Mechanical Energy Revision Notes for Grade 10 NSC Matric Physical Sciences

Kinetic Energy

Definition

Kinetic energy is the energy that moving objects possess. Any object that is in motion has kinetic energy, while stationary objects have zero kinetic energy.

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The key distinction is simple: if an object is moving, it has kinetic energy. If it's completely still, its kinetic energy is zero.

Quantity: Kinetic energy (EK)
Unit: Joule (J)
Symbol: J

The kinetic energy formula

The amount of kinetic energy an object has can be calculated using the fundamental formula:

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$E_K = \frac{1}{2}mv^2$

Where:

$E_K$ = kinetic energy (measured in joules, J)
$m$ = mass of the object (measured in kilograms, kg)
$v$ = velocity of the object (measured in metres per second, m·s⁻¹)

Factors affecting kinetic energy

Kinetic energy is determined by two main factors:

Mass: The heavier an object is, the more kinetic energy it has
Velocity: The faster an object moves, the more kinetic energy it has

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Critical Concept: Velocity has a greater effect on kinetic energy than mass because velocity is squared in the formula. A truck moving at 100 km·hr⁻¹ has more kinetic energy than a car with half the mass moving at the same speed.

Understanding through examples

Consider an object at rest on a cupboard. Since it's not moving, its kinetic energy equals zero:

$E_K = \frac{1}{2}mv^2 = \frac{1}{2}(1 \text{ kg})(0 { m·s}^{-1})^2 = 0 \text{ J}$

When the same object falls and reaches a velocity of 6.26 m·s⁻¹, its kinetic energy becomes:

$E_K = \frac{1}{2}mv^2 = \frac{1}{2}(1 \text{ kg})(6.26 { m·s}^{-1})^2 = 19.6 \text{ J}$

This demonstrates that kinetic energy is minimum when an object is stationary and maximum when it moves fastest.

Worked examples

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Worked Example 1: Basic kinetic energy calculation

Question: A 1 kg brick falls from a 4 m high roof. It reaches the ground with a velocity of 8.85 m·s⁻¹. What is the kinetic energy of the brick when it starts to fall and when it reaches the ground?

Solution:

Step 1: Identify the given information

Mass of brick: $m = 1$ kg
Velocity at bottom: $v = 8.85$ m·s⁻¹
Both values are in correct units

Step 2: Determine what is being asked

We need to find the kinetic energy at the top (when stationary) and at the bottom (when moving).

Step 3: Calculate kinetic energy at the top

Since the brick is not moving at the top, its kinetic energy is zero.

Step 4: Calculate kinetic energy at the bottom

$E_K = \frac{1}{2}mv^2$
$E_K = \frac{1}{2}(1 \text{ kg})(8.85 { m·s}^{-1})^2$
$E_K = 39.2 \text{ J}$

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Worked Example 2: Comparing kinetic energies of different objects

Question: A herder is herding sheep into a kraal. A mother sheep and her lamb are both running at 2.7 m·s⁻¹ towards the kraal. The sheep has a mass of 80 kg and the lamb has a mass of 25 kg. Calculate the kinetic energy for each animal.

Solution:

Step 1: Identify given information

Mass of sheep = 80 kg
Mass of lamb = 25 kg
Both animals have velocity = 2.7 m·s⁻¹

Step 2: Calculate the sheep's kinetic energy

$E_K = \frac{1}{2}mv^2$
$E_K = \frac{1}{2}(80 \text{ kg})(2.7 { m·s}^{-1})^2$
$E_K = :success[291.6 \text{ J}]$

Step 3: Calculate the lamb's kinetic energy

$E_K = \frac{1}{2}mv^2$
$E_K = \frac{1}{2}(25 \text{ kg})(2.7 { m·s}^{-1})^2$
$E_K = :success[91.13 \text{ J}]$

Note: Even though both animals move at the same velocity, the sheep has more kinetic energy because it has greater mass.

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Worked Example 3: Unit conversion and calculation

Question: A bullet having a mass of 150 g is shot with a muzzle velocity of 960 m·s⁻¹. Calculate its kinetic energy.

Solution:

Step 1: Convert mass to correct units

Mass in grams ÷ 1000 = Mass in kg
150 g ÷ 1000 = 0.150 kg

Step 2: Apply the kinetic energy formula

$E_K = \frac{1}{2}mv^2$
$E_K = \frac{1}{2}(0.150 \text{ kg})(960 { m·s}^{-1})^2$
$E_K = 69,120 \text{ J}$

Checking units

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Unit Verification for Kinetic Energy

The unit for kinetic energy should be kg·m²·s⁻². We can prove this equals the joule (the unit for energy):

$(kg)(m·s^{-1})^2 = (kg·m·s^{-2})·m = N·m = J$

This confirms that our kinetic energy calculations will always result in joules when using the correct SI units.

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Key Points to Remember:

Kinetic energy is energy of motion - only moving objects possess it
The formula is $E_K = \frac{1}{2}mv^2$ - half mass times velocity squared
Stationary objects have zero kinetic energy - no motion means no kinetic energy
Velocity has more impact than mass - because velocity is squared in the formula
Always check your units - mass in kg, velocity in m·s⁻¹, energy in J

Mechanical Energy (Grade 10 NSC Matric Physical Sciences): Revision Notes

Kinetic Energy

Definition

The kinetic energy formula

Factors affecting kinetic energy

Understanding through examples

Worked examples

Checking units

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