Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Define and differentiate between potential and kinetic energy.
• Calculate gravitational, elastic, and kinetic energy.
• State and apply the principle of conservation of mechanical energy.
• Describe how non-conservative forces affect mechanical energy.
• Explain and calculate power.

Lesson summary

This week, we delve into the fascinating world of energy, specifically focusing on mechanical energy and its conservation. Understanding these concepts is crucial because energy is fundamental to everything around us, from the food we eat to the cars we drive. In South Africa, with our reliance on energy resources and a growing focus on sustainable solutions, comprehending energy principles is more important than ever. For instance, consider the potential of renewable energy sources like solar and wind power; these systems operate based on the very principles we'll be learning. Understanding energy also helps us optimize designs for efficiency in homes, transportation and industries.

Lesson notes

2. 1.

Types of Mechanical Energy: Kinetic Energy (KE): This is the energy an object possesses due to its motion. A moving taxi, a running springbok, or even a breeze blowing across the Highveld all have kinetic energy. The faster the object moves, and the more massive it is, the more kinetic energy it has.

Formula: KE = 1/2 mv 2 , where: KE is kinetic energy (measured in Joules, J) m is mass (measured in kilograms, kg) v is velocity (measured in meters per second, m/s)

Potential Energy (PE): This is stored energy that an object has due to its position or configuration. We will focus on two types of potential energy: gravitational and elastic.

Gravitational Potential Energy (GPE): This is the energy an object has because of its height above a reference point (usually the ground). A soccer ball held high above the ground has GP

E. If released, the GPE is converted to KE as it falls.

Formula: GPE = mgh, where: GPE is gravitational potential energy (measured in Joules, J) m is mass (measured in kilograms, kg) g is the acceleration due to gravity (approximately 9.8 m/s 2 on Earth) h is the height above the reference point (measured in meters, m)

Elastic Potential Energy (EPE): This is the energy stored in a deformable object, such as a spring or a rubber band, when it is stretched or compressed. The more it is deformed, the more EPE it stores. Think about the springs in the suspension of a bakkie driving across a bumpy road.

Formula: EPE = 1/2 kx 2 , where: EPE is the elastic potential energy (measured in Joules, J) k is the spring constant (measured in Newtons per meter, N/m) x is the extension or compression of the spring (measured in meters, m) 2.

2. Mechanical Energy (ME): The total mechanical energy of a system is the sum of its kinetic and potential energies. ME = KE + PE ME = KE + GPE + EPE (if applicable) 2.

3. Conservation of Mechanical Energy: This principle states that in a closed, isolated system (i.e., no external forces like friction or air resistance are doing work), the total mechanical energy remains constant. This means that energy can be converted from one form to another (e.g., from GPE to KE), but the total amount stays the same.

Mathematically: ME initial = ME final KE initial + PE initial = KE final + PE final 2.

4. Non-Conservative Forces and Energy Loss: In reality, most systems are not isolated. Forces like friction, air resistance, and even the internal forces within a material (e.g., heat generated when bending a metal rod) can convert mechanical energy into other forms of energy, primarily thermal energy (heat). In these cases, mechanical energy is not conserved. The energy is "lost" to the system, typically dissipated as heat into the surroundings. The conservation of energy principle ALWAYS holds; it is the mechanical energy which may be decreased due to non-conservative forces. 2.

5. Work-Energy Theorem: The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. W net = ΔKE = KE final - KE initial This theorem links the concepts of work and energy, providing an alternative way to calculate the change in an object's motion. 2.

6. Power: Power is the rate at which work is done or energy is transferred. It tells us how quickly energy is being used or transformed. A powerful engine, like those found in taxis, can accelerate quickly because it can transfer energy at a high rate.

Formula: P = W/t = ΔE/t, where: P is power (measured in Watts, W) W is work done (measured in Joules, J) ΔE is the change in energy (measured in Joules, J) t is time (measured in seconds, s) 2.

7. Worked

Examples: Example 1: Gravitational Potential Energy A bag of mielie meal with a mass of 5 kg is placed on a shelf 2 meters above the ground. Calculate its gravitational potential energy relative to the ground.

Solution: GPE = mgh GPE = (5 kg)(9.8 m/s 2 )(2 m) GPE = 98 J Example 2: Kinetic Energy A taxi with a mass of 1200 kg is travelling at 25 m/s (approximately 90 km/h). Calculate its kinetic energy.

Solution: KE = 1/2 mv 2 KE = 1/2 (1200 kg) * (25 m/s) 2 KE = 375,000 J Example 3: Conservation of Mechanical Energy A soccer ball with a mass of 0.45 kg is dropped from a height of 10 meters. Assuming air resistance is negligible, calculate its velocity just before it hits the ground.

Solution: ME initial = ME final KE initial + GPE initial = KE final + GPE final 0 + mgh = 1/2 mv 2 + 0 (Initially, the ball is at rest, and finally, the height is zero) gh = 1/2 v 2 v 2 = 2gh v 2 = 2 (9.8 m/s 2 ) * (10 m) v 2 = 196 m 2 /s 2 v = √(196 m 2 /s 2 ) = 14 m/s Example 4: Elastic Potential Energy A spring with a spring constant of 200 N/m is compressed by 0.15 m. Calculate the elastic potential energy stored in the spring.

Solution: EPE = 1/2 kx 2 EPE = 1/2 (200 N/m) * (0.15 m) 2 EPE = 2.25 J Example 5: Work-Energy Theorem A crate of groceries with a mass of 15 kg is pushed across a rough floor, increasing its speed from 1 m/s to 3 m/s. Calculate the net work done on the crate.