Unit 1: Motion in One Dimension

​Reading
BJU book: Read Ch. 3 "Motion in one dimension"
AP students additional reading: Princeton Review Ch. 4 "Kinematics". You can skip the part on "Projectile Motion", as we will cover that topic later. 

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

Labs
  • 2021-2022: Skate Park Velocity-Acceleration Weblab
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
2021-2022 Class:  Skate Park Velocity-Acceleration Weblab, part 1
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
skate_park_velocity-acceleration_weblab, part 1.docx
File Size: 894 kb
File Type: docx
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2020-21 Class:  Galileo's Inclined Plane experiment
Cart-track velocity lab using tracker video analysis https://www.compadre.org/osp/items/detail.cfm?ID=7365. 
  • 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 lab report! 
galileo_lab__part_1_raw_data_table_example_.pdf
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galileo_lab__part_1_distance_vs_time_plots_examples_.pdf
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galileo_lab__part_2_final_report_example_.pdf
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Use this graph paper: http://www.printfreegraphpaper.com/gp/e-i-110.pdf
Homework
Velocity problems: BJU Ch. 3 Review Questions #20-27 and 38 (9 problems). Enter your answers in Canvas. 
AP: Velocity problems posted in Canvas.
2._acceleration_homework_problems_2021.docx
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