HP Cycle 3

🟢 8: W 9/17 - motion graphs & linearization

Then, we'll start the next activity where we'll practice our graphing skills - Motion Graphs & Linearization.  In this activity, you will look at the motion of two different objects.  Then analyze the motion by doing the following:

1. Describe the motion in words.  Discuss in your lab group.

2. Predict the x vs. t and v vs. t for trial 1 and sketch it on the whiteboard (no numbers required).  Discuss in your lab group.  

3. Take data and plot position vs. time  for each trial.  Think about what measurement needs to be taken:  AB, BC, CD, ... or AB, AC, AD, ...

4. Take data and plot velocity vs. time  for each trial.  Think about what measurement needs to be taken:  AB, BC, CD, ... or AB, AC, AD, ...  You may use the additional columns to make calculations if you need to.

5. Draw a best fit curve on each of your graphs.  Remember to NOT connect the data points; each data point has a margin of error.  To draw the best fit curve, draw a smooth line or curve that best represents the trend in your data.  If you think the graph is linear, use a ruler to make a perfectly straight best fit curve.

6. If any of your graphs are linear, find the equation of the line.  Find two points for the slope calculation that are far away from each other and circle them.  Then show your calculations to get the slope and find the intercept.  Using the slope-intercept form, write your equation on the same page as your graph.  Remember not to use x and y as the variables in your equation; use the variables on the axes of your graph (e.g. x, v, t ).  All numbers (slope and intercept) should be in decimals with the correct number of sig figs and also have appropriate units.

The final step in our activity may be something new to you - linearization.  In order to find a mathematical relationship between two variables, it is common to graph the data.  If the relationship between the two variables is linear, you can write a mathematical relationship by finding the slope and writing a slope-intercept equation.  However, if the relationship is not linear, finding an equation that relates the two equations is a little more difficult.  While one way to get an equation is with a computerized curve fit, today we will learn how to do it by hand with "linearization."  We'll first read through determining relationships from graphs to review what different curves look like and then figure out how to linearize the graph.

Then, we'll continuing to work with Motion Graphs & Linearization and try to get a linearized the position vs. time graph for trial 2.  What do you think the slope of the linearized graph represents?

Presentation:  Motion Graphs & Linearization Presentation

Handout:  Motion Graphs & Linearization, determining relationships from graphs

Homework:  ❗ Assessment on all of graphical analysis of motion next class - Thursday, September 18th.  This assessment will only include graphical analysis of motion (big graph homework).  It will not include kinematics equations (Tesla, textbook problems above) or linearization (lab).  

We've already learned about the equations that DEFINE average velocity and average acceleration.  Today, we'll start to use our mathematical definitions to solve problems in "It's Your Lucky Day" Packet (aka Tesla Problem).  Here are the goals for work in this packet:

• Learn how to manipulate the definitions of average velocity and average acceleration in order to derive other kinematics equations.

• Learn the expectations for communicating solutions to kinematics problems:

  • diagram/graph

  • sign convention

  • listing of knowns & unknowns

  • stating equation

  • using algebra to find an expression for the unknown in terms of all the knowns

  • solving the problem with numbers

In class, we'll try to do #1-3.  

Handouts: "It's Your Lucky Day" Packet

Homework: Make sure you've completed #1-3 on "It's Your Lucky Day" Packet.  See my solutions below.  (The solutions below are for an older problem, so the numbers are different, but the solutions are the same except for the numbers.)

💚 8: F 9/19 - kinematic equations 

Today, we'll get back to discussing findings from #1-3 on "It's Your Lucky Day" Packet.  We'll take a look at some new "equations of motion with constant acceleration" (aka kinematic equations).  We'll fill out a chart Equations of Motion Graphic Organizer which will aid you in finding the most efficient equation to use.   

Finally, we'll do an activity to practice equation selection:  Which Equation Should I Use.  During this activity, you'll see a problem.  Write down the knowns and unknowns, and select the best equation to use to solve the problem.  

Then, we'll talk about how to do #4 from  "It's Your Lucky Day" Packet, and learn how to use equations of motion to solve problems with more than one object.  

Then, with any time remaining, we'll collaboratively work on some kinematics problems from chapter 2 in your textbook:  

Chapter 2 Problems: 28, 32, 38, 60, 14, 12, 33, 39, 43, 73

Ask other students or me for help if you need it.  In writing out your solutions, be sure to practice including all the components of problem solving reviewed in class as this will help solidify good habits for the assessment next week:

1. Draw a picture or diagram or graph.

2. Pick a sign convention.

3. List your knowns and unknowns.

4. Write the formula you'll be using.

5. Rearrange the formula with algebra so that your unknown is on the left side of the equals and all the knowns are on the right.  STAY IN VARIABLES!

6. Plug in numbers and box your answer.

Handout:  Equations of Motion Graphic Organizer

Homework:   Take your freefall video and post to ✏️ Google Classroom by Sunday at 10pm!  

Recommended Additional Practice Problems:  Ch 2 #3, 4, 8, 18, 24, 19, 25, 20, 22, 36 (answer in Mastering Physics so you can see if you're right in preparation for your quiz next week)