The Physics of an Elephant-Powered Slam Dunk

deflated basketball

What might be higher than crusing 30 ft by the air for a two-hand jam? Staying house and analyzing it!

You have been sheltering in place for weeks now, and you can actually use some extra enjoyable physics puzzles to resolve, am I proper? Don’t panic. All of the physics issues you’ll be able to think about are proper right here on the web—together with some you by no means may have imagined. Here is one you will not discover in any textbook:

  • A person with a basketball stands on one finish of a seesaw. An elephant stomps on the opposite finish. What occurs?

Properly, naturally, the man strikes by the air and over the elephant—then over one other elephant (as a result of the place there’s one pachyderm there’s most likely one other). Then he slam-dunks the ball by a hoop earlier than hitting a bale of hay. You may’t make these things up. Here is the video—critically, it’s a must to see this.

Are you considering what I am considering? That is simply begging for some physics evaluation. Let’s get began!

1. Is it actual?

Oh, this an amazing query. As you might have heard, there’s a number of pretend stuff on-line. To see if that is legit, we wish to analyze the movement and see if it follows primary physics fashions. For that, we have to get some information from the video. Utilizing the Tracker video evaluation app, I can discover the place of the man in every body of the video. Consider x,y coordinates—horizontal motion is within the x route, vertical within the y route.

So for an actual (not pretend) projectile human, there’s just one power performing on him after he leaves the flip board, and that’s the downward gravitational power (assuming a negligible air-resistance power). During which case, his trajectory ought to have the next options of normal projectile movement:

  • Fixed horizontal velocity
  • Fixed vertical acceleration
  • Vertical acceleration of –9.Eight m/s2 (close to Earth’s floor)

Usually, this is able to be simple to verify. I’d plot the horizontal place as a perform of time to see if it is a straight line, which might point out fixed velocity. I’d do the identical factor for the vertical place to point out that it is a parabola related to fixed downward acceleration. However that gained’t work right here, as a result of the video shifts to slow-motion within the center, so the time from one body to the subsequent isn’t fixed.

Don’t fret. I can repair this. As a substitute of plotting x vs. t and y vs. t, I’ll plot y vs. x—that is referred to as the trajectory plot, because it reveals the precise place of the man as he strikes by the air. Right here’s what I get:

That is the trajectory for the entire thing, together with the top the place he bounces off the hay bale and flips over. However simply trying on the center of the plot, it does certainly appear like a parabola. Tracker additionally match a quadratic equation to the info for me, and you may see from the stable curve above that it’s a great match. Listed here are the ensuing parameters:

Illustration: Rhett Allain

Does that imply it is actual? Not essentially. However it’s encouraging; if it did not have a parabolic form it might completely be pretend.

However let’s simply verify some stuff. A basic equation for the trajectory of any regular projectile movement appears like this (right here’s an previous submit the place I derive this equation):

Illustration: Rhett Allain

Word: x0 is the beginning horizontal place, which I set because the origin (x0 = 0), in order that goes away. θ is the launch angle. Now I can examine this with the fitted quadratic equation from the plot above. First, the coefficient on x, 1.447, equals the tangent of the launch angle, which provides us an angle of 55 levels. That appears about proper.

Illustration: Rhett Allain

From the coefficient on the x2 time period, –0.1816, I can discover the preliminary velocity v0 (assuming this elephant soar takes place on Earth, with a gravitational area of g = 9.Eight N/kg, which looks as if a secure wager).

Illustration: Rhett Allain

If you do not have a great really feel for velocities in meters per second, that is about 20 mph. That is a pleasant and affordable velocity. OK. I am fairly glad. I believe it is a actual video. Though this makes me a little bit anxious about this man. If he thinks leaping over two elephants is a good suggestion, what different crazy-dangerous stuff will he attempt?

Now for some extra homework questions. I will provide you with some hints, however I’m supplying you with an opportunity to reply these earlier than I come again to them sooner or later.

2. What are the acceleration and power through the launch?

Ignoring what occurs later, the launch itself might be harmful too. A large animal is exerting a big power on a puny human by the board. Are you able to estimate the power that the board exerts on the man through the launch? Additionally, discover the acceleration through the launch part (so you will not have to know the precise mass of the dude). Will probably be helpful to search out the acceleration in items of g’s, the place 1 g = 9.Eight m/s2. So you understand, a human can stand up to round 20 g’s with out severe harm. My guess is that this motion is lower than 20 g’s.

One trace: Throughout the launch movement, he strikes slightly below 2 meters. It is most likely higher to make use of distance fairly than time when calculating the (common) power and acceleration.

3. What are the acceleration and power on the touchdown?

That is mainly the identical query, however on the opposite finish. So how a few twist? What if he landed solely on the bale of hay? What would his touchdown acceleration be if his middle of mass moved 60 centimeters through the touchdown part? This distance would come with the movement of his legs bending and the compression of the hay. In fact, within the video, the hay would not totally cease him, however as a substitute simply slows him down a little bit. That is a wise transfer.

4. Estimate the elephant energy.

When the elephant pushes down on the launching board, discover the ability enter. You may wish to calculate the power from the elephant pushing down (that’s non-compulsory). However even with out that, you’ll be able to nonetheless calculate the ability. Belief me. Oh, what’s the energy of an elephant in horsepower, the place 1 hp = 746 watts? Sure, the one motive for this query is to arrange elephant energy as a unit of measure.

5. Right for the slow-motion section.

Clearly the center of the video is in gradual movement. This implies the playback body fee is just not the identical as the true time in between frames. So, what’s the playback velocity for this video? Let me give a fast instance so that you perceive what is going on on right here. Suppose the conventional playback fee is 30 frames per second. If this was in gradual movement at half velocity, it might play at 15 fps—however every body would nonetheless characterize 1/30th of a second in actual time.

So, what’s the playback velocity in the course of the video? If you’d like a bonus problem, see when you can edit the video to make the movement in actual time.

6. How a lot margin of error was there?

I’ve already estimated the launch velocity at 9.14 m/s at an angle of about 55.35° in order that the dude lands on the hay. However it’s fairly a small goal. What if his preliminary velocity or angle are off by just a bit bit? What sort of variation within the preliminary situations can this man have and nonetheless hit the goal? Is there a number of “wiggle” room, or does he must be tremendous correct to keep away from a painful crash into the bottom?

I do not know. Perhaps that’s why the opposite elephant was there—to avoid wasting him if he missed.

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About Rhett Allain

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