Unit 1: Motion in One Dimension
Reading (Weeks 1-3)
BJU book: Read Ch. 3 "Motion in one dimension"
AP students additional reading: Princeton Review Ch. 4 "Kinematics"
Topics
Labs
BJU book: Read Ch. 3 "Motion in one dimension"
AP students additional reading: Princeton Review Ch. 4 "Kinematics"
Topics
- Displacement, speed, velocity, and acceleration
- The "Big Five" equations of motion
Labs
- Cart-track velocity lab using tracker video analysis https://www.compadre.org/osp/items/detail.cfm?ID=7365. We'll review when we get here.
The Skydiving Cat and Elephant Formation illustrate "free fall". All satellites, including the Moon, are actually in "free fall" towards the earth. The reason they don't crash into the Earth is because they "side step" at just the right amount so as to stay in orbit. The Moon orbits the Earth at about 2,000 miles per hour. The Earth orbits the Sun at about 80,000 miles per hour. A man-made satellite orbiting near the Earth's surface needs to travel at about 18,000 miles per hour to stay in orbit, and completes its journey around the Earth in about 90 minutes. We will cover gravity and orbits later in the year.
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Lecture video
Lecture outline:
Velocity
vavg = (x2 – x1) / (t2 – t1)
Acceleration
aavg = (v2 – v1) / (t2 – t1)
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 = (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 = (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.
Galileo's Inclined Plane lab
Galileo Lab, part 1
Galileo Lab, part 2
- 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
- Elevate one end of the track at 3 different heights, such that you have a 'slow', 'medium', and 'fast' cart moving down the track.
- 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.
- 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.
- 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.
Galileo Lab, part 2
- 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.
- 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.
- Using the principle of "similar triangles", calculate the acceleration of gravity 'g' for each of the 3 runs. See example below.
- 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.
| galileo_lab__part_1_raw_data_table_example_.pdf |
| galileo_lab__part_1_distance_vs_time_plots_examples_.pdf |
| galileo_lab__part_2_final_report_example_.pdf |
Use this graph paper: http://www.printfreegraphpaper.com/gp/e-i-110.pdf
Conversions homework problems
| 1._conversions_homework__problems.docx |
BJU Ch. 3 problems - Show your work!
Set 1: #20-27 and 38 (9 problems)
Set 2: #28-33 (6 problems)
Set 1: #20-27 and 38 (9 problems)
Set 2: #28-33 (6 problems)
AP additional homework from Princeton Ch. 4 "Kinematics"
Set 1: MC #1-2, and FR #1 (3 problems)
Set 2: MC #5-6 and 12 (3 problems)
Set 1: MC #1-2, and FR #1 (3 problems)
Set 2: MC #5-6 and 12 (3 problems)
| ap_phys_accel_problems_princeton_#1, 2 and #1.docx.docx |
| ap_phys_accel_problems_princeton_#5, 6, 12.docx |
| 1._velocity___distance_homework__problems.docx |
| 2._acceleration_homework_problems.docx |