expfrictionFind a smooth, cylindrical support column, such as those used to support open-air roofs for breezeways and outdoor hallways (check your local public school or local church). Wind a length of rope one time around the column, and pull on one end while three friends pull on the other in a tug-of-war fashion.

Experiment with the number of friends and the number of winds around the column. Can you hold your end with just two fingers against an entire team of football players? You bet!

[am4show have='p8;p9;p11;p38;p92;' guest_error='Guest error message' user_error='User error message' ] Here's what you need:

  • nylon long rope (10 feet or longer)
  • column or pillar (as talked about in the video)
  • at least two people, but more is better
What’s going on? This is a great example of what “exponential growth” truly means. There is friction between the rope and the support column – you can feel it as you tug on the rope. With every additional turn around the pole, the amount of friction increases (exponentially grows), until it skyrockets so much the rope feels as if it’s welded to the pole.

Download Student Worksheet & Exercises

Einstein himself stated that “exponential growth” was the eighth wonder of the world! Exercises 
  1. How much money would you earn on Day 20 if I gave you one penny on Day 1, and doubled it every day after so Day 2 you received 2 pennies, and Day 3 you got 4 pennies?
  2.  Why do you think this experiment with friction works? Does it work with a flat surface the same way as a curved surface?
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Comments

9 Responses to “Exponential Friction”

  1. Thanks for writing! I totally understand your thinking, and this science excerpt actually came from a college physics class I taught about friction and mechanics called the Euler-Eytelwein (or the Capstan) equation, which has the term “e” in it for exponential. You can read about it here. – it’s used for calculating the friction of belts around pulleys, etc. Here’s a more plain-English explanation of how it works.

    The Euler-Eytelwein equation relates the tension of two ends of a rope like this: T2 = T1 eμθ, where T2 is the tension in the rope due to the load, T1 is the tension you need to hold the load, μ is the coefficient of friction between the rope and the thing you’re wrapping around, and θ is the angle made by all the rope windings (measured in radians, so one full winding is 2∏ radians).

    Hope this helps – and I appreciate your sharing feedback – sometimes I do make mistakes and it’s important to correct those!

    Aurora

  2. Aurora,
    I believe the increase in friction from aditional wraps around the pole is in fact less than linear, not exponential. The available normal force is not multiplied by wrapping, the coeffficient of friction is constant, only the area increases. In fact as friction reduces tension in the rope for successive wraps, normal force decreases. It is a very effective trick for anchoring or controlling a load, I use it often in rigging. But NOT “exponential”, a mathematical term of specific meaning.

  3. I got my nylon rope at the hardware store.

  4. Yes as long as it’s not too slippery!

  5. Adilah Muhammad says:

    can it be nylon cord?

  6. Adilah Muhammad says:

    were can i find cheap nylon rope

  7. Mary Silvernagel says:

    It should have stated, the rope getting smaller (tighter) “rather” than friction. oops.

  8. Cool! Glad you enjoyed the experiment! I wasn’t sure what you meant by “rope getting smaller than friction…” so if you still have a question about this experiment, can you clarify a little more so I can help?

  9. Mary Silvernagel says:

    Hi! After we did this experiment, we wondered if it was more the loop in the rope getting smaller than friction. We repeated this experiment with a smooth metal rod to reduce friction and found that it is definitely friction. Really nifty way to understand exponential friction. Thanks, Alex and Evan