In physics exams, there are always some questions that despite being straightforward can leave us baffled. One of the most notorious in recent years is a 2014 qualifying exam question for the US Physics Team because almost no one could agree on the answer. Many continue to disagree with the solution provided by the American Association of Physics Teachers so Derek Muller, the mind behind the YouTube channel Veritasium, set out to demonstrate the correct answer once and for all.
To do that, he took to the sky because the hypothetical question calls for a helicopter and a rope and frankly Muller runs a very successful YouTube channel so he can rent a helicopter. (Muller is no stranger to going to extremes to prove physics.)
“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,” the question reads. "Which of the following diagrams best shows the shape of the cable as the helicopter flies through the air to the right?"
The exam takers were given five diagrams from which to pick.
This question has proven contentious among physicists, students, and science enthusiasts. In his new video, which has already had 4 million views, Muller talked to the author of the question, Professor Paul Stanley, who noted how many people after taking the exam built their own version of the hypothetical scenario to prove their answer (or what they considered to be the correct answer).
A poll run on Veritasium’s channel shows hardly an agreement on which is the correct diagram, although diagram C is the one favored by most people, followed by B, and then D.
Do you have your answer yet? If not, now is your chance to do so as we'll give a full explanation after the video.
The answer from the exam and demonstrated by Muller is B. The question is all about forces and so we need to look at what the rope is experiencing. It has a weight, it has a tension being attached to the helicopter, and since the helicopter is moving at constant velocity, it's experiencing air resistance.
If the rope is divided into little segments, each will have a certain weight and experience the same air resistance, which is comparable to the weight of the rope. The segment at the bottom has little tension given its little weight. As we move up the rope the tension increases, reaching a maximum at the top.
But the direction of this tension and the direction of the rope doesn’t change because the weight is pulling the rope down and the air resistance is pulling the rope across, so their ratio stays the same. Changing the constant speed of the helicopter would change the strength of the air resistance and the direction of the rope but not its overall shape.
Muller loves going that little bit further however with these experiments and in the video actually reproduces the original version of the question (not used in the exam) that had a weight attached to the bottom of the rope. What do you think will happen to the rope in that case?
The shape changes as you would expect for little air resistance on the weight. And the right answer, in that case, is the shape marked as D.