Science quiz

I've had an assessment today and I'm impressed of the creativity they had in those tests.

Here's one:

Two barrels are filled with water and they have holes in it, which one is the right one?



I picked the first one, but I still don't know why and if its the right choice...

I say the bottom one. Notice that the furthest down hole is spraying the water further. I'd gather that to mean there's more pressure at the bottom than in the first one, in which the lower two holes seem to be "gushing" (exit with lower pressure) rather than "spraying" (exiting with high pressure).

Damn, damn, damn. You're right, I just figured it out.

Aargh.

Explanation:

The top hole has potential energy: rho. g. h. But has also pressure energy also rho. g. (H-h). H = length of the barrel and h = length from ground to the hole.
The bottom hole has the same energy because it has half the height/potential energy but double the pressure energy.

So basically they have the same energy! So they have to SPURT the same LENGTH of water. Which means you're right and I'm so dumb... But I got only 30 seconds to think about it, not ten minutes!


I still am not sure of the answer, can someone try it out?

I tried it out, and the experiment wasn't a success, because of too much friction. But I think it's safe to say that the bottom one is correct.

We have two similar cars on a 45 ° hill standing still. There is no friction between wheels and ground.

Now in the first car we place a fat guy of 200 kg.
In the second car we place a skinny guy of 25 kg.

Who has the highest acceleration when letting the cars roll?

I would say that the car with the fat guy in it would accelarate more since the mass is greater even though the resistance is the same.

Okay, it is a common mistake to say that the mass is greater => greater acceleration.

You have to take in account that the greater the mass, the greater the inertia of the material.

An example: with the same force it is more difficult to move a standing car than moving a bike.

So basically the greater mass makes the acceleration higher, but the greater mass has higer inertia. They cancel each other out so that leaves the answer to be:

They both have the same acceleration. (without the friction included)

Think about this too: when you are on your bike, would you rather be a fat guy or a slim guy to have the advantage of a high speed when riding off a mountain? I always thought that the fat guy would be faster but it's the slim guy! It has to do with friction. The fat guy has more friction on the wheels. That's also why cyclists want their bike to be light weight.

Edit: I was wrong, it's the fat guy who is the fastest, because he has more inertia and is less influenced by the wind. The friction of the wheels is less powerful as the friction of the wind.

Some of you could ask why cyclists put this added weight in the back wheel. It's just to reduce wind vortices with the plates and reduce turbulence of the wheel by adding weight.

New problem:

We have a rectangular magnet with North-South pole. You sprinkle neutral ferromagnetic particles in the middle of the magnet. What happens?

1) The particles spread over the entire magnet
2) The particles stay in the middle
3) The particles go to the North Pole
4) The particles go to the South Pole
5) The particles go to both poles

This happens.

We're not talking 2D/3D here. I'm talking about the alignment on the surface of the magnet. (Gravitational force is still stronger than magnetic force at those distances. The particles will fall down instead of floating in the air.)

Both poles. And that drawing is of ferro-magnetic fillings scattered over a white sheet of paper resting on a magnet (or a magnet on it with the result photographed) Nothing floating in mid-air.

That's right, the flux is greatest at the poles and is zero on the mid section of the magnet's surface. All the flux is situated inside the magnet not outside the magnet. Answer 5.


New problem:

We have a wooden barrel with water. We place this 10 m long plastic thing of 1cm diameter in a little hole on top of the barrel and fill it with water.

The barrel can withstand 1kg/cm^2.

What will happen:

1) The barrel explodes
2) The water gushes out from the top
3) Nothing happens

Originally Posted by katchum

We place this 10 m long plastic thing of 1cm diameter..

We place this 10 m long plastic thing of 1cm diame..

We place this 10 m long plastic thing of 1cm di..
We place this 10 m long plastic thing of 1cm..

We place this 10 m long plastic thing of 1cm diameter

Oh the science..

Yeah I know, when you say that on a job interview, they shoot you down... Let's say tube then.

Are we doing your homework here, by any chance?

heh, even if we are it's sort of fun..

My guess, read:GUESS, is that nothing will happen, i don't think 0.10Pi x 0.5 is enough volume to cause more than a kg of pressure.

Basically the original problem comes down to finding the velocity at which the water leaves the hole and then you simply use kinematics to figure out where each lands. Now the question comes down to finding the velocity at which it leaves the can. Unfortunately neither of those pictures are completely right. Lets pose the problem well.

We have a canister filled with water sitting on top of a table. The canister is filled with water to a height of H and there are holes on its side of equal size at intervals of h down from the top of the water.

Then v(velocity of water out from a hole h down from the top of the water) = sqrt(2gh)
You can use the correct application of Bernoulli's equation to get this interesting result.

Now we get v = 1.26 sqrt(h).

Now the problem is down to kinematics.

Find t using y and g.
0 = H - h - .5 (9.8) t^2
t = .45 sqrt(H-h)

Now use an equation of x using v and t and the fact that a_x=0
x = 0 + 1.26 sqrt(h) (.45 sqrt(H-h))
x = .569 sqrt(H h) -.569 h

So now as you can see it's a parabola. Graph it if you're interested in what it will look like. Remember to fix H though, H is the height of the water. h is your variable.

This equation is absolutely consistent with what we would expect. The very top where h = 0 has x = 0 and the very bottom when h = H , x = 0. Also I myself suspected that in the middle the distance x would actually reach it's maximum, which it in fact does.

Well, Giro?

Does it explode?

DOES IT EXPLODE DAMMIT???

Hehe I understand, nice, nice! Thanks!

There is still one thing I don't understand: the velocity is the same when the hole gets bigger? This means only the mass flow gets higher with a bigger hole then...

Well, it explodes. I think. Because:

rho.g.h is the pressure and its: 1000kg/m^3 . 9.81m/s^2 . 10 m [Pa]

This would be the pressure at the bottom of the tube. And it's higher than 1 kg/cm^2. It's not the volume that makes the pressure, it's the height!


New problem:

Two cold glasses of -20 degrees °C are put in 90 °C water, which cracks?

The famous glasses problem. You have to take in account many, many factors!!!!

(mechanical strength, microscopic allignment of the glass, warmth transfer both in time and place, volumetric expansion)

http://two.xthost.info/katchum9/glasses.JPG

Originally Posted by Giro0001

Basically the original problem comes down to finding the velocity at which the water leaves the hole and then you simply use kinematics to figure out where each lands. Now the question comes down to finding the velocity at which it leaves the can. Unfortunately neither of those pictures are completely right. Lets pose the problem well.

We have a canister filled with water sitting on top of a table. The canister is filled with water to a height of H and there are holes on its side of equal size at intervals of h down from the top of the water.

Then v(velocity of water out from a hole h down from the top of the water) = sqrt(2gh)
You can use the correct application of Bernoulli's equation to get this interesting result.

Now we get v = 1.26 sqrt(h).

Now the problem is down to kinematics.

Find t using y and g.
0 = H - h - .5 (9.8) t^2
t = .45 sqrt(H-h)

Now use an equation of x using v and t and the fact that a_x=0
x = 0 + 1.26 sqrt(h) (.45 sqrt(H-h))
x = .569 sqrt(H h) -.569 h

So now as you can see it's a parabola. Graph it if you're interested in what it will look like. Remember to fix H though, H is the height of the water. h is your variable.

This equation is absolutely consistent with what we would expect. The very top where h = 0 has x = 0 and the very bottom when h = H , x = 0. Also I myself suspected that in the middle the distance x would actually reach it's maximum, which it in fact does.

Think about it another way, though. Say you put the canister on a really fucking tall table. So tall that the height of the hole in the can relative to the height of the table is insignificant. In that case, the difference in acceleration due to gravity once leaving the can shouldn't matter, and all that really matters is the initial velocity in the x direction.

Also, it should be easy to guess the trajectory will be a parabola because it's moving like a projectile under gravity.

As for the glasses, there's a turning point in which would crack. In the limit of the 90°C glass equaling the volume of the -20° glass, you shouldn't have any cracking since the volume of water trying to heat it up would be zero. In the limit of the -20°C glass being extremely thin, then there wouldn't be enough of a temperature gradient across it in order to produce thermal cracking no matter which situation we were in.