = \frac{k Q _{1} Q _{2}}{r ^{2}}$
  1 mark · Apply Coulomb's law
2. ✓
  Substitution $F = \frac{9 \times 1 0 ^{9} \times 12 \times 1 0 ^{- 7} \times 20 \times 1 0 ^{- 7}}{( 0 , 17 ) ^{2}}$
  $F = 0, 7474$ N
  1 mark · Apply Coulomb's law
3. ✓
  Triangle of forces $\frac{m g}{s i n 70°} = \frac{0 , 7474}{s i n 20°}$
  1 mark · Find resultant of perpendicular vectors
4. ✓
  Weight $m \times 9, 8 = 2, 053$
  1 mark · Find resultant of perpendicular vectors
5. ✓
  Answer with unit $m = 0, 21$ kg
  1 mark · Calculate weight
8. Question 2.3 · September 2026 · Paper 1 · Provincial · 5 marks
A block of mass $m$ rests on a fixed wedge of angle $θ$ , as shown in the diagram below.

The coefficient of static friction between the block and the surface is $μ_{s}$ .
2.3 Show that the value of $θ$ at which the block starts to slide, is given by $θ_{ma x} = tan^{- 1} μ_{s}$ . (Show all your workings)(5)
Show the memo (5 ticks)Memo
1. ✓
  Newton's first law (Fnet = 0)Parallel to the incline: $F_{n e t ∥} = 0$
  $m g sin θ - f_{s} = 0$
  (Any one of: $F_{n e t ∥} = 0$ ; $W_{∥} + (- f_{s}) = 0$ ; $m g sin θ - f_{s} = 0$ ; $f_{s} = m g sin θ$ ; $F_{n e t ⊥} = 0$ )
  1 mark · Apply Newton's second law
2. ✓
  Formula for fs(max) $F_{N} = F_{g ⊥} = m g cos θ$
  BUT: $f_{s}^{ma x} = μ_{s} F_{N}$
  1 mark · Calculate and explain frictional force
3. ✓
  Expanding for Fg parallel $F_{g ∥} = f_{s}^{ma x}$
  $m g sin θ_{ma x}$ = ...
  1 mark · Resolve a vector into components
4. ✓
  Expanding for fs(max) $m g sin θ_{ma x} = μ_{s} (m g cos θ_{ma x})$
  1 mark · Calculate and explain frictional force
5. ✓
  Substituting tan $sin θ_{ma x} = μ_{s} cos θ_{ma x}$
  $μ_{s} = \frac{s i n θ _{ma x}}{c o s θ _{ma x}}$
  $μ_{s} = tan θ_{ma x}$
  $θ_{ma x} = tan^{- 1} μ_{s}$
  1 mark · Calculate and explain frictional force
9. Question 2.3.1 · September 2026 · Paper 1 · Provincial · 3 marks
A box with a mass of $70$ kg is pulled up an incline at a constant acceleration of $0, 5$ m·s $^{- 2}$ . The incline makes an angle of $60°$ with the horizontal. The rope is parallel to the slope. The kinetic frictional force between the box and the surface is $15$ N.
2.3 Calculate the:
2.3.1 Magnitude of the parallel component of gravitational force acting on the box(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $F_{g ∥} = m g sin θ$
  1 mark · Resolve a vector into components
2. ✓
  Substitution $F_{g ∥} = (70) (9, 8) sin 60°$
  1 mark · Resolve a vector into components
3. ✓
  Answer with unit $F_{g ∥} = 594, 09$ N
  1 mark · Resolve a vector into components
10. Question 1.3 · November 2025 · Paper 1 · Provincial · 2 marks
Various options are provided as answers to the following questions. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in your ANSWER BOOK, for example, 1.11 D.
1.3 In the vector diagram below, the resultant (net) vector is ...(2)
1. A Zero
2. B $F_{1}$
3. C $F_{3}$
4. D $F_{2}$
Show the memo (1 tick)Memo
1. ✓
  Correct option B $F_{2}$ and $F_{3}$ are drawn head to tail: $F_{3}$ starts at the head of $F_{2}$ . $F_{1}$ runs from the tail of $F_{2}$ to the head of $F_{3}$ , so $F_{1} = F_{2} + F_{3}$ is the resultant.
  
  Answer: B
  2 marks · Draw a closed vector diagram

Vectors in Two Dimensions Grade 11 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

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Grade 11 Physics Closed Vector Diagrams: Triangle of forcesMiss Martins Maths and Science

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