## Lesson 4: The Law of Conservation of Energy

## Overview:

The Law of Conservation of Energy is one of the most useful tactics in problem solving in any physics course. Here you will review the basics from Grade 11 and be introduced to how the formula you used is derived.

## Curriculum Expectations:

**Overall Expectations:**

**C3.**Demonstrate an understanding of work, energy, momentum, and the laws of conservation of energy and conservation of momentum, in one and two dimensions.

**Specific Expectations:**

**C2.1**Use appropriate terminology related to energy and momentum, including, but not limited to:

work, work–energy theorem, kinetic energy, gravitational potential energy, elastic potential energy, thermal energy, impulse, change in momentum–impulse theorem, elastic collision, and inelastic collision.

**C2.2**Analyze, in qualitative and quantitative terms, the relationship between work and energy, using the work–energy theorem and the law of conservation of energy, and solve related problems in one and two dimensions.

**C2.3**Use an inquiry process to analyse, in qualitative and quantitative terms, situations involving work, gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy, in one and two dimensions (e.g., a block sliding along an inclined plane with friction; a cart rising and falling on a roller coaster track; an object, such as a mass attached to a spring pendulum, that undergoes simple harmonic motion), and use the law of conservation of energy to solve related problems.

**C2.4**Conduct a laboratory inquiry or computer simulation to test the law of conservation of energy during energy transformations that involve gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy (e.g., using a bouncing ball, a simple pendulum, a computer simulation of a bungee jump).

## Success Criteria:

- If energy is conserved i a system, what information does it give in terms of mechanical energy? What if energy is lost due to friction/sound/light?
- What do you need to consider for a diver on a platform to be an isolated system?
- Compare and contrast the properties of (i) closed systems, (ii) open systems and (iii) isolated systems.
- Describe the law of conservation of energy.
- What is biochemical energy? How do humans, plants, and animals apply biochemical energy transformations to survive?
- What is power and how to we measure it?
- Make a distinction between power consumption and power output.

## Time Allocation: 3 hours

## Learning A

ctivities:**Read**pages 184 - 190 from Nelson 4.5 and

**copy the sample problems**into your notes.

Pendulum LabPlay with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. It's easy to measure the period using the photogate timer. You can vary friction and the strength of gravity. Use the pendulum to find the value of g on planet X. Notice the anharmonic behaviour at large amplitude. What type of energy does it have at its lowest point? highest point? halfway? |

Energy Skate Park: BasicsLearn about conservation of energy with a skater dude! Explore different tracks and view the kinetic energy, potential energy and friction as he moves. Build your own tracks, ramps and jumps for the skater. |

In the playlist below, video:

- Will show and explain the conservation of energy equations.
- Will show how to calculate the distance an object will travel up a (frictionless) incline.
- Will show how to calculate the final velocity of a roller-coaster.
- Will show how to calculate the final velocity of an atwood machine.
- Will show you how to find the period of oscillation of an ideal pendulum.

**Practice**question 1 on page 187.

**Practice**question 1 on page 190.

## Task:

**Solve**questions 3, 4, 7, and 8 from Nelson 4.5 Review on page 191.

*Optional Extension:*- Solve questions 5 and 6 on page 191.
- Practice

## Reflect:

An apple falls from a branch to the ground below.

(a) At what moment is the kinetic energy of the apple greatest?

(b) At what moment is the gravitational potential energy greatest?

(a) At what moment is the kinetic energy of the apple greatest?

(b) At what moment is the gravitational potential energy greatest?