Grade 12 Physical Sciences · Mechanics

Solve energy problems with friction

Solve energy problems where friction or a push does work, using W_nc = ΔEk + ΔEp (a box sliding down a rough slope).

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Question 1.3 · November 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.

1.3 A motor fixed to the ground is used to lift a box vertically upwards at a CONSTANT VELOCITY, as shown in the diagram.

Consider the statements below for the upward motion of the box.

(i) The rate at which work is done by the motor on the box increases.
(ii) The rate at which work is done by the motor on the box is constant.
(iii) The mechanical energy of the box increases.
(iv) The mechanical energy of the box is constant.

Which of the statements above are CORRECT?(2) Diagram for question 1.3

A (i) and (iii) only
B (ii) and (iv) only
C (ii) and (iii) only
D (i) and (iv) only

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More past paper questions: solve energy problems with friction

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3. Question 5.3.1 · May/June 2025 · Paper 1 · National (DBE) · 3 marks
Water is drawn from a water source $12, 5$ m below the ground by an electric pump. The water is lifted vertically upwards at a constant speed, as shown in the simplified diagram below.

The pump lifts the water upwards at a rate of $2, 5$ kg·s $^{- 1}$ . Ignore ALL frictional and capillarity effects.
5.3 The pump lifts $200$ kg of water from the source to the ground at a constant speed. Calculate the:
5.3.1 Work done by the pump(3)
Show the memo (3 ticks)Memo
1. ✓
  METHOD 1: Formula $W_{n c} = Δ E_{p} + Δ E_{k}$ (or $W_{p u m p} = m g Δ h$ / mgh)
  1 mark · Solve energy problems with friction
2. ✓
  METHOD 1: Substitution $W_{p u m p} = 200 (9, 8) (12, 5)$
  1 mark · Solve energy problems with friction
3. ✓
  METHOD 1: Answer $W_{p u m p} = 24500$ J
  1 mark · Solve energy problems with friction
4. Question 5.3 · November 2022 · Paper 1 · National (DBE) · 4 marks
A $12$ kg block is initially at rest at point A at the bottom of a ROUGH inclined plane. The block is pulled up the incline by a constant force F acting parallel to the incline. The block reaches point B, which is at a vertical height of $4, 5$ m above the horizontal, with a speed of $2, 25$ m·s $^{- 1}$ . See the diagram below.
5.3 Calculate the total work done on the block by the NON-CONSERVATIVE forces when the block moved from point A to point B.(4)
Show the memo (4 ticks)Memo
1. ✓
  Formula $W_{n c} = Δ E_{k} + Δ E_{p}$ (any one: $W_{n c} = \frac{1}{2} m (v_{f}^{2} - v_{i}^{2}) + m g (h_{f} - h_{i})$ )
  1 mark · Solve energy problems with friction
2. ✓
  Substitution of $Δ E_{k}$ $= \frac{1}{2} (12) (2, 2 5^{2} - 0)$
  1 mark · Solve energy problems with friction
3. ✓
  Substitution of $Δ E_{p}$ $+ (12) (9, 8) (4, 5 - 0)$
  1 mark · Solve energy problems with friction
4. ✓
  Answer $W_{n c} = 559, 58$ J
  1 mark · Solve energy problems with friction
5. Question 5.4 · November 2025 · Paper 1 · National (DBE) · 5 marks
A crate of mass $3$ kg is at rest at point A on a frictionless horizontal surface. A constant horizontal force F of $12$ N acts on the crate and moves it from point A to point B. The crate then moves down a rough plane, inclined at $20°$ to the horizontal. The distance from point A to point B is $7$ m and from point B to point C is $6, 8$ m, as shown in the diagram below.
5.4 Using ENERGY PRINCIPLES ONLY, determine whether the crate will pass point C.(5)
Show the memo (5 ticks)Memo
1. ✓
  METHOD 1: Work done by gravity $W_{n e t} = Δ E_{k}$
  $W_{F_{g}} + W_{f_{k}} = E_{k f} - E_{ki}$
  $m g sin θ Δ x cos θ + f_{k} Δ x cos θ = E_{k f} - E_{ki}$
  $(3) (9, 8) sin 20°Δ x cos 0°$
  1 mark · Calculate work done by a force
2. ✓
  METHOD 1: Work done by friction $+ 21Δ x cos 180°$
  1 mark · Calculate work done by a force
3. ✓
  METHOD 1: Change in kinetic energy $(3) (9, 8) sin 20°Δ x cos 0° + 21Δ x cos 180° = 0 - 84$
  1 mark · Use the work-energy theorem
4. ✓
  METHOD 1: Final answer $Δ x = 7, 68$ m
  1 mark · Use the work-energy theorem
5. ✓
  METHOD 1: Conclusion $7, 68$ m $> 6, 8$ m
  The crate will pass point C.
  1 mark · Use the work-energy theorem
6. Question 5.4 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
A crate of mass $18$ kg, initially at rest, slides down a frictionless slope from point A to point B. The crate then moves along a rough horizontal surface from point B towards point C. Point A is $3$ m above the horizontal surface. See the diagram below.
5.4 Using ENERGY PRINCIPLES only, calculate the distance that the crate travelled from point B to point C.(4)
Show the memo (4 ticks)Memo
1. ✓
  OPTION 1: Formula $W_{n e t} = Δ E_{k}$
  
  Any one: $W_{f} = Δ E_{k}$ or $f Δ x cos 180° = \frac{1}{2} m v_{f}^{2} - \frac{1}{2} m v_{i}^{2}$
  1 mark · Use the work-energy theorem
2. ✓
  OPTION 1: Work done by friction $(40, 6) Δ x (- 1)$
  1 mark · Use the work-energy theorem
3. ✓
  OPTION 1: Change in kinetic energy $(40, 6) Δ x (- 1) = \frac{1}{2} (18) [(0)^{2} - (7, 67)^{2}]$
  1 mark · Use the work-energy theorem
4. ✓
  OPTION 1: Answer with unit $Δ x = 13, 04$ m
  1 mark · Use the work-energy theorem

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