Physics Puzzle: the Climber’s Free Lunch
June 24th, 2009
| Categories: Mechanics, Physics Puzzles
Level of Difficulty: Highschool
A guy has to climb up a rope (left). He gets an idea: tie the rope around himself and put it through a pulley (right). Now by pulling on the rope, he reasons, he’ll get pulled up by two ropes instead of one - hence by twice the force, making it twice as easy to climb up. Is he correct or is there a fallacy? If not, how can you explain this “free lunch” - doubling the force without “paying” for it? Treat the rope and pulley as massless. Neglect friction.
EDITED, 25/June/2009: hats off to our reader Mike for his solution in the comments section. I’ve added a more detailed solution, which you can view here.
For every inch he pulls his hands up the rope without the pulley, he is moving his whole body one inch from the ground. For every inch he moves his hand relative to the rope with the pulley, he is moving his body only 1/2″ from the ground (1/2″ on the hand side of the pulley and 1/2″ on the body side of the pulley). He is doing half as much work with that i” pull, but will take twice as many pulls t get to the top. A pulley does not let you do less work. It only distributes the work over more time, so that less effort, but more time, is required to do it.
Correct. That has to be the quickest response to a post ever on this blog :).
I’d just be careful with the term “work”, since work in the physical sense (the integral of the force over the distance) is unaffected by the use of pulleys (this can also be deduced via thermodynamic reasoning).
I’ll post a detailed solution tomorrow.