Grade 10 Physical Sciences · Mechanics

Calculate kinetic and potential energy

Calculate kinetic energy with Ek = ½mv² or gravitational potential energy with Ep = mgh (a 2 kg ball 5 m high has about 98 J of potential energy).

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Question 1.3 · November 2024 · Paper 1 · National (DBE) · 2 marks

1.3 A ball moving horizontally has constant momentum p and kinetic energy K. The ball collides with a wall and bounces back horizontally.

Immediately after the collision, the ball has momentum

\frac{1}{2}

p.

The mass of the ball remains constant.

Which ONE of the following is the kinetic energy of the ball immediately after the collision?(2) Diagram for question 1.3

A $\frac{1}{4}$ K
B $\frac{1}{2}$ K
C 2K
D 4K

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

More past paper questions: calculate kinetic and potential energy

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3. Question 1.2 · May/June 2022 · 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.
1.2 A ball is dropped from a small height above the ground.

Ignore air resistance.

The following pairs show physical quantities associated with the ball while it is falling to the ground.

In which ONE of these pairs will BOTH quantities change while the ball is falling?(2)
1. A Mechanical energy and weight
2. B Kinetic energy and momentum
3. C Gravitational acceleration and kinetic energy
4. D Gravitational potential energy and gravitational force
Show the memo (1 tick)Memo
1. ✓
  Choose the correct optionAs the ball falls its speed increases, so $E_{k} = \frac{1}{2} m v^{2}$ and $p = m v$ both increase. With no air resistance mechanical energy stays constant (A), $g$ stays $9, 8$ m·s $^{- 2}$ (C), and the gravitational force $m g$ stays constant (D), even though $E_{p}$ decreases.
  
  Answer: B
  2 marks · Calculate kinetic and potential energy
4. Question 3.3.1 · November 2023 · Paper 1 · National (DBE) · 5 marks
A ball of mass $0, 5$ kg is thrown vertically upwards from the top edge of a building which is $15, 3$ m high. The ball reaches a maximum height of $5, 89$ m above the top of the building. The ball strikes the ground and bounces vertically upwards, reaching a maximum height at point $P$ , as shown in the diagram below.

Ignore the effects of air friction.
3.3 After the collision with the ground, the ball leaves the ground with a speed of $11, 92$ m·s $^{- 1}$ .

Calculate the:
3.3.1 Amount of kinetic energy lost by the ball during the collision with the ground(5)
Show the memo (5 ticks)Memo
1. ✓
  Formula leading to the speed at the groundOption 1 (top of building to ground), upwards positive:
  $v_{f}^{2} = v_{i}^{2} + 2 a Δ y$
  1 mark · Use equations of motion for projectiles
2. ✓
  Substitution $v_{f}^{2} = (10, 74)^{2} + 2 (- 9, 8) (- 15, 3)$
  $v_{f} = - 20, 38$ m·s $^{- 1}$
  1 mark · Use equations of motion for projectiles
3. ✓
  Formula for change in kinetic energy (any one)During the collision:
  $Δ E_{k} = E_{k f} - E_{ki}$
  $Δ E_{k} = \frac{1}{2} m v_{f}^{2} - \frac{1}{2} m v_{i}^{2}$
  $Δ E_{k} = \frac{1}{2} m (v_{f}^{2} - v_{i}^{2})$
  1 mark · Calculate kinetic and potential energy
4. ✓
  Substitution $Δ E_{k} = \frac{1}{2} (0, 5) [(11, 92)^{2} - (20, 38)^{2}]$
  
  OR
  
  $Δ E_{k} = \frac{1}{2} (0, 5) [(20, 38)^{2} - (11, 92)^{2}]$
  1 mark · Calculate kinetic and potential energy
5. ✓
  Answer with unit $Δ E_{k} = - 68, 31$ J, so $E_{k}$ lost $= 68, 31$ J
  1 mark · Calculate kinetic and potential energy
5. Question 8.2 · November 2023 · Paper 1 · Provincial · 4 marks
A cricket ball of mass $180$ g is travelling at $30$ m·s $^{- 1}$ .
8.2 Calculate the kinetic energy of the ball.(4)
Show the memo (4 ticks)Memo
1. ✓
  Formula $E_{k} = \frac{1}{2} m v^{2}$
  1 mark · Calculate kinetic and potential energy
2. ✓
  Substitute mass in kg $= \frac{1}{2} (0, 18) \times \dots$
  1 mark · Calculate kinetic and potential energy
3. ✓
  Substitute velocity $= \frac{1}{2} (0, 18) \times (30)^{2}$
  1 mark · Calculate kinetic and potential energy
4. ✓
  Answer with unit $= 81$ J
  1 mark · Calculate kinetic and potential energy
6. Question 1.4 · November 2022 · Paper 1 · Provincial · 2 marks
Four options are provided as possible answers to the following questions. Each question has only ONE correct answer.
1.4 In the diagram below, a pendulum bob of mass $m$ is released from point A and swings past points B, C and D. Ignore all effects of air resistance.

In which of the following positions will the value of the gravitational potential energy of the pendulum bob be the smallest?(2)
1. A A
2. B B
3. C C
4. D D
Show the memo (1 tick)Memo
1. ✓
  Choose the correct option $E_{P} = m g h$ . The mass and $g$ are the same at every point, so $E_{P}$ is smallest where the height is smallest. C is the lowest point of the swing (the bob hangs straight down).
  
  Answer: C
  2 marks · Calculate kinetic and potential energy

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