Can you solve the helicopter riddle?

Key Concepts

• Air Friction (Drag): The force exerted by the air on a moving object, opposing its motion. In this problem, it is explicitly stated as "not negligible."
• Uniform Cable: A cable with constant mass per unit length.
• Constant Velocity: The helicopter is flying at a constant speed in a straight line, meaning there is no acceleration. This implies that the net forces acting on any segment of the cable are in equilibrium.
• Forces in Equilibrium: When an object moves at a constant velocity, the vector sum of all forces acting on it is zero. The relevant forces on any segment of the cable are gravity, air drag, and tension.

The Physics Problem

The summary addresses a specific physics problem presented as Question 19 on the 2014 qualifying exam for the US physics team.

• Scenario: A helicopter is in horizontal flight at a constant speed. A perfectly flexible and uniform cable hangs beneath it.
• Critical Condition: Air friction on the cable is a significant factor and cannot be ignored.
• The Question: The problem asks to identify the correct shape of the cable from five possible diagrams as the helicopter flies to the right. The options were:
  • A: Hanging straight down.
  • B: Hanging in a straight diagonal line to the left.
  • C: A "hook shape."
  • D: An "inverted hook shape."
  • E: An "S-bend" shape.
• Context: The video notes that the correct answer to this question has been a subject of some controversy.

The Real-World Experiment

To definitively solve the problem and end the controversy, a real-world experiment was conducted using a helicopter.

• Objective: To observe the actual shape of a cable suspended from a helicopter in flight.
• Equipment:
  • Vehicle: A helicopter.
  • Cable: A "battle rope," typically used in gyms, was used as the flexible, uniform cable.
  • Rope Specifications: The rope was approximately 15 meters long and weighed 20 kilograms.
• Methodology and Safety:
  • The rope was deployed from the side of the helicopter.
  • To ensure safety and prevent the rope from interfering with the helicopter's rotors, the pilot, named Craig, kept the rope on the right side of the aircraft.
  • Consequently, the helicopter's motion was not straight forward but "diagonally forward and to the left" to maintain visual contact with the rope.

Experimental Observation and Result

The experiment provided a clear visual answer to the physics problem.

• Observation: As the helicopter flew, the deployed battle rope was observed to form a straight diagonal line. Relative to the helicopter's forward motion, the rope angled backward and downward.
• Significant Statement: The narrator observes, "you can clearly see the rope is hanging straight diagonally to the left. That's a pretty good diagonal, man."
• Conclusion: The observed shape directly matched one of the provided options in the exam question.

Conclusion and Final Answer

The experiment successfully validated one of the theoretical answers, resolving the debate surrounding the question.

• Main Takeaway: The experiment demonstrated that for a uniform cable subject to gravity and significant air drag while moving at a constant velocity, the cable maintains a straight, diagonal shape. Each segment of the cable is in equilibrium under the forces of tension from above, its own weight (gravity), air drag, and tension from below. The combination of a constant downward gravitational force and a constant backward drag force on each unit length results in a constant angle for the cable.
• The Correct Answer: Based on the direct visual evidence from the flight, the correct answer to the question is B.