Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Define and calculate kinetic energy (Ek) and gravitational potential energy (Ep).
• State the principle of conservation of mechanical energy.
• Apply this principle to solve problems.
• Understand the role of non-conservative forces like friction.
• Distinguish between conservative and non-conservative forces.

Lesson summary

Energy is a fundamental concept in physics, and understanding energy and its conservation is crucial for explaining how the world around us works. This week, we'll be diving deep into the concept of mechanical energy, focusing specifically on kinetic energy, potential energy (gravitational), and the principle of conservation of mechanical energy.

Think about it: Every time a soccer ball is kicked, a car brakes, or a rock falls from a cliff, energy transformations are happening. Understanding these transformations allows us to predict the motion of objects and design safer, more efficient technologies.

Lesson notes

2.1 Kinetic Energy (Ek): The Energy of Motion Kinetic energy is the energy an object possesses due to its motion. The faster an object moves, the more kinetic energy it has. The formula for calculating kinetic energy is: Ek = ½ mv² Where: Ek is kinetic energy (measured in Joules, J) m is the mass of the object (measured in kilograms, kg) v is the velocity of the object (measured in meters per second, m/s)

Why this matters: If a minibus taxi is speeding and has to brake suddenly, its kinetic energy needs to be dissipated quickly, which can cause skidding and accidents. Understanding kinetic energy helps us understand factors involved in road safety.

Example 1: A soccer ball with a mass of 0.45 kg is kicked and travels at a velocity of 20 m/s. Calculate its kinetic energy.

Solution: Ek = ½ mv² Ek = ½ (0.45 kg) (20 m/s)² Ek = ½ (0.45 kg) (400 m²/s²) Ek = 90 J Explanation: The soccer ball has 90 Joules of kinetic energy. 2.2 Gravitational Potential Energy (Ep): The Energy of Position Gravitational potential energy is the energy an object possesses due to its position above the Earth's surface (or any other reference point). The higher an object is, the more gravitational potential energy it has. The formula for calculating gravitational potential energy is: Ep = mgh Where: Ep is gravitational potential energy (measured in Joules, J) m is the mass of the object (measured in kilograms, kg) g is the acceleration due to gravity (approximately 9.8 m/s² on Earth) h is the height of the object above a reference point (measured in meters, m)

Why this matters: Water stored behind a dam has significant potential energy that is converted into electrical energy. The height and mass determine how much energy it can potentially generate.

Example 2: A bag of maize meal with a mass of 5 kg is placed on a shelf 1.5 meters above the ground. Calculate its gravitational potential energy.

Solution: Ep = mgh Ep = (5 kg) (9.8 m/s²) (1.5 m) Ep = 73.5 J Explanation: The bag of maize meal has 73.5 Joules of gravitational potential energy relative to the ground. 2.3 Mechanical Energy (Em): The Total Energy Mechanical energy is the sum of kinetic energy and potential energy. Em = Ek + Ep 2.4 Conservation of Mechanical Energy The principle of conservation of mechanical energy states that in the absence of non-conservative forces (like friction or air resistance), the total mechanical energy of a system remains constant. This means energy can transform between kinetic and potential energy, but the total amount stays the same. Em (initial) = Em (final) Ek (initial) + Ep (initial) = Ek (final) + Ep (final)

Why this matters: Engineers use this principle when designing roller coasters. At the highest point (maximum potential energy), the coaster has minimal kinetic energy. As it descends, potential energy converts into kinetic energy, causing it to accelerate. In ideal scenarios, the total mechanical energy would remain constant (no friction).

Example 3: A rock with a mass of 2 kg is held 10 meters above the ground. It is then dropped. Assuming no air resistance, calculate the velocity of the rock just before it hits the ground.

Solution: Initial state: Ek (initial) = 0 J (at rest), Ep (initial) = mgh = (2 kg)(9.8 m/s²)(10 m) = 196 J Final state: Ep (final) = 0 J (at ground level), Ek (final) = ½ mv² = ½ (2 kg) v² = v² Applying the conservation of mechanical energy: Ek (initial) + Ep (initial) = Ek (final) + Ep (final) 0 J + 196 J = v² + 0 J v² = 196 m²/s² v = √196 m²/s² v = 14 m/s Explanation: The velocity of the rock just before it hits the ground is 14 m/s. All the initial potential energy was converted into kinetic energy. 2.5 Non-Conservative Forces and Work Done Non-conservative forces, like friction and air resistance, do not conserve mechanical energy. These forces convert mechanical energy into other forms of energy, such as heat and sound. When non-conservative forces are present, the total mechanical energy of the system decreases. The work done by non-conservative forces (Wnc) equals the change in mechanical energy: Wnc = ΔEm = Em (final) – Em (initial) If Wnc is negative (e.g., due to friction), mechanical energy is lost from the system.

Example 4: A 1 kg block slides down a ramp. At the top of the ramp, its height is 2 m and it's initially at rest. At the bottom of the ramp, its speed is 4 m/s. How much work was done by friction (a non-conservative force)?

Solution: Initial Mechanical Energy: Em(initial) = Ep(initial) + Ek(initial) = (1 kg)(9.8 m/s²)(2 m) + 0 J = 19.6 J Final Mechanical Energy: Em(final) = Ep(final) + Ek(final) = 0 J + ½(1 kg)(4 m/s)² = 8 J Work Done by Friction: Wnc = Em(final) - Em(initial) = 8 J - 19.6 J = -11.6 J Explanation: The work done by friction is -11.6 J. This negative value indicates that friction removed 11.6 J of mechanical energy from the system, converting it into heat.