Unit Plan - Energy and Work

Unit 3: Energy and Work

Unit Objectives:

To understand the principles of work and energy.
To explore the conservation of energy and its applications.
To analyze collisions and the conservation of momentum.

Essential Questions:

What is work and how is it related to energy?
How can we use the principle of conservation of energy to solve problems?
What happens during collisions and how can we describe them mathematically?

Key Concepts:

Work and Energy
- Work done by a constant force
- Kinetic and potential energy
- Conservation of energy
Momentum and Collisions
- Momentum and its conservation
- Elastic and inelastic collisions

Key Formulas:

Work Done (W)
$W = F d \cos (θ)$
Where $F$ is force, $d$ is displacement, and $θ$ is the angle between them.
Conservation of Energy
$Δ U + W_{n c} = Q$
Where $Δ U$ is change in internal energy, $W_{n c}$ is work done by non-conservative forces, and $Q$ is heat transferred.
Conservation of Momentum
$m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{1}^{'} + m_{2} v_{2}^{'}$
Where $m_{1}$ and $m_{2}$ are masses, and $v_{1}, v_{2}, v_{1}^{'}, v_{2}^{'}$ are initial and final velocities.

Lesson Breakdown:

Lesson 1: Introduction to Work and Energy

Overview of work and energy.
Introduction to the concept of work done by a constant force.

Lesson 2: Work Done by a Constant Force

Calculating work done by a constant force.
Lab activity: Measuring work done using an inclined plane.

Lesson 3: Kinetic and Potential Energy

Introduction to kinetic and potential energy.
Lab activity: Exploring the conversion between potential and kinetic energy.

Lesson 4: Conservation of Energy

Derivation and application of the conservation of energy principle.
Problem-solving session: Solving energy conservation problems.

Lesson 5: Work Done by Varying Forces

Calculating work done by varying forces.
Lab activity: Measuring work done by a spring.

Lesson 6: Energy in Non-Conservative Forces

Understanding work done by non-conservative forces.
Lab activity: Analyzing energy transfer in a system with friction.

Lesson 7: Introduction to Momentum and Collisions

Overview of momentum and its conservation.
Introduction to elastic and inelastic collisions.

Lesson 8: Momentum and Its Conservation

Derivation and application of the conservation of momentum principle.
Problem-solving session: Solving momentum conservation problems.

Lesson 9: Elastic Collisions

Characteristics of elastic collisions.
Lab activity: Investigating elastic collisions using air tracks.

Lesson 10: Inelastic Collisions

Characteristics of inelastic collisions.
Lab activity: Investigating inelastic collisions with carts and masses.

Lesson 11: Momentum in Two Dimensions

Calculating momentum in two dimensions.
Problem-solving session: Solving momentum problems in two dimensions.

Lesson 12: Center of Mass

Understanding the concept of center of mass.
Lab activity: Determining the center of mass of various objects.

Lesson 13: Rocket Propulsion

Applying the principle of conservation of momentum to rocket propulsion.
Lab activity: Building and launching model rockets.

Lesson 14: Energy and Momentum in Collisions

Analyzing energy and momentum in collisions.
Problem-solving session: Solving combined energy and momentum problems.

Lesson 15: Review and Practice

Review of key concepts and formulas.
Practice problems and quizzes to prepare for the unit test.

Lesson 16: Unit Test

Assessment of understanding of work, energy, momentum, and collisions.

Assessments:

Formative Assessments
- In-class discussions and think-pair-share activities to gauge comprehension.
Summative Assessments
- Final unit test covering all topics in the unit.
Performance Tasks
- Students will be required to solve a series of problems involving work, energy, and momentum.

Additional Resources:

Interactive simulations for work, energy, and collisions (e.g., PhET Interactive Simulations)
Videos explaining key concepts (e.g., Khan Academy, TED-Ed)