1. You are given an arbitrary rigid object (say, a statue of the head of Elvis ) and asked to determine/estimate the position of its center of mass without doing any calculations. You can perform any simple experiment you’d like. Can you do it? Can you do it in under 30 seconds?
2. You can balance a broom horizontally on your finger by placing its center of mass right on your finger. Suppose you’ve done that. Is the part of the broom to the right of your finger equal in weight to the part that’s on the left? If so, why? If not, give a counterexample.

As always - good luck & have fun!

If you stand in front of the mirror with a shirt that has something written on it, you will see it “inverted” (left-to-right becomes right-to-left). Informally, we can say that a mirror inverts left and right. However, note that up & down are not inverted! That is, you do not appear “upside-down”. Why is this so? What is so special about left & right?

Good luck & have fun!

I’ve been writing this blog for quite a while now (almost half a year). It has been an enjoyable experience, but it seems a bit lonely sometimes, as only a brave few have attempted to solve the puzzles I’ve put on the site.

Basically, I’d like to ask you, my readers - if there are any out there - for two things:

• First of all, if you’re here, just drop a comment. I know some people may be shy to answer the puzzles, or don’t have time/strength, or simply don’t know the answers, which is just fine. But I’m just curious as to how many interested readers are there out there. So, if you’re one, just say hi in the comments :).
• Any suggestions & criticisms you might have would be welcome. Too many puzzles? Too few? Too hard? Too easy? Badly worded? Diagrams not clear? Solutions not clear? Would you rather see something else? Change the format somehow? Let me (and everyone else) know - leave a comment!

That’s it. Your feedback is very much appreciated.

Quite a few physics puzzles ask you to find the equivalent resistor of a given network - a particularly famous one is finding the equivalent resistor between two opposite corners of a cube having a resistor R on each of its edges.

This puzzle is even trickier: can you find the equivalent resistance between points A & B in the following (infinite!) network?

All resistors have the same resistance (say, R), and - as mentioned - the network is infinite in all directions.

Good luck & have fun!

ADDED 03/May/2008: I’ve added a solution. To read it, just view the comments (it’s comment #3).

Of all of physics, mechanics is my favorite subject (followed by electromagnetism). It’s the easiest to grasp, because it deals with daily phenomena, but the problems can be very challenging. As a service to the aspiring physics undergraduate and graduate student, here is a list of my top 5 mechanics textbooks.

1. An Introduction to Mechanics / Kleppner & Kolenkow. This is THE book on Newtonian dynamics, aka F=ma. It goes into great detail, despite being for undergraduates, and provides ample intuition without shunning away from the mathematics. Its greatest feature is the abundance of solved problems - just great pedagogy. The problems at the end of the chapters are hard. If you can solve all of them, then you really know mechanics. Really.
2. Introductory Classical Mechanics,  with Problems and Solutions  / David Morin.  A much more recent book. Much like Kleppner and Kolenkow’s book, it grew out of a course on Newtonian mechanics given to outstanding freshmen, this time at Harvard. It goes into great detail and is very complete, but its true strength lies in the exhaustive problem sets at the end of each chapter, which come complete with solutions. Many of the problems are very interesting and challenging. I highly recommend this text.
3. Mechanics / Lev Landau. The first of Landau’s set of books about Lagrangian & Hamiltonian dynamics. Landau, may he rest in peace, was a true mathematical physicist, and it shows in his writings. I’m not too fond of his books, but this one is an exception. It’s very thin and lean, but it goes straight to the heart of the matter and covers an astounding amount of material compared to its ~ 150 pages. If you have to get just one book on advanced mechanics, get this one. Don’t get Goldstein.
4. Problems and Solution on Mechanics / Yung-Kuo Li. Not strictly a mechanics book, but rather a collection of problems with solutions. Everybody knows that to master mechanics you need to practice, practice, and practice some more, and this book is ideal for the job, with plenty of non-trivial and interesting problems with detailed solutions.
5. Symmetry in Mechanics – a Gentle Introduction/ Stephanie Frank Singer. Once again, not strictly a mechanics textbook, but rather one that uses a famous problem from mechanics – the two body problem – to illustrate how modern concepts from mathematical physics, such as differential forms and lie groups, can be incorporated into the framework of mechanics. This is how advanced mechanics will be taught in the future (let’s hope!).  A great place to get intuition about these things.

The inside of the bulb is kept at a perfect vacuum. Here’s the riddle: what will happen when the radiometer is placed in direct sunlight?

Scientist X argues that the plates will rotate clockwise, i.e., the silver side of the plates will face the positive rotation angle, because the black side will absorb photons, and hence momentum from light, which will “push it forwards”, like blowing wind on it.

Is scientist X correct?

What will happen as air is slowly (slowly!) let into the vacuum?

Good luck & enjoy!

An ideal gas of temperature T1 is stored in a container with walls at a fixed temperature T2. Will the pressure exerted by the gas on the container’s walls depend on T2? If not, why? If yes, will it be greater when T1>T2 or when T2>T1?

Good luck & enjoy!

This week’s puzzle is about finding the maximal sum of a vector. Suppose you are given a vector (x(1),x(2),x(3),….,x(N)) of numbers, which can be positive or negative (or zero). You’re interesting in finding the vector’s maximal sum, meaning: starting out from an index i and ending at an index j, you want the sum of x(i)+x(i+1)+….+x(j) to be maximal.

 What is the fastest algorithm you can devise for this? Can you find an algorithm log-linear in N? Can you find anything faster?

This would be an easy puzzle if the x(i)s were all positive numbers: then you’d just sum all of them!

X = (5,9,1,20,4)  –>  maximal sum = 5+9+1+20+4.

However, when you introduce negative numbers into the game, it complicates things significantly:

X = (5,9,1,-20,4)  –> 5+ 9 + 1 + (-20) + 4 is obviously not maximal. 5+9+1 IS.

Good luck & enjoy!

Consider an infinitely long stick, with masses m initially placed along it (at rest) at distances d:

A constant force F is applied to the first, leftmost mass. Assume completely inelastic collisions. Can you compute, after a long enough time, the velocity of the initial mass? Can you compute the velocity of the rightmost mass (that has been struck)?

Now - can you repeat the computation for the case of completely elastic collisions? Can you compute the velocity of the initial, leftmost mass? Can you compute the velocity of the “shock wave” that will be created?

Notes: Neglect gravity & gravitational forces, assume the problem is one dimensional and that the masses are point-objects, and that they are free to move without friction on the infinite stick.

Two students live in adjacent houses in the dorms (ignore the dodgy art, I can only draw as well as Microsoft Word lets me … and yes, the weird beings are the students, courtesy of the Office Clipart). The lightbulbs in their rooms are connected in series. Both students have a physics exam coming up. The students agree to put in 100W lightbulbs. However, they both try to cheat: student A puts in a 50W light bulb, while student B puts in a 200W lightbulb, without informing the other (i.e., neither told the other of what he’d done).

Which student failed the physics exam?