Timothy wrote on 03/17/10 at 04:56:01:

The surface area could be different, though. The shot bullet will spin and stay horizontal, but the dropped bullet might rotate or tip over vertical. Another (very) tiny difference is the curvature of the earth.

@Cooper: they would be equal if the pivot was in the middle, but it isn't. Imagine you've got a long wooden plank and you place a cat and horse on opposite ends. If you put the pivot in the middle, the horse wins. To balance them you'd need the pivot very close to the horse. They will balance. To prove that they will balance, imagine this extreme case: remove the cat and put the horse right on top of the pivot (distance of 0) so that it balances on the plank by itself. Now put the cat anywhere, and the plank will topple over towards the cat. So the cat wins. So in one configuration the horse wins, in another the cat wins, which means that there exists something in between where they balance. And yet, the horse is always heavier than the cat if you ignore the whole balancing act (i.e. cut the broom).

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The problem though Alex is that the broom is not a plank balancing two massive objects. The mass of the plank itself is being called into question.

TvL wrote on 03/17/10 at 02:47:42:


Are they Nerf bullets?

AlexPenev wrote on 03/17/10 at 09:01:00:


Actually, I think at best the question is poorly worded and can be argued either way. I understand how levers work but you can also argue that his ambiguous wording allows for the unique case where the broom can be evenly weighted around either side of the lever.

lol, last question is hilarious  

I think you can use that telescope to see the dinosaurs.  The light that those dinosaurs reflected millions of years ago is still somewhere in the universe. If it would have been reflected by said mirror you could use a telescope to watch this light and see dinosaurs.

Some problems you might encounter
1. The light intensity has gotten so low that only like 1 or 2 photons made the journey all the way to the mirror and back
2. Earth has moved in all those million years
3. The light may be absorbed in some dust clouds in the universe
4. Light may have refracted due to extreme gravity like black holes and huge stars.
etc

So i think it's A

I got some other questions I was thinking about while driving the other day, since I am anything but a mechanic:

1. Gas mileage while driving is based on RPMs, right? Meaning, you get the same gas mileage at 3krpms in first gear as you do at 3krpms in fifth gear? This means you get significantly better gas mileage at your highest gear because you are covering much more distance per gallon used. Is that true?

2. If you're gunning down the highway at 6krpms, you're obviously using a lot of gas. If you take your foot off the gas pedal, you will start to slow down, yet your rpms don't drop immediately following the release of the gas pedal. This is because the transmission is still turning the car's engine in the act of moving, similar to the pedals on your bike still rotating after you lift your feet off them while riding. So my assumption then is that at 6krpms, if you are not pressing the gas pedal, you are using the same amount of gas as if you were idling. Is that right?

So shift into neutral before you slow down

Camster wrote on 03/18/10 at 08:02:04:


1. Gas mileage is also affected by drag which is a function of velocity (driving speed) through a fluid (air). Assuming that your car has non-0 drag, the faster you drive the more drag, via air resistance, you will encounter which should cause your efficiency to decrease. Even though driving at 3K RPMS in 5th gear is most likely more efficient than driving at 3K RPMS in 1st gear, I would assume that most common cruising speeds in the lower gears will be more efficient than most common cruising speeds in the higher gears due to drag.

2. See explanation regarding drag in answer 1.

The decrease in efficiency would only apply to standard driving/crusing conditions not in the example of 3K RPMs in 1st vs. 3K RPMs in 5th. I've definitely seen data that shows driving faster = less fuel efficiency. Obviously each car is different due to it's transmission, engine and aerodynamics but I'm sure that each car would have an optimal cruising speed/RPM ratio that achieved the optimal fuel efficiency and in every case I can almost assure you that the optimal speed will not be the car's top-end speed.

Edit: See also http://en.wikipedia.org/wiki/Fuel_economy_in_automobiles#Physics

The answers to my questions with explanation, although much of it has already been said:

1. Take a broom, and balance it horizontally on your finger. At the exact point of balance, cut the broom. Which part is heavier: the part with the brush or the stick?
a) The brush
As said by many before me, balance is a combination of weight and distance. To be precise, the total sum (or integral) of all the mass times its distance to the pivot must be equal. Since the stick has its weight further away on the average, the brush must be compensating this by being heavier.

2. There are two identical bullets. One is fired horizontally with a gun from a few feet above the ground. The other is dropped from the exact same height at the exact same time. Which bullet hits the ground first?
c) There is no significant difference
Above a completely flat surface, in vacuum, there would be no difference at all: the vertical acceleration is the same for both bullets, irrespective of their horizontal velocity (as already said by Ivo).
There are two things that would cause a difference, as already mentioned by Mark: one is the curvature of the earth. That's way I stated that the gun is fired a few feet above the ground. Over a distance of a few hundred meters, the extra height difference is of the order of millimeters, so not significant.
The other aspect is air friction. Since the fired bullet encounters a lot more air, the friction (in the vertical direction) will be higher than for the dropping bullet. Hence the fired bullet will accelerate slower, and thus take longer to reach the ground. Again, the time difference is negligible. (I do not know what the effect would be of a spinning bullet though).
This has in fact been put to the test by the Mythbusters. I believe they found a time difference of about 40 ms.

3. Which of the following is not conserved in sub-atomic interactions?
c) Total mass
Energy and momentum are always conserved (in the absence of external interactions). Charge won't (dis)appear either. However, on the quantum scale, mass can be converted into energy and vice versa. In fact, this happens all the time in the vacuum and within protons and neutrons.
Someone said that they're equivalent, but not completely. Mass can be considered to be equivalent to energy (via the famous E=mc²), and in fact in elementary particle physics it's common practice to express mass in terms of energy. Energy however cannot always be considered equivalent to mass, kinetic energy for instance.

4. Are you safe in a car during a thunderstorm?
d) Yes, because a car is made of metal
Indeed the question is somewhat incomplete; no, it doesn't work in a convertible. There is a myth that the fact that the tyres are made of rubber insulate the car and that that would help. It does, but it's very much insignificant; the lightning has overcome the large distance between the clouds and the car, it will make it from the car to the ground. The fact that (most) cars are made of metal makes them a more prone target, but it's the same metal that saves you (if it forms a cage), by diverting the electricity around you, via the principle of Faraday's cage.

5. Consider a very bright laser on earth, illuminating the entire moon (the beam is not completely focussed). Take a pen and quickly move it through the laserbeam; the shadow will move faster than the pen itself. Can the shadow it makes on the moon go faster than the speed of light?
b) Yes, if you move the pen quickly enough
The maths is straightforward, but since nothing can go faster than the speed of light, it should get physicists slightly worried. The keyword (or part of it) however is "thing": no particle and no information can go faster than the speed of light. A shadow, however, is more of a concept: it's a collection of spots that are not illuminated. It "moves" by illuminating new spots at one end and darkening spots at the other end. Therefore, nothing is "moving" faster than the speed of light, but the shadow, as a concept, has a "velocity" larger than the lightspeed. Note also that such a shadow cannot be used to transfer information faster than the speed of light.

6 d
It will not move simultaneously, since nothing can go faster than the speed of light. Because of this, the speed of light would be the minimum. However, the metal rod can be thought to be a set of atoms held together by springs. The "springs" are very stiff, but I suppose that over a large distance, there will eventually be some kind of "recoil".

7 b
You're doomed I tell you. Doomed!!

9
Damn, I should know this, I took General Relativity a few months ago...
If I remember correctly, you would appear to get taller as you are stretched out, but black hole physics can be quite tricky...

10 b
No - You idiot! Of course not! The intensity would be too small; in fact you'd probably only get one photon back at a time, with huge time intervals in between (depending on the size of the mirror).

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What if a road a light year long is filled bumper to bumper with cars, all bumpers touching and leaving no empty space in between, and each person stepped on the gas pedal simultaneously. Or maybe only the car in the back pressed the gas pedal and pushed the rest of the cars, assuming it had the strength. Wouldn't in both cases all cars would move simultaneously? And in turn, isn't that the same as moving a metal rod that's a light year in length?