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to a rocket and a box of Mentos creating a pulley system. (Pulley as a Machine in that as the string was connected to a pulley system, in that ...

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and assume the pulley to be massless

Physics Puzzle: Famous Mechanics “Paradoxes”

Level of Difficulty: Highschool

I probably won’t get around to updating this blog for the next couple of days, so I’m leaving you with four puzzles in one. Here are four “paradoxes” portraying seemingly impossible scenarios. Can you explain them or reason what will happen?

A common argument made by freshmen goes like this: to walk your feet must exert a force F (due to friction) on the surface you’re on; but according to Newton’s third law, the surface should exert a force equal in magnitude and opposite in direction. The two forces should sum to zero, so how is it possible for you to move? A lazy sailor decides to propel his boat by tying a sail and using a fan to blow on it. Practical considerations aside, is this idea sheer nonsense or will his ship actually move forward? A guy is standing on a platform. The platform is connected to a rope which goes through a pulley. The guy is holding the other end of the rope in his hand. The platform isn’t attached to anything except the rope. Will the guy be able to pull himself up by pulling on the rope, or will Newton’s third law prevent this from happening? Assume the rope and pulley are massless. Neglect friction.

I can get the first two, at least.

1. You can’t add these two forces, because they are acting on different objects. The normal force exerted on you by the surface keeps you from falling through the floor and allows you to walk.

2. It won’t work. The fan exerts a force forward on the air, which (by Newton’s 3rd law) exerts a force backward on the fan, which is attached to the boat. If the sail weren’t there, the boat would move backward. When the sail is added to catch the air, the air exerts a forward force on the sail (which is also attached to the boat), which, under ideal circumstances, would be identical to the force exerted on the air by the fan. Thus, the forces on the boat would cancel out, and it would not move.

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