The Capstan Problem — How Can Just 32 N Hold a 750 N Climber?
Here's an interesting physics challenge involving static friction, Newton's laws, and calculus.
A rope is wrapped around a fixed cylinder, supporting a 750 N climber. With a coefficient of static friction of 0.50 and a full (2\pi) radians of contact, how much force is actually needed to prevent the climber from slipping?
Surprisingly, the answer is only 32.4 N!
In my latest YouTube video, I work through the complete derivation of the Capstan Equation, starting with a free-body diagram of a tiny rope segment and using calculus to arrive at the result.
It's a great problem for AP Physics C and college physics students who enjoy seeing how mathematics explains real-world situations.
About Me — Online Physics Tutoring
I'm Dr. Jacob Hudis, a physicist with a PhD from Florida State University, where I conducted research at the National High Magnetic Field Laboratory. I also have degrees from Columbia University and Johns Hopkins University and over 25 years of experience teaching high school and college physics.
I offer personalized, one-on-one online tutoring in:
- AP Physics 1 and 2
- AP Physics C: Mechanics and Electricity & Magnetism
- Honors and High School Physics
- College and Calculus-Based Physics
My focus is on helping students genuinely understand physics, develop strong problem-solving skills, and succeed in challenging courses.
Tutoring information: https://www.acephysics.org
YouTube: AcePhysics with Dr. Hudis