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Today, we will study velocity dependent forces with a lab in ↩️ Pivot Interactives called "Falling Coffee Filters." We'll do a lab where we investigate the concepts of air resistance (drag) and terminal velocity. Some of you may elect to do an in-person version of the lab. Others will choose to analyze videos in Vernier. The choice is yours! There are up-sides to each method and challenges to each. In the end, no matter how you perform the lab, you'll see how drag force relates to velocity.
For the in-person version, use the motion sensors we have in the classrooms to get data. You will have to use Vernier Graphical Analysis which is available on ClassLink. In ↩️ Pivot, do the parts that are labeled EVERYONE and PHYSICAL ONLY.
For the virtual video version, use the Vernier Video Physics web app which is accessible through ClassLink. Instead of motion sensors, you'll track the motion of the filters in this app. In ↩️ Pivot, do the parts that are labeled EVERYONE and VIDEO ONLY.
For both groups, you'll be graphing position vs. time and velocity vs. time in Vernier. You'll see how the drag force (air resistance in this case) relates to terminal velocity. Make sure to add rows in the data table to have 6-7 trials. You're trying to answer the question: if drag can be modeled as FD = -bv n, what are the values of b and n ? Make sure you linearize your graph to find the relationship.
After completing the lab, your group will get together with another group to talk about the benefits and challenges to the in-person vs. virtual version of the lab.
By the end of this lab, you will be able to:
Describe the force of air resistance.
Describe the motion of an object falling in the presence of air resistance.
Describe how air resistance varies with velocity.
Name some other variables that affect air resistance other than velocity.
Name some real-life situations where air resistance is beneficial or detrimental.
Homework: Lab due in ↩️ Pivot on Monday, April 6th at pm. Watch the following video on velocity dependent forces. At time 6:00, pause the video and practice solving the differential equation on your own. (It will probably be faster than watching the whole video.) After you make your best attempt, fast forward to see if you were right. Then, at 17:00, listen to the notes at the end. Be prepared for a daily quiz next class.
Today, contine working on the labs above.
Homework: Lab due in ↩️ Pivot on Friday, March 27th at 3pm. Watch the following video on velocity dependent forces. At time 6:00, pause the video and practice solving the differential equation on your own. (It will probably be faster than watching the whole video.) After you make your best attempt, fast forward to see if you were right. Then, at 17:00, listen to the notes at the end. Be prepared for a daily quiz next class.
Homework: Finish the above velocity dependent force AP problems. Watch the following video on simple harmonic motion (SHM):
Check out this video for a better understanding of "angular frequency" ω (aka frequency of oscillation) and how it relates to the angular speed ω we already studied in rotation:
Today, we'll continue with a brief discussion of the equations that describe simple harmonic motion. It will be a more in-depth review of the video that you watched last night.
If you missed class or if you'd like to review, watch the following video explaining the calculus of solving simple harmonic motion. This video is really similar to the lecture I would have given in class. This is one of the videos I would really pay attention to! There's a lot of important information packed in here! Watch it slowed down, pause to think about the analyses (especially in the graph section at the end), and watch it multiple times!
With any time remaining, watch the homework videos below, and start the required Oscillation AP Problems (2009M2, 1990M3, 1999M2).
Homework: Finish oscillation problems above. More Mechanics Unit Assessment on Thursday, April 10th (marking period 3). Watch the following two videos on simple harmonic oscillators with springs and pendulums. Alternatively, learn about simple harmonic oscillators using the available media of your choice - textbook, internet, etc.
Small angle approximation: For small angles
θ (in radians) ≈ sin θ ≈ tan θ