Bicycle answer *LINK*
Alex Y
Ed may have gotten this one-his comment about gearing was on target.
The surprising answer is that the bicycle will move backwards. And not only that, it will move backwards (at least initially) FASTER THAN YOU ARE PULLING THE ROPE!
The reason this seems so counter-intuitive, is that we naturally think of the forces applied to the pedal from the perspective of the bike rider, with the rider applying that force. Two things are different in this puzzle: The force is applied from the outside, and while the pedal moves backward with respect to the bike at the bottom, it is still moving forward w.r.t. the road surface.
Below is a video showing the resulting motion, which looks just plain weird-as if he is pushing the pedal with the string.
The physics is actually pretty straight-forward.
Some assumptions about the bike (designed to make calculations easy, but not too far off a real case):
Crank length: 8"
Wheel diameter: 24"
Front sprocket: 40 teeth
Rear sprocket: 20 teeth
There will be two forces acting on the bike, the string trying to pull it backwards and the rear tire trying to push it forward.
Now assume you apply a 12-lb force pulling backward on the bike at the bottom pedal.
That will apply a 96 in-lb torque to the crank axle.
The chain going over the two sprockets will double the rotational speed while cutting the torque in half, to 48 in-lbs.
Applying that torque to the axle of the wheel gives us 4 lb of force applied to the road 12" from the axle center, trying to move the bike forward.
The net then, is a 8 lb force moving the bike backwards.
Now consider the work done, which is preserved (ignoring friction losses); Pulling the string 4" with 12 lbs of force is 48 inch-pounds of work. But we know that only 8 pounds of force was working on the bike, so it had to have moved 6" to "use up" that 48 inch pounds of energy.
And I don't know about you, but that is the kind of physics 101 argument that always had me shaking my head and saying "something must be wrong with that--my intuition tells me it can't be right".
But it is! Watch this. At the end, he does show how a mountain bike with a super-low climbing gear would move forward when you pull the string.
You tube video on bike puzzle