The Very Spring and Root

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

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From the Classroom

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.



Keep Calm and Carry On

Ooof. Had my first student blowup yesterday. This particular student is in his senior year, he really needs to pass this class to graduate, and first quarter grades come out this week. And… his quiz grade was not so hot. Long story short: weeks of pent up frustration with physics coming out, pretty aggressively and with lots of swearing. Not a pleasant situation and very uncomfortable. I sat down, not retreating or exacerbating, and tried to calmly explain why I had given him the grade I did. I also tried to gently point out that the time to come in with your misunderstandings is not right before the test.

To be honest, I think in that moment he really needed to vent. I’d like to think that I was able to show that I sympathized with his position and listened to his concerns, but in the moment it was really hard to think. In retrospect I think I handled it decently well, but it’s not the kind of thing that lends itself to easy self-reflection.

I’ll keep an eye out to make sure this student is doing ok and maybe check in with him in a few days.

One more thing to add to the list of things that are really hard about this job… it’s tough to care and not know what to do.



It’s Snowing on Venus: Students as Sense-Makers

Oh yeah, almost forgot to post it here. My latest blog post for BTR was posted about a week ago: It’s Snowing on Venus: Students as Sense-Makers.

Here’s a teaser:

As I enter deeper into the “disillusionment” phase of the new teacher cycle, I’m certain that there will be times in which I doubt myself and the systems in which I find myself. But it’s moments like these, in which students show that they are brilliantly capable of making sense of science on their own terms, that provide the islands of inspiration that I know will keep me going.

It’s an outbrief of sorts from one of the clinical interviews that I am conducting with specific case study students throughout the year.



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).

Work with your partner:
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

Estimated Instructional Time: 52 min

 

[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?



5 Minute Lesson: Kepler’s 2nd Law

Instructor: Mr. Nalin Ratnayake
Subject: Physics (algebra-based)
Target Grade Level: 11/12
Lesson Objective: Understand the major implication of Kepler’s 2nd Law.

Good morning class. Have you ever wondered about the motion of the planets? My name is Mr. Ratnayake (Mr. Rat will do). Today we will discuss Kepler’s 2nd Law of Planetary Motion, building on your previous knowledge of basic mechanics, algebra, and geometry.

In the early 1600’s, most astronomers believed that if the planets orbited around the sun, they must do so in circles. However, astronomical observations did not agree; planets seemed to move randomly in the sky. It was a mystery. A German mathematician named Johannes Kepler forever changed astronomy by demonstrating in his *first* law of planetary motion that by simply treating an orbit as an ellipse, instead of the previously-assumed circular shape, the simplicity and harmony of planetary motion became clear. He then went on to explain the consequences of elliptical motion in his *second* law, which states: A line connecting a planet to the sun sweeps out equal areas in equal times.

Refer to the diagram on your handout, or follow me on the board. Suppose I have here my orbital ellipse, and I consider the area swept out by the radius r in some interval of time. The planet has moved on an arc, by an angle θ as measured from the sun. Now we have set up our problem and will commence, like good scientists, to ask questions.

What basic geometric shape does this look like? (Triangle). Let me draw this triangle. Who knows how to find the area of a triangle? (one-half the base times the height). Ok. Do we have a variable on our diagram that looks like it would be the height of the triangle?  (the radius r).  And this arc forms the base. What is the length of an arc (You remember from geometry of course, it is the radius of the arc times the subtended angle.)  So the area (A) of this pie wedge is…. ½ (r θ) r , or ½ r2θ.

Let’s assume, as Kepler did, that this area must remain constant for the same time interval in an orbit. Consider our diagram. If our planet moved closer to the sun, say here, then the radius, our distance to the sun, is much smaller. To maintain the same area of triangle, what must happen to its base? (must get larger). Remember, this is the arc length we traveled in our orbit for a set time interval. We traveled farther in the same amount of time than we did out here! What can we deduce about our speed? (we went faster!). We move faster when we are near the sun on our orbit and slower when we are far from the sun on our orbit.

Was Kepler right? It turns out that his theory exactly matched observational data from astronomer Tycho Brahe; this explained previously erratic motions of the heavenly bodies with a simple concept. Today, Kepler’s Laws enable us to predict the motion of the planets, asteroids, comets, and satellites in space. NASA’s Mars Curiosity probe just launched this week. It will take 8 months to reach Mars. Thanks to Kepler’s Laws we know exactly where Mars will be and how fast it will be going in 8 months; and Curiosity will be in the right place at the right time.

Check for understanding, all together now, and I’m looking for every one of you to answer. As a planet gets closer to the sun, does it speed up or slow down? (Speeds up!) As a planet gets further away on its orbit, does it speed up or slow down? (Slows down!) Good. Any questions?




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