5. Puzzle Series [#4, #5, #6, #7]

See this post for the explanation of the ‘puzzle series’ posts. This time the puzzles are physics puzzles. If you are a physics, math, or engineering undergrad student, I encourage you to solve these puzzles right away.

Puzzle #4. The Bicycle Pulling

Consider a normal bicycle with wheels that do not slip and only rotate on the ground. You tie a rope to the bottom pedal, and pull it backward. Will the bicycle move forward or backward? Explain why.

Fig. 5.1) Pulling a rope attached to the bottom pedal of a bicycle.

Puzzle #5. Breaking A Chalk

Take a cylindrical chalk and break it with twisting. The fracture pattern will be a 45 degrees helix. Explain why.

Puzzle #6. Train & Rails

Trains are really stable on top of the rails, and they turn without any problem, although the wheels are attached together with no differential system. How is this possible? Remember that the flanges on the wheels are for severe cases and are only there for safety.
Hint: This is an engineering problem, you need to come up with a solution. Imagine that it is thousands of years ago and you want to have a rail transportation. Think about how you can play with the shape of the wheels. If you couldn’t come up with a solution, check this figure and explain why it works.

Puzzle #7. Catching Blindly

Consider this game that you wanna catch your friend in a really big pool. You swim with velocity u and your friend swims with velocity v, and we know v < u. You see your friend at a point P, which is at distance L from you. Now the referee blindfolds you. Assume your friend is gonna start swimming on a straight line away from point P with his max velocity v. You have no idea which direction though. Plan a path that you can take and be sure that you will catch your friend at some point.

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