# The Very Spring and Root

## An engineer's adventures in education (and other musings).

This content shows Simple View

## Lesson Plan: Predictions With Conservation of Energy

by Nalin A. Ratnayake

Unit: Work and Energy, Component 2: Conservation of Energy
Date: January 15th, 2013
Day/Block: Day 4, Blocks A(3) / E(2) / F(6)
Time Available: E 58 min, A 58 min, F 65 min

Objective: You will be able to predict and analyze motion using the Law of Conservation of Energy.

Criteria for Success:

1. Can I predict the final mechanical energy of an object in motion using energy conservation?
2. Can I determine if and how an object’s mechanical energy has changed?
3. Can I solve a physics problem using energy conservation?

Assessment: Handout and Exit Ticket
The handout will show qualitative understanding of Criteria for Success 1 and 2.
The short worksheet will show quantitative understanding of the Criterion for Success 3.

### [10 min] Do Now

Please have a seat and work quietly on the Do Now. A ball of mass 15.5 kg is released from rest at a point 1.2 m high.

1. If we ignore air resistance, what will be the velocity of the ball at the lowest point of motion?

2. If we assume that air resistance does -20 J of work on the ball as it falls, what will be the velocity at the lowest point of motion?

Share out. Specific questions to ask students: Can you step me through how you found the velocity? How do you know much initial mechanical energy the ball has? How do you know that the total mechanical energy will remain constant? Where does the kinetic energy of the ball come from?  What does the work done by friction do to the mechanical energy of the ball?

### [2 min] Framing the Day

The scenario we will be looking at today will be very similar to the Do Now… only more dangerous!

Objective: You will be able to predict and analyze motion using the Law of Conservation of Energy.

Criteria for Success:

1. Can I predict what will happen to the mechanical energy of an object by using energy conservation?
2. Can I determine if and how an object’s mechanical energy has changed?
3. Can I solve a physics problem about the motion of an object using energy conservation?

Can someone please raise his or her hand and explain what we are doing today?
Can someone please raise his or her hand and remind us how we will know if we are successful today?

### [35 min] Will Professor Lewin Survive?

Note: The following activity will be outlined on a handout / graphic organizer.

We are handing out a worksheet. These will be collected today at the end of the period. Please take a couple of minutes to read the first two sections, labeled “Video” and “Directions”.

VIDEO
Professor Walter Lewin is going to put his life on the line to prove the law of the conservation of energy. He will release a 15.5 kg pendulum bob from his chin, and wait to see what happens when the ball swings back at his face! Will the ball smash his face in? Or will the laws of physics protect him? We will find out….
Can someone please raise their hand to volunteer to read the first paragraph for us?

Directions

• We will be watching a video that goes along with this handout. Do not move ahead. Some questions we will do as a class, some as a table, and others individually.
• Write your answers in complete sentences wherever possible. This helps organize your thinking and gives you better study materials later for quizzes and tests.

Can someone please raise their hand and tell us, what is one direction we should follow today? Why should we do that?
Can someone please raise their hand and tell us, what is another direction we should follow today? Why should we do that?

Play the video of Walter Lewin putting his life on the line to prove Conservation of Energy.

Stop the video at 2:54.  (Right after “…this will be my last lecture.”) PREDICTIONS

1. What kind(s) of mechanical energy does the ball have right now and how do you know?
Quick share, check for agreement or disagreement and why.

Take a couple of minutes to work with your table group on the first column of the table (question 2).
After each column, ask a student to share out what their group answered. Questions to ask: Why do you think that the mechanical energy will increase/decrease? Why will this make the height higher/lower? What does positive/negative work do to the mechanical energy of the pendulum? How will we know if the mechanical energy is higher/lower?

Repeat for questions 3 and 4.

 2. Prof. Lewin does not push the ball and we assume no air resistance 3. Prof. Lewin does not push the ball but we include air resistance 4. Prof. Lewin accidentally pushes the ball as he lets go What kind of work will be done on the ball (positive / negative / none)? What will happen to the total mechanical energy of the ball (increase / decrease / constant)? What will be the height of the ball when it swings back to Prof. Lewin (higher / lower / same)? Will Professor Lewin be safe (yes / no)?

Add this diagram to the slide to be clear about what I mean by “height”: 5. Make your prediction: What will happen to the mechanical energy of the ball? How will you know if your prediction is right or wrong?

Play the rest of the video.

Show a side by side of the before (at the time of release) and after (1 cycle):  I was careful to stop the video exactly when the ball reached its maximum height on the return swing. Is he at the same position or not? What do you notice about the ball’s position?

At this point there should be at least 20 min remaining in the period.

ANALYSIS
6. What happened to the mechanical energy of the ball, and how do you know?  What evidence tells you so?

DISCUSSION
Possible questions:What happened to the mechanical energy of the ball, and what evidence do you have? Was there work done on the ball? If so, by what force and was it positive or negative work? How can we explain what happened using the Law of Conservation of Energy? As students answer, ask for agreement or disagreement and why.

CONFER
In a couple of minutes, I’m going to ask you to answer question 7 individually. But before we do that. you have 2 minutes to check with your partner and make sure you agree on what happened. This is your only chance to confer before answering question 7 on your own.

7. Write out a short story of what happened to Prof. Lewin’s swinging pendulum. You must answer the following questions in your story: Was work done on the ball and by what force?  What did this work do to the mechanical energy of the ball? What did we observe that told us what happened to the mechanical energy of the ball?

### [5 min] Exit Ticket

Professor Lewin released a 15.5 kg pendulum from 1.20 m high. We carefully measure the height of the ball when it swings back towards him, and determine that the ball only went 1.05 m high when it came back. How much work was done by air resistance on the ball?

Collect student work. If running out of time, ask co resident to help photograph worksheets and exit tickets of case study students as a worst case fallback option.

52 min total:  ~5 min of buffer
If need be, the CONFER section of the plan can be eliminated without impact to the cognitive demand or student sense-making in the lesson.

## Lesson Plan: Exploring Newton’s 3rd Law in Sports

EXPLORING NEWTON’S 3rd LAW IN SPORTS

Unit: Dynamics
Date: November 19th, 2012
Day/Block: Day 3 / A Block
Time Available: 65 min

Teacher Prep:

• Ensure prerequisite knowledge of: introduction to Newton’s 3rd Law
• Make slides (including one for Objective and Criteria for Success)
• Print and copy exit tickets
• Rehearse lesson and do the work of the students

Lesson Objective:
You will be able to identify action-reaction force pairs and make predictions about motion using Newton’s Third Law.

Criteria for Success:
You will be able to explain what Newton’s 3rd Law says about forces.
You will be able to use Newton’s 3rd Law to predict what forces will act on an object in physical scenarios.

Assessment:
Exit ticket.

Agenda:

### [5 min] Do Now Newton’s 3rd Law tells us that all forces come in action-reaction pairs. List the action-reaction force pairs that you can think of on the red football player. (Hint: Mr. Ratnayake sees at least 4). Draw a free body diagram of the red football player.

### [1 min] Making Explicit the Content of the Lesson

Hang on to what you did for the Do Now. We will be returning to it later on in the lesson.

Lesson Objective: You will be able to identify action-reaction force pairs and make predictions about motion using Newton’s Third Law.

Criteria for Success:
You will be able to explain what Newton’s 3rd Law says about forces.
You will be able to use Newton’s 3rd Law to predict what forces will act on an object in physical scenarios.

* Ask students to revoice the objective and CfS.

### [10 min] Mini-Lecture 1: Review of Newton’s 3rd Law

[7 min for lecture] Review the main points of the third law.

• There is no such thing as a single force — forces always come in action-reaction pairs.
• Action-reaction pairs are the same kind of force acting on different objects.
• Action-reaction pair have equal magnitude forces acting in opposite directions.

* Ask students, what do you think I mean by “same kind of force”? (Gravity, perpendicular contact force, parallel contact force, etc).
* Ask students, what do you think I mean by “magnitude”? (Strength of the force, size of the force, the value of the number, etc).

[3min for processing time] Take 2 minutes to check with a partner next to you. Look back at your list of action-reaction pairs from the Do Now. Do the pairs on your list fit what we just wrote down about Newton’s 3rd Law? I will ask someone to tell me about what their partner wrote.

* Ask students to name a force pair that their partner wrote down, and why they think it fits the description of an action reaction pair.  Draw the force pairs on the football player.

[10 min] Mini-Lecture 2: Review of Free Body Diagrams.

[5 min for lecture] A Free Body Diagram of an object only shows the forces acting on that object.
Free Body Diagrams do not include the forces that the object itself applies on other things.

Ask yourself: if I were this object, which forces would I feel acting on me?

Block on a surface example. There are two action-reaction pairs:

1. gravity from the earth on the block, with gravity from the block on the earth
2. contact force from the block to the surface, with contact force from the surface to the block

Which of these forces do you think the block is feeling? (normal force and weight). Draw FBD.

[2 min for processing time] Take 1 minute to check with a partner next to you. Look back at your free body diagrams from the Do Now. Does your partner’s FBD of the football player obey the rules of a free body diagram?

[3 min for closure on the Do Now] * Have a student draw the free body diagram for the red football player. Use questions for students to correct it if necessary.

### [1 min] Instructions for Scenarios

Take 1 minute to read the directions for this next segment. I will call on a student to explain what we are doing for the class.

• You will be given a scenario and several questions for discussion in your table group.
• I will call on someone for each part of the discussion questions.
• If they represent their group well, the whole group gets a stamp.

*Ask students: What are we going to be doing?

### [15 min] Scenario 1: Serena Williams — Tennis

[15 min total, 8 min to discuss with group and work out the scenario, 7 min for discussion] Tennis star Serena Williams uses Newton’s Laws to get the tennis ball to move.

• Describe the action-reaction force pair that acts to accelerate the tennis ball. What are the forces? In which direction do they act? On what does each force at?
• Draw a free body diagram of the tennis ball. In which direction is the net force on the tennis ball? Predict what will happen to the tennis ball and racket, using Newton’s Laws.

### [15 min] Scenario 2: Ron Weasley — Quidditch

[12 min total, 7 min to think-pair-share, 5 min for discussion] Quidditch keeper Ron Weasley blocks a quaffle coming in from the left of the image.

• Describe the action-reaction force pair that acts to block the quaffle at the time of impact. What are the forces? In which direction do they act? On what does each force at?
• Draw the FBD for the quaffle and the FBD for Ron. In which direction is the net force and acceleration for the quaffle? What about for Ron?
• Which will accelerate more, the quaffle or Ron? If Ron and the quaffle both experience an equal force from the impact, why are their accelerations different?

### [7 min] Exit Ticket

How can you tell if two forces are an action-reaction pair according to Newton’s 3rd Law?

An archery target stops an arrow on impact. The arrow experiences high acceleration to go from a fast speed to at-rest very quickly. Do the arrow and the target experience the same force from the impact? Do the arrow and the target experience the same acceleration? Why or why not?

64 min total:  ~1 min of buffer

Pacing: If necessary due to unexpected time constraint, one of the scenarios can be cut out and the other extended slightly.

## Lesson Plan: Introduction to Newton’s Second Law of Motion

### [7 min] Do Now

Review from 1st Law, introduce 2nd Law:

In which of these cases do we have balanced forces? Explain why.

• A cat is moving with constant velocity towards his date.
• A car is moving with constant acceleration to pick up more physics homework.
• A cow is at rest, taking a nap.
• An apple is hanging from a tree.

Share out and discuss. Bridge the transition between Newton’s First Law and the idea of net force into Newton’s Second Law.

### [1 min] Making Clear the Objective

Objective: You will derive the relationship between force and acceleration from simulated experimental data.
Criteria for Success: Graphs of data will show proof of Newton’s 2nd Law of Motion.

### [12 min] Simulation: Newton’s Second Law

We will be using the simulation of Newton’s 2nd Law located at: http://phet.colorado.edu/en/simulation/forces-1d

Set: show horizontal force, show total force.
Turn friction off.
Turn on graphs for acceleration and velocity.

Use students to run simulation and call out the data for their classmates to record.

We will be using a simulation. For each trial, record the following:

• mass of the object
• force applied to the object
• acceleration of the object

Run the simulation for the dog (25 kg) with three forces: 50 N, 100 N, 200 N. Ask the students to make a prediction before the last one. Make sure to reset the simulation and graphs before each trial.

Run the simulation  for the textbook (10 kg) with the same three forces.

### [15 min] Graphing the Data

Turn and Talk:
What was the independent variable and why?
What was the dependent variable and why?
What was the main control variable and why?

What do we put on the y-axis? What do we put on the x-axis?
The independent variable of our experiment always goes on the x-axis (Force). The dependent variable of our experiment always goes on the y-axis (Acceleration).

Draw 2 graphs. Don’t forget units and labels!

• Acceleration vs force variable for the dog
• Acceleration vs force variable for textbook

### [15 min] Analyzing the Data

We seem to have found a correlation between two variables, force and acceleration. Let’s see if we can define a relationship between them.

Find the slope of each graph and write it next to the plot.
Find the inverse of the slope for each graph and write it next to the plot.

Think-Pair-Share:
Do we see any patterns? Does the slope look like a variable we recognize? How would I write the equation of this line?

a = 1/m F   →   F = m a

### [2 min] Summarize Findings

Newton’s 2nd Law of Motion:
The acceleration of an object is directly proportional to the net force acting on the object. The acceleration will be in the same direction as the net force. The acceleration is resisted by the mass of the object.

F = m a

### [6 min] Exit Ticket The catapult on an aircraft carrier can can accelerate a fighter jet from rest to 56 m/s in just 2.8 s. If the fighter jet has a mass of 13,000 kg, what is the force required?