Embedded Files
Our Film
Our Film
PhySportsBoomerang2.mp4
The aim of this project was to create an informational video which described how to perform some sports-related action as well as the physics behind it. Originally, our group decided to use throwing a frisbee as our action, but we later switched to throwing a boomerang since it involves much more interesting physics related to lift and aerodynamics. We began creating our video by creating a rough storyboard sketch (shown below) so that we would know exactly what we needed to film. After we had finished our storyboard, we wrote a script to match it (shown at left) and formalized what we needed to film.
Our rough storyboard sketches.
Over the course of the next week, we shot the film that we needed in order to be completely prepared for the editing stage. There was a good deal of difficulty with this since to throw a boomerang properly you need a strong and consistent headwind, which we did not have for the first few filming days. Luckily, on the last day there was a spurt of wind which yielded a few throws that were perfect for our film.
Next, we began editing. The first draft was edited by one of my groupmates, Nicholas. We watched through the video in the following class session to brainstorm improvements and feedback. During that class session, we also recorded all the voice-overs so that we would be able to edit the final cut in a way that would be completely synced with all voice-overs. After that class, I took the rough draft and added in the voice-overs, more footage, and background music to create our final draft. I used iMovie as the editing software since I don't have any professional editing software (and iMovie was sufficient to create a polished final product). I made sure that the video was edited together smoothly and all crossfades, audio dissolves and voice-overs were synced with the video's content. In the end, our final product was smooth and fairly professional.
Core Concepts
Core Concepts
fly_and_catch.m4vForce of Impact
Force of Impact
The force of impact is the force exerted on an object when some external object collides with it. This force can be found through the equation mΔv=FΔt, where m is the mass of the external object, v is velocity of the external object at the time of impact, F is the force of impact and t is the duration of the impact.
In the video at left, you can see the boomerang fly and then exert a force of impact on my hand. That force of impact is approximately 5.625N (around 1.26lbs) when it impacts me. This was found by using m = 0.1kg (the boomerang's mass), v = 7.5m/s (the catching velocity), and t = 4/30s (the duration of impact) in the above equation.
Horizontal, Vertical and Total Velocity
Horizontal, Vertical and Total Velocity
Pick any vector in the 2D plane. At right, we have chosen such a vector 𝑎.
Let this vector represent the velocity of a particle 𝑝 also moving in the 2D plane. We can say that the total velocity of the particle is this vector — that is, vector 𝑎 is the total velocity of our particle 𝑝.
This is what we traditionally think about when we think of "velocity" — we have some thing (𝑝) moving in some direction at some speed (which constitutes 𝑎). This is essentially thinking of velocity in polar form, where 𝛳 is our direction and 𝑟 is our speed.
But, we can think of it in another way as well: Cartesian form. Any given velocity in a 2D plane has two components: horizontal velocity and vertical velocity. In our picture, the horizontal component of 𝑎 is 𝑎₁ and the vertical component of 𝑎 is 𝑎₂.
This Cartesian notation is usually more applicable — if we let 𝑠 be the position function of 𝑝, then the horizontal component of 𝑎 is ∂/∂𝑥 (𝑠) and the vertical component is ∂/∂𝑦 (𝑠).
When the boomerang is first thrown, it has a total velocity with magnitude (speed) of around 15m/s. Because it is thrown at a 10° angle upwards, its horizontal velocity is cos(10°) · 15m/s ≈ 14.8m/s and its vertical velocity is sin(10°) · 15m/s ≈ 2.6m/s. We can therefore say its total velocity is approximately the vector ⟨14.8m/s, 2.6m/s⟩, which (as expected) has magnitude 15m/s.
Our vector 𝑎
A polar vector. The tangent ( r̂) and the normal ( θ̂) should be ignored.
The sliced dowel.
Lift
Lift
Lift is the force exerted upwards on an object due to a downwards deflection of the fluid it exists in. (This leads to an important corollary — an object cannot have lift if there is no fluid around it.) A common (but incorrect!) belief is that lift is caused by Bernoulli's principle. Bernoulli's principle, in short, states that if a moving object has more surface area on one side than the other it will cause a low pressure region to form above the side with larger surface area. Breaking that down, we can imagine a dowel cut in half. This dowel has more surface area on top than on bottom — the curved side is clearly "longer" than the flat side. If we move this dowel through the air, what happens to the air molecules right in front of it? Well, they must either:
Go "the long way around": over the curved top
Go "the short way": straight across the flat bottom
Since air molecules don't have minds, they evenly split between these two options. But clearly, the ones going straight across will reach the other side first! The air molecules going around the top will end up having to go faster to cover the same horizontal distance, since they must go over the entire long curved surface. This is what causes a low-pressure region.
While this theory is completely correct, the misconception arises when people say that Bernoulli's principle causes lift. There is a difference in pressure over a commonly-shaped airfoil, but it is not the dominant force that causes the wing's lift! Instead, an almost simpler explanation exists: The airfoil is shaped in a way that "rotates" (deflects) the air fluid around the wing. Newton's third law tells us that every action results in an equal and opposite reaction — so if a wing deflects the air fluid down, the wing will get pushed up. This is the real cause of lift.
Lift is, of course, the main reason why a boomerang flies so interestingly. In the air, our boomerang had a lift of approximately 0.8221N (or around 0.18lbs). Detailed calculation steps for this can be found on the calculation doc, linked below — the basic principle used was finding the difference between the expected acceleration on the boomerang (9.8m/s²) and the actual acceleration the boomerang was experiencing in total.
Reflection
Reflection
Overall this project was generally successful. Our communication throughout the project was very prompt and precise, so we always knew exactly what to do and who would be doing it. We kept all our shared files in a neat folder hierarchy so that we could all see exactly what we had and what we needed. Additionally, our conscientious learning was very successful. We effectively set goals and timeframes, met them, and always ended up with what we wanted when we wanted it. Finally, our collaboration was strong. During the project, we properly divided up our tasks and made sure that everyone got a chance to help as much as they could. The case-in-point of this is our film: both Nicholas and I wanted to edit the film, so we decided to split up the editing half-and-half so that we all could participate.
As with before, however, this project was not entirely perfect. I feel like critical thinking (as a whole) could've been more of an emphasis with this project — it often seemed as though the goal of the project was to make the film, and the physics seemed to be secondary. I (personally) tried my best to work as many calculations into it as possible, but it felt like the calculations didn't really help solve any problem or achieve any goal ("math for math's sake"). Additionally, I feel like our presentation-side communication could've been slightly better — there were a few things in the video that, if I were to do the project again, I would've changed (such as making the point that the boomerang's lift isn't due to Bernoulli's principle rather than just stating it indirectly).
Although it had a few flaws, I think the project was mostly successful. We ended up with a fairly polished final product, and we had many group collaboration successes which I will remember for future reference.
Calculation Document
Calculation Document
PhySportsCalc.pdfPage updated
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