## Lesson 10: Head-on Elastic Collisions

## Overview:

Playing pool requires some knowledge of physics, and in here we will focus on perfectly elastic collisions, which have kinetic energy conserved. We will explore, why kinetic energy is conserved.

## Curriculum Expectations:

**Overall Expectations:**

**C2.**Investigate, in qualitative and quantitative terms, through laboratory inquiry or computer simulation, the relationship between the laws of conservation of energy and conservation of momentum, and solve related problems.

**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.

**C2.6**Analyze, in qualitative and quantitative terms, elastic and inelastic collisions in one and two dimensions, using the laws of conservation of momentum and conservation of energy, and solve related problems.

## Success Criteria:

- What is a head-on elastic collision?
- Derive the equation that expresses the final velocity of the first object in terms of the masses and initial velocities of the two objects.
- Derive the equation that expresses the final velocity of the second object in terms of the masses and initial velocities of the two objects.
- Write the equations for the final velocities after a head-on collision with a stationary object occur.
- Describe what happens to the conservation of total mechanical energy during elastic collisions.
- What do you need to consider in determining the maximum compression of the spring during collisions? Explain why it is necessary.

## Time Allocation: 3 hours

## Learning A

ctivities:**Read**pages 240 - 247 from Nelson 5.4 and

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

Collision LabUse an air hockey table to investigate simple collisions in 1D and more complex collisions in 2D. Experiment with the number of discs, masses, and initial conditions. Vary the elasticity and see how the total momentum and kinetic energy changes during collisions. |

In the playlist below, video:

- Will show you how to solve a problem when a block slides down and sticks to another block on a semispherical bowl using conservation of momentum and conservation of energy.
- Will find velocity final of an elastic collision, example 1.
- Will find velocity final of an elastic collision, example 2.
- Will find velocity final of an elastic collision, example 3.
- Will find velocity final of an elastic collision, example 4.

**Practice**question 2 on page 243.

## Task:

**Solve**questions 3 and 4 from Nelson 5.4 Review on page 248.

Quiz Chapter 5 on Moodle.

*Optional Extension:*- Solve question 6 on page 248.
- Practice

## Reflect:

In this chapter, momentum and collisions has been applied mostly to idealized lab situations involving dynamics carts and billiard balls. How does this theory apply to your everyday activities? Would you consider changing some of your behaviours based on what you have learned?