Ch. 3: Motion in One Dimension

​Reading
BJU Physics, Ch. 3
AP Classroom: Unit ​1 "Kinematics"
AP Princeton Review: Ch. 4

Topics
  • Displacement, speed, velocity, and acceleration
  • The "Big Five" equations of motion 

Labs
  • Galileo's Inclined Plane lab. Instructions below. Remember to bring the lab handout to class! 
  • Skate Park weblab. Instructions below. 
Homework
Homework is hosted in Canvas. Other handouts/videos below...
1._Velocity problems_Canvas MCQ's WORKED 2023.docx
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1._Acceleration_problems_to use with Canvas ALSO SEE VIDEO__2023_.docx
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Lecture outline:
Velocity
  • Velocity indicates how your location changes with time. It is distance divided by time, as in “miles per hour” or “meters per second”
  • We write the formula as follows:
                vavg = ∆x/∆t  ….or in more expanded form as
                vavg = (x2 – x1) / (t2 – t1)

Acceleration
  • Acceleration indicates how your velocity changes with time.
  • Positive acceleration means "speeding up". Negative acceleration (i.e. deceleration) means "slowing down". 
  • We use units of "meters per second per second" or "meters per second squared".
  • We write the formula as follows
                 aavg = ∆v/∆t  ….or in more expanded form as
                 aavg = (v2 – v1) / (t2 – t1)
The five (5) equations of motion: "The Big Five"
  • You will use these 5 equations for the next several chapters! Locate them in your book and mark the page; you will be referring to them over and over again.
Lecture video
This vid is important and covers the "typical" velocity-acceleration problems
Greek Alphabet assignment
We use the Greek alphabet a lot in Physics. Write-out the entire Greek alphabet, both capital letters and lower case letters (make it look professional!). Include the letter’s “names”. All this can be found in the appendix of your book. Next, write out John 1:1-5 in the original Greek (5 verses total) https://www.biblegateway.com/passage/?search=John%201&version=TR1550 . Write a short essay explaining what is meant by the “Logos” as it is used in this passage.  
Galileo's Inclined Plane lab
​REMEMBER TO BRING THE LAB HANDOUT! 
  • In this lab exercise we reproduce Galileo's famous inclined-plane experiment using a modern Vernier cart and track set at 3 different angles.
  • This is exactly what Galileo did using a bronze ball and wooden track with a groove down the middle. Galileo, however, didn't have a movie camera with an electronic timer; his "clock" was allowing water to drip into a container and then weighing the container!
  • Our goal is to estimate 'g', the acceleration due to gravity on planet Earth, and compare with the known value of 9.8 m/sec^2.
​
Galileo Lab, part 1
  1. Elevate one end of the track at 3 different heights, such that you have a 'slow', 'medium', and 'fast' cart moving down the track. 
  2. Using a movie camera (or motion app) and cart, record "distance vs. time" down the 2-meter track for each scenario: 1) slow, 2) medium, 3) fast. Record the raw data in the form of a table. See example below. 
  3. Create a "distance-vs-time plot" of the raw data we gathered. You will have 3 curves, one for each ramp angle we used. See example below. 
  4. Label everything and make it look nice & professional. Use circles, squares, and triangles as shown. Sketch nice-looking best-fit curves. TAKE PRIDE IN YOUR WORK. 
Upload to Canvas by the due date: 1) table with raw data, and 2) distance-vs-time plot with 3 best-fit curves, all labeled, with your name and date, and the title of the lab written on both. I expect to see professionally-looking work.   

Galileo Lab, part 2
  1. Compute the final velocity of the cart for each track-scenario: Do this by carefully drawing a tangent line (at a convenient spot near the top of each curve), constructing a triangle, and calculating the slope of the curve at that point. Recall that slope is equal to (y2-y1)/(x2-x1), which is the same as "rise-over-run". If you draw your triangle carefully, you can fairly-easily count-out (y2-y1)/(x2-x1) on your graph paper, which will give you the slope at that point, which is equivalent to 'velocity' in m/s. Again, recall that when you plot "distance-vs-time", with distance on the Y-axis, the slope of the curve at any point is equal to 'velocity'. The velocity you are calculating is the 'final velocity' of the cart - or at least the final velocity at the 'time' you draw your tangent line at. See example below. 
  2. Use equation #5 of the Big Five (listed above) to compute the acceleration of the cart down each track: 1) slow track, 2) medium track, and 3) fast track. 
  3. Using the principle of "similar triangles", calculate the acceleration of gravity 'g' for each of the 3 runs. See example below. 
  4. Analysis: compare your 3 values of 'g' with the known value of 9.8 m/s^2. Compute the % error between your average value and the 'true' value of 9.8 m/s^2. Try to explain any differences. 
Upload to Canvas by the due date: 1) Your 3 best-fit curves showing 3 tangent lines and 3 triangles, 2) your 3 computations using Big Five #5, and 3) your computation of the acceleration due to gravity "g" for all 3 runs, the average value, the % error, and your explanatory comments. I expect a professionally-looking final report.  
galileo_lab__part_1_lab handout_-_graphs_and_raw_data_table
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galileo_lab__part_2_lab handout_-_final_lab_report
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Use this graph paper: http://www.printfreegraphpaper.com/gp/e-i-110.pdf
"Skate Park" weblab
Follow the instructions in the handout below. Upload your completed work to Canvas by the due date. 
​Online Curve Fitting Calculator:  elsenaju.eu/Calculator/online-curve-fit.htm
1._skate_park_weblab__rev_2023_.docx
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