Physics puzzles

[mitsun]

Mosquito meets train:

The solution has been given correctly a few times already, but maybe a little graph will make it clear that the mosquito does stop momentarily, while the train does not. The elasticity of the collision affects the sharpness of the velocity changes, but not the basic structure.

Horizontal axis = time
Vertical axis = velocity (positive in direction of train)

Giant mosquito meets toy train:

train
------------|

|
|---------- train + mosquito
|
|
|

0 ---------------------- zero velocity

|

mosquito |
------------|

[mitsun]

Soda ramp problem in another form:
How can you tell a raw egg from a hard-boiled egg, without breaking the egg?

[SpongeBob]

O.k., nobel prize for experimental physics goes to Dusk Eagle, nobel prize for theoretical physics goes to Harleqin.

[cyclops]

The title "Physics puzzles" reminded me of this one:



from xkcd

13/18 Ohm is my answer apart from miscalculations.

Here is my reasoning:

Get your infinite go-board and choose Tengen. For each point p define n(p) as the (least) number of steps to get to Tengen. Define a potential V(p) = 3^-n(p). Check that at each p ( apart from Tengen ) the potential is equal to the average at its neighbours and that the potential drops to zero far away. Apart from Tengen for each point the net incoming current equals the net outgoing current. We have a solution for the case that one of Herman's points is kept at 1 Volt and infinity at 0 Volt.
Herman's other point will turn out to be at 1/27 Volt. Tengen's neighbourpoints will be at 1/3 V each. They will receive (1 - 1/3)/1 Ampere each from Tengen. In total Tengen radiates 8/3 Ampere. Next get your other infinite goboard out of your cupboard and choose Tengen again and put it at -1 Volt keeping infinity at zero. Next make a sandwich of them but choose the Tengens not to coincide but to correspond with Herman's points. Now we add the potentials. The first Tengen will be at 1 - 1/27 Volt = 26/27 Volt. The other at -26/27 Volt. A potentialdifference of 52/27 V. It (still) gives rise to a current of 8/3 Ampere. ( check yourself ) The resistence is (52/27)/(8/3) = 13/18 Ohm.

Pooh

Problem for Herman: Next 3 dimensions?

edit: nice try but wrong. First assertion only true at both axes.

[Tommie]

Mosquito meets train:

The solution has been given correctly a few times already, but maybe a little graph will make it clear that the mosquito does stop momentarily, while the train does not. The elasticity of the collision affects the sharpness of the velocity changes, but not the basic structure.

Horizontal axis = time
Vertical axis = velocity (positive in direction of train)

Giant mosquito meets toy train:

train
------------|

|
|---------- train + mosquito
|
|
|

0 ---------------------- zero velocity

|

mosquito |
------------|

Your idea with the graph is nice, Mitsun.

I just realize how many assumptions we do (automatically), without reflecting a bit
and checking with reality.
Did we book-wise think of masses, carrying on their movevements frictionless for eternity through imaginary endless space?

'The locomotive is pulling strongly' the unprepossessed child says, 'of course the train doesn't stop!'.
Hence, the refinement of wording such a puzzle is iterative.

[cyclops]

The title "Physics puzzles" reminded me of this one:



from xkcd

I was only a few percents off in my nonsense solution
Solution as you might have guessed:

circuit.jpg (72.33 KiB) Viewed 10617 times

Fill in n_= 1 and p_ = 2 for the endpoints ( or the other way around ) and you get

4/pi - 1/2 ~= 0.77 Ohm

published by D. Atkinson and F.J. van Steenwijk. link.
The first one, curious enough, is the professor who taught me Quantum Electrodynamics in the seventies. qed

[ethanb]

Even disregarding flOvermind's (correct, I believe) argument from conservation of momentum, there is also the point that the collision with the insect is partly elastic. I didn't see you mention "a spherical mosquito of uniform density" but you did say that it squished. Therefore the transfer of kinetic energy actually took place over time, not in a single instant. So zero wasn't a factor anyway.

Did we book-wise think of masses, carrying on their movevements frictionless for eternity through imaginary endless space?

Sorry for merging the quote blocks like that, but that was what I was getting at with the "spherical mosquito of uniform density" bit - the "reality vs. theory" (or rather an incomplete theory) idea. There's an old joke that I don't actually know, but have seen/heard a reference to somewhere, and the punchline is something like "and the physicist goes 'First you have to assume a spherical chicken of uniform density!'" Oh, and the "therefore" was related to the squishing, not to the shape or density of the mosquito.

And yeah, I knew it was a puzzle to enjoy - and I was, just in a joking tone. Sorry if I wasn't clear on that.

But no, the mass of the mosquito is comparatively so small that even if it were a completely inelastic collision, its velocity would have to oppose the train's at an appreciable fraction of the speed of light before it made a noticeable impact.

[flOvermind]

http://xkcd.com/669/

[cyclops]

The title "Physics puzzles" reminded me of this one:



from xkcd

Finally, I got the humor of your contribution. It takes longer for a nerd, you know. I enjoyed to have been sniped totally. To share some of my pleasures here some youtube.

[Tommie]

Three people are the last survivors of a capsized, sunk cruise ship,
an engineer , a physicist and an economist (macro~).

They can save themselves onto a small unihabited island.

Some last cans of beluga caviar and other essential nourriture is washed-up as well.

Exhausted and starving, they hurry to get the food.

The engineer takes shells, stones etc. and opens the cans within 2 minutes.

The physicist/mathematician mumbles erh_pi_square_time_m_c_v.... and lays the cans under a coconut tree.

The macro-economist ponders: " Assuming that we had had a tin-opener .... "
[img]
http://www.cowart.info/Cool%20Stuff%20I ... age005.gif[/img]