Grade 10 Physical Sciences
Term 3 · Weeks 10–11

Energy

Paper 1 — Physics · Grade 10

Energy cannot be created or destroyed — only converted from one form to another. In mechanics, potential energy (stored) and kinetic energy (motion) continuously interchange, and their sum remains constant in the absence of friction.

Week 10

Gravitational Potential Energy and Kinetic Energy

Define gravitational potential energyDefine kinetic energyCalculate Ep = mgh and Ek = ½mv²Define mechanical energy
Ep

Definition

Gravitational potential energy (Ep)

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field; Ep = mgh.

Ek

Definition

Kinetic energy (Ek)

Kinetic energy is the energy of an object due to its motion; Ek = ½mv².

Em

Definition

Mechanical energy (Em)

Mechanical energy is the sum of the gravitational potential energy and kinetic energy of an object: Em = Ep + Ek.

Formula

Gravitational potential energy

Ep=mghE_p = mgh

m = mass (kg), g = 9,8 m·s⁻² (gravitational acceleration), h = height above reference point (m)

SI unit: J

Formula

Kinetic energy

Ek=12mv2E_k = \frac{1}{2}mv^2

m = mass (kg), v = speed (m·s⁻¹)

SI unit: J

Conservation of Mechanical Energyground — h = 0, Ep = 0mEp = mghEk = 0Em = mghAll potentialmEp = mgh/2Ek = mgh/2Em = mghHalf and halfmEp = 0Ek = mghEm = mghAll kineticEm = Ep + Ek = constant (no friction)
Figure 20.1 — Energy interchange during free fall. At the top (maximum height): Ep is maximum, Ek = 0. As the object falls: Ep decreases, Ek increases. At the bottom (h = 0): Ep = 0, Ek is maximum. The total mechanical energy Em = Ep + Ek remains constant throughout (no friction).

Potential energy is zero at the reference point (usually the ground). As an object falls, Ep decreases and Ek increases — total mechanical energy stays the same (if no friction or air resistance). This interchange between Ep and Ek is the basis of the Law of Conservation of Mechanical Energy.

ℹ

Note

The reference point for height is arbitrary — we can choose the ground, a table, or any convenient level as h = 0. Only the CHANGE in height matters for calculating the change in potential energy.

Worked Example

A 3 kg book is on a shelf 2 m above the floor. Calculate its gravitational potential energy relative to the floor. (g = 9,8 m·s⁻²)

Given

  • m = 3 kg
  • h = 2 m
  • g = 9,8 m·s⁻²

Find

Ep = ?

Solution

  1. 1Ep = mgh
  2. 2Ep = 3 × 9,8 × 2
  3. 3Ep = 58,8 J
Answer: Ep = 58,8 J

Worked Example

A 0,5 kg ball moves at 10 m·s⁻¹. Calculate its kinetic energy.

Given

  • m = 0,5 kg
  • v = 10 m·s⁻¹

Find

Ek = ?

Solution

  1. 1Ek = ½mv²
  2. 2Ek = ½ × 0,5 × 10²
  3. 3Ek = ½ × 0,5 × 100
  4. 4Ek = 25 J
Answer: Ek = 25 J
?

Practice Question

A 2 kg object is held 5 m above the ground. Calculate: (a) its potential energy, (b) its kinetic energy at that height (object is at rest), (c) its mechanical energy. (g = 9,8 m·s⁻²)

(4 marks)

Week 11

Conservation of Mechanical Energy

State the Law of Conservation of Mechanical EnergyApply Em = Ep + Ek = constant (no friction)Solve energy conservation problems

Definition

Law of Conservation of Mechanical Energy

In the absence of friction and other non-conservative forces, the total mechanical energy of an object remains constant; Em₁ = Em₂.

Formula

Mechanical energy (constant — no friction)

Emech=Ek+Ep=12mv2+mghE_{\text{mech}} = E_k + E_p = \frac{1}{2}mv^2 + mgh

Em = total mechanical energy (J), m = mass (kg), g = 9,8 m·s⁻², h = height (m), v = speed (m·s⁻¹)

SI unit: J

Formula

Conservation of mechanical energy

mgh1+12mv12=mgh2+12mv22mgh_1 + \frac{1}{2}mv_1^2 = mgh_2 + \frac{1}{2}mv_2^2

subscripts 1 and 2 refer to two different positions; all other symbols as above

SI unit: J

✓

Exam Tip

Common shortcuts when using energy conservation: (1) At maximum height, v = 0 so Ek = 0 and all energy is Ep. (2) At the lowest point (h = 0), Ep = 0 and all energy is Ek. These two conditions give the simplest calculations.

⚠

Watch Out

Conservation of mechanical energy only applies when there is NO friction or air resistance. If the problem mentions a 'friction force' or 'air resistance', you cannot use this method — you must use the work-energy theorem (Grade 11 topic).

Worked Example

A 2 kg object is dropped from 5 m height. Calculate its speed just before hitting the ground. (g = 9,8 m·s⁻²)

Given

  • m = 2 kg
  • h₁ = 5 m
  • v₁ = 0 m·s⁻¹ (starts from rest)
  • h₂ = 0 m (ground)

Find

v₂ (speed at ground)

Solution

  1. 1At top: Ep = mgh₁ = 2 × 9,8 × 5 = 98 J; Ek = 0; Em = 98 J
  2. 2At ground (h = 0): Ep = 0; all energy is Ek
  3. 3Em = Ek → 98 = ½mv²
  4. 498 = ½(2)v² = v²
  5. 5v² = 98 → v = √98 = 9,9 m·s⁻¹
Answer: v = 9,9 m·s⁻¹

Worked Example

A ball of mass 0,5 kg is thrown upward at 14 m·s⁻¹. Calculate the maximum height. (g = 9,8 m·s⁻²)

Given

  • m = 0,5 kg
  • v₁ = 14 m·s⁻¹
  • h₁ = 0 m (ground level)
  • v₂ = 0 at max height

Find

h₂ (maximum height)

Solution

  1. 1At ground: Em = ½mv₁² = ½(0,5)(14²) = ½(0,5)(196) = 49 J
  2. 2At max height: Em = mgh₂ + 0 = (0,5)(9,8)h₂ = 4,9h₂
  3. 349 = 4,9h₂
  4. 4h₂ = 49/4,9 = 10 m
Answer: h = 10 m

Worked Example

A 3 kg ball rolls off a table 1,5 m high. Calculate its speed at the bottom (ignore friction). (g = 9,8 m·s⁻²)

Given

  • m = 3 kg
  • h₁ = 1,5 m
  • v₁ = 0 m·s⁻¹ (starts from rest)
  • h₂ = 0 m

Find

v₂ at the bottom

Solution

  1. 1Apply conservation: mgh₁ + ½mv₁² = mgh₂ + ½mv₂²
  2. 23(9,8)(1,5) + 0 = 0 + ½(3)v₂²
  3. 344,1 = 1,5v₂²
  4. 4v₂² = 44,1/1,5 = 29,4
  5. 5v₂ = √29,4 = 5,42 m·s⁻¹
Answer: v = 5,42 m·s⁻¹
?

Practice Question

A 4 kg rock falls from a cliff 20 m high. Calculate: (a) the initial mechanical energy (at rest at top), (b) the kinetic energy when it has fallen 12 m (i.e. it is now 8 m above the ground), (c) its speed at that point. (g = 9,8 m·s⁻²)

(6 marks)

?

Practice Question

A pendulum of mass 0,2 kg is released from rest at a height of 0,45 m above its lowest point. What is its speed at the lowest point? (g = 9,8 m·s⁻²)

(4 marks)

Previous

Equations of Motion

Energy Grade 10 Physical Sciences CAPS Notes | MathSciBuddy