Physical Puzzles

The following puzzles are not simply tests of logic or calculating ability. They all require some level of physical insight or intuition. Detailed knowledge of physics is not necessary, but an appreciation of underlying physical principles will be a great help.

1. Hot Metal

If an iron torus (dounut / innertube shape) is heated uniformly, does the diameter of hole in the middle get bigger, smaller, or stay the same?

Image of a Torus

2. Bathtime Teaser

Little Jimmy is playing with a toy boat in the bath. It is floating in the water with a cargo of a wine cork and a metal bolt (Jimmy's family was not a rich one). Jimmy takes the cork out of the boat and is intrigued to see that it too floats in the water. He then takes the bolt out at watches it sink quickly to the bottom. Your problem is about what happens to the level of the bath water during Jimmy's experimenting. How does the water level at the beginning (cork and bolt in boat in bath), compared to that half way though (cork in bath, bolt in boat in bath), and that at the end (bolt and cork in bath, boat still floating in bath)?

3. Backwards and Forwards

Take a normal bicycle with stabilizers to keep it upright without being held. Now arrange the pedals so that the cranks are vertical, and tie a piece of string on to the lower pedal. If this string is now pulled backwards from the rear of the bicycle, which way does bike move?

4. In the Shadows

You are walking along pavement late at night, but luckily it is fitted with street-lamps at regular intervals. You are walking at a constant velocity and passing directly under each lamp. You notice that as you pass under a lamp, the end of your shadow starts off behind you, and then overtakes you as you walk. But what happens to it's velocity? Does it get faster, slower, or stay the same as you pass under the lamp?

5. Nailing It

You have a mass atached to a loop of light frictionless string, and there are two nails in a vertical wall. If you loop the string once over one nail then the mass will be suspended and if that nail is removed then it will fall. If you loop the string simply over the top of both nails, then the mass will be suspended, but if you remove either nail, the mass may fall a short distance, but will remain suspended on the other nail. Your task is to find a way to pass the string around the two nails so that the mass is suspended securely, but if either one of the two nails is removed, then it will fall.

As an extension can you do the same for three nails (i.e. the string is wrapped round the three nails in some way such that is is securely suspended, but is any signle nail is removed the mass will fall to the floor)? What about four, five, six, ... n nails?