Physics Question #5

It has been a while since I've posted an interesting physics problem and I have been thinking that it would be good to post a new one. I just ran across this problem while familiarizing myself with the fundamentals of dynamo theory.

Imagine a copper disk rotating about its axis in a uniform magnetic field, H. The disk has a radius a and has a tangential velocity v at its periphery. A conducting brush is simply connected to the disk and the disks axis and has a negligible effect on the system. Will a current flow through the system? If so, what will be the value of this current?

Good luck and, as always, no searching Google or Wikipedia for the answer!

Physics Question #4

Indeed, the return of the Physics Question post! So, here it is:

Starting with an ordinary cup of water, you add exactly one ice cube. Now, after you add the ice cube, you notice that the level of the water in the cup rises (I believe that everyone would agree with this scenario). After about an hour, you return to your cup of water and notice that the ice cube has melted entirely. Ignoring the evaporation of the water over time, has the water level risen, fallen, or has it remained the same? Explain.

Bon chance!

Physics Question #3

Since I know everyone loves a brain teaser, I have another physics question for everyone to ponder! This is nothing new and I am sure that everyone has heard the scenario, if not the solution. It is the infamous Twin Paradox.

One result of Einstein's Special Relativity is that moving clocks run slower! I will not delve into the details of this, but if you would like to know, feel free to inquire. So here is the scenario:

Two twins, Alice and Bob, are both at rest at some point in space, at some initial time, with their clocks synced. Alice moves away from Bob and travels for 30 years, according to her watch, with uniform velocity (near c), in a straight line. After 30 years, Alice returns back to rest where she began, next to Bob, who has remained at rest. When Alice returns, though, she notices that while she is 30 years older, Bob has fared worse than she, and has aged considerably more.

It is obvious to us, the observers, that there is no paradox here, since Alice was moving, thus her clock runs slower. But now consider it from both the reference frame of Alice and Bob, separately. In Alice's frame, Bob is moving away from her at constant velocity, and it would appear that she is stationary, while on-the-other-hand, Bob sees Alice move away from him with constant velocity and he appears to be stationary! So what does this imply? It suggests that Bob would believe that Alice is younger than he is, due to her motion, but Alice would believe that Bob was the younger twin, not her! Yet, he has clearly aged more than she has. How can Bob and Alice reconcile their different views of what should have transpired?

Physics Question #2

This problem has come to be known as Olber's Paradox, something familiar to those involved in astrophysics:

Suppose that the Universe is infinitely large and would then contain an infinite number of uniformly distributed stars. This would indicate, then, that the night sky should not, in fact, be dark, it should be infinitely bright! Even if the stars are at a great distance away, there would be more stars at that distance, and thus a large amount of light. So why then, does the night sky appear dark?

Now, one could easily use Google to find a solution to this apparent paradox, but try not to do that, you won't be exercising your mind if you do. Just take a few moments, think, and then post your proposed solution. If you would like, you can then Google it, but I shouldn't take as long to answer this one as I did the previous.

Physics Question

Here we go, why not throw out an age old physics question:

Imagine, if you will, a plane sitting on a large conveyor belt which is as wide and as long as a runway. The treadmill is designed to match the speed of the wheels, moving in the opposite direction. Can the plane take off?

This question normally stirs up quite a debate, do you think you know without looking it up on the internet? Just think about it, consider the system and the particular physical interactions that are occurring. I'll post an answer to this in a week or so.