In 2014, the qualifying
exam for the US Physics Team had this as question 19: A helicopter is flying
horizontally at constant speed. A perfectly flexible
uniform cable is suspended beneath the helicopter. Air friction on the
cable is not negligible. So, which of the following diagrams best shows the shape of the cable as the helicopter flies
through the air to the right? Is it A. hanging straight down. B, hanging diagonally to the left? C, this hook shape. D, the inverted hook shape, or E, a kind of S bend. Now, apparently there's been a
certain amount of controversy about the correct answer to this question. So, today we're gonna go
up in this helicopter, and put this question to
rest once and for all. Let's go. (intense music)
(helicopter blades whirring) A portion of this video was
sponsored by SimpliSafe, which allowed us to rent this helicopter. More about them at the end of the show. I've got several thousand
hours of carrying sling loads, fire buckets, concrete buckets, doing power line construction,
actual power poles. You name it, anything
that needs to be moved around the mountains, I've done. Biggest concern that I have is that the rope's gonna
interact with the rotor wash as its interaction with the
ambient air around the aircraft. And we'll get a whipping
action that falls down the rope and flips around on the end. To a point that we worry
if it will have a tendency to work its way back up
towards the aircraft. Obviously, we don't want
it getting in the rotors or the tail rotor. (helicopter blades whirring) - [Derek] Alright, we're all set. Movin' up. (helicopter blades whirring) (intense music) Here I'm deploying a battle rope, like you'd see at the gym. This one is about 15 meters
long and it weighs 20 kilograms. - [Craig] See, the
whipping action's begun. - [Derek] I see it. So, if we go really
slow, will we avoid that? - We'll see. We'll see where the rotor wash stops interacting with the rope and the ambient wind. Now the setup looks pretty simple, but few people agree on what
the right answer should be. (peaceful music) When I polled YouTube, the
most common answer was C. Well done on making that
beautiful bell curve by the way. We got in touch with
the question's author, professor Paul Stanley. There was some creative students
who actually constructed their own homemade scenarios. One had a fan to the side and
another fan blowing downward so that they could mimic
the motion of the helicopter and suspended a string and
said, "Oh, it's this design." And the faculty members
looked at it and said, "Oh, obviously I can prove that
the answer is this answer." They just didn't agree with each other. - If we approximated as
a chain of rigid links - I don't think you can just do that. - What do you think? - I think you're more likely to be C. - I think it is D. - D. - My guess is B. - What do you think?
- B. - B? - Imma go with A. - Interestingly, no one chose E. Have you locked in your prediction? (helicopter blades whirring) To make sure the rope doesn't come up into the rotors of the helicopter, pilot Craig wanted to keep
the rope on our right side so he could keep an eye on it. Looks pretty good. - I'm trying to make it look good. I mean I'm really working on it. - You're working hard. So, we're not going straight forward. We're actually going diagonally
forward and to the left. (upbeat music)
(helicopter blades whirring) But you can clearly see the
rope is hanging straight, diagonally to the left. That's a pretty good diagonal, man. So, the correct answer
to the question is B. You wanna pull it in? - Up it comes. - [Derek] We're going to
try a few more experiments, adding a weight to the end of
the rope and then a parachute. But first I want to discuss
why the answer is B. There are two external
forces acting on the rope, gravity pulling it down and
air resistance to the left. When flying along at constant speed, these forces must be perfectly balanced by the tension in the rope. Now, when I set out to do this experiment, I wondered if the rope would be affected by the air pushed down
by the helicopters rotor, but judging by our results. This was not the case. - The rotor wash doesn't extend
down below the helicopter, all that far. It
dissipates pretty quickly. - So, you can consider the
air resistance on the rope as entirely due to its
motion through still air. Imagine dividing the rope
up into many short sections. Each section has the same weight and experiences the same
amount of air resistance because it has the same
cross-sectional area. And it's moving at the same speed. Now, the tension in
any section of the rope must balance the sum of the air resistance and weight of all the sections beneath it. So, the tension is zero
at the bottom of the rope, and it increases linearly
up to a maximum at the top. You can see the tension is
small at the bottom of the rope, and that's why it wiggles around while the top is much steadier. Now, although the magnitude
of tension changes throughout the rope,
it's direction doesn't. And that's because the
ratio of air resistance to weight is the same at
every point along the rope. That is why a uniform flexible cable hangs in a straight diagonal line
when pulled at constant speed by a helicopter. If the helicopter flies faster, the angle of the rope changes, but it still makes a
diagonal straight line because the ratio of
air resistance to weight is still constant along the
entire length of the rope. But this got me wondering, "What would happen if we added a weight to the end of the rope?" Here, I have a 20 pound, that's an eight or nine kilos kettlebell. And I want to ask you
to make a prediction. What shape do you think
the rope will make now? Will it still be that diagonal, or will it be one of
the other five options? One more question for you. If we chucked a weight at the bottom, which shape would it be? - Oh.
- Probably D. - B, or possibly C. - [Derek] Does that change it? - Then I think it would be B. (whimsical music) - Easy to do on the ground. (helicopter blades whirring) Alright, we're dropping
the rope over the side. This one has 20 pound
kettlebell off the end of it. How's that feel when it's dangling? - No lateral displacement at all. - Alright. - How's your forearms doing? - I'm feeling good, you know. I feel like this is the
easy way, obviously. Gonna feel different
when I gotta pull it up. - Okay, is it down?
- Yup. Okay, let's give it a shot. (whimsical music)
(helicopter blades whirring) Here the helicopter is flying at nearly a hundred kilometers per hour, and the rope makes a different shape. You can clearly see, it looks like an inverted J. This is option D. In fact, this is how the question on the qualifying exam originated. - So, I taught for a
semester in Hong Kong, and we'd go hiking in the new territories. One of the times I was hiking, I saw a helicopter fly
with a cable beneath it. It was carrying something
to one of the remote parts of the Hong Kong new territories. And I saw the shape of the
cable and thought to myself, "That looks a little counter
intuitive and very neat. This might make a good
multiple choice question for the selection exam for the students." The cable that I saw had a
weight hanging on the end, which gave it a certain curved shape. When I shared this with the
other coaches, another coach, Andrew Linn, looked at it and said, "I think the question
might even be more fun if there is no weight on the cable because that is even harder to imagine." - [Derek] To understand why
the rope makes this shape, we can use the same analysis as before. But now we need to add a large weight to the end of the rope. And this means at the bottom, the tension needs to be almost vertical to support the weight of the kettlebell, which has a lot of weight
but not much air resistance. As you go up the rope, the
ratio of total air resistance to weight for everything
beneath increases. So, the rope turns more horizontal
in order for the tension to balance out that
increasing air resistance. - You're more than halfway. You got it. (woman laughing) - [Derek] For the final test, I wanted to add something
to the bottom of the rope that added almost no weight,
but significant air resistance. So, I picked a Veritasium flag, of course. So, what do you think about hanging this at the end of the rope? - Well, it's all science experiment for me 'cause these are all the
things you'd never do with a helicopter in a row. - What would it be the real risks, like tail rotor or this rotor, or both? - Either. Any kind of this getting
into the inner tail rotor would be destruction to the aircraft. (helicopter blades whirring)
(intense music) And we'll start, here we go. - [Derek] Now the rope still
seems to be pretty straight. I think it's because the flag isn't actually adding much drag. Still looks pretty crazy, interestingly. So, we decided to add a small parachute to the end of the rope. All right, let's try it. The concern here was that the parachute could get flipped up into
the rotors during deployment. So, we bundled the shoot
up into a backpack. - [Craig] Very nicely done. - [Derek] Does it deploy more than that? - [Craig] No, but once we start moving, its gonna grab a lot of air. - [Derek] Now, with the
parachute at the end of the rope, it makes a J shape, which is answer C. With extra air resistance
at the end of the rope, but not much weight, the tension has to be
virtually horizontal. And then as you go up the rope, the ratio of total air
resistance to weight for everything beneath decreases. So, the rope becomes more vertical to balance out the increasing weight. So, depending on what's
on the end of the rope, you could get answers B, C or D. Now, if you enjoyed this video, I bet you would also like my
bullet block experiment series. So, check it out. (retro beeping sound effect) Now, hanging out the side of a helicopter was not my safest moment, but I do always feel safe here at home. Thanks to SimpliSafe, the
sponsor of this portion of the video. SimpliSafe is an easy to use, totally customizable home security system. They allow you to design a
set up to fit your space, and they ship it directly
to your doorstep. Then their interactive
monitoring service ensures that your home is
professionally monitored 24/7. You know, I started thinking
seriously about home security when there was a police
helicopter circling overhead one day, and it was
not dangling any ropes. It turned out the house across the street had been broken into. Luckily, SimpliSafe makes it
easy to protect your home. They sent me a kit that took
only about an hour to set up. I currently use the
simply safe base station, the cameras and sensors to keep tabs on what's going on around my house. I also installed their new
wireless outdoor security camera, which doesn't require an outlet. So, you can set it up literally anywhere. This camera has eight times
zoom, color night vision, and two-way audio. So, you can speak to
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of communication open for the most protective service. Visit simplisafe.com/veritasium
to learn more and get at least 30% off your
SimpliSafe security system. I want to thank SimpliSafe
for sponsoring this portion of the video. And I want to thank you for watching.
This is the third Veritasium video this year on an old USA Physics Olympiad question, and for good reason: they're mathematically elementary, but designed to stretch your intuition.
I fondly remember participating in high school, back in 2012 and 2013. When I returned as a junior coach in 2015, I bragged that I was obviously qualified, since I could easily get perfect scores on the qualifying round. They sprung this 2014 problem on me. I went with my gut and got it wrong, and they still won't let me live it down!
There was quite a lot of excitement about this question at the time. Apparently, the coaching staff was buried in emails from students, teachers, and retired engineers.
If you're a high school student who wants to see more problems like these, you can check out our website for all previous exams. Also, consider registering for the upcoming 2022 exam! We try to keep the questions fresh, interesting, and accessible.
I see this exact scenario 8 hours a day flying avalanche fence construction materials up to the peaks in the Alps.
Didn't somebody just post this question and the top comment said the answer was C??? I thought it was B! I'm not even a physicist! I need to go back to college.
Anyone thinking of the catenary equation??
From the video, the correct answer seems to rely on the wash from the helicopter's rotor not extending below the helicopter. Which is surprising to me, I would have expected it to go fairly far down.
But yet the rotor wash is great at raking leaves
Stupid question because an average person would assume the wash would have a greater effect.
Ive got an equally interesting question too and am hoping someone could answer and explain to me what happens to a bicycle when you cycle without hands and have a significant weight (for eg. 5kg) hanging in excess on the left handlebar as compared to the right. Will the bicycle, while moving, tilt left or right? Also do consider that the bicycle is moving because I am physically riding it, truly many complex factors at play here but you can simplify it if you wish too
Answer is obvious (if you can tell that its a trick question) but could someone explain pleasee
I'm really confused by this video. I would of thought intuitively that air resistance would have nothing to do with it and the two biggest forces are just gravity and something like a pulling force from the helicopters movement or something creating a diagonal, rather than air resistance playing such a large role. Could someone explain what the shape would be if this sort of experiment was done in space (but still experiencing gravity but no air)? I would of thought because the vehicle is moving horizontally but gravity is vertical it would of been the same diagonal shape even without air resistance. Very confusing lol.