High School physics questions

[Berzerker]

therfore the water level sinks as less of it is being displaced.

But doesn't the brick continue displacing water regardless where it is? Why does the brick displace less water when it's submerged?

[Cruddy]

Originally posted by raghar

If it wouldn't rebound from athmosphere it would hit the ground. If of course it wont burn.
BTW not the spot directly under space station.

Eventually the orbit will decay and it will enter the atmosphere... but if you consider the difference of the orbital velocity (1000s of MPH) with the tiny vector from an astronaut throwing it, you'll see the orbit isn't hugely affected at first.

Give it a couple of 100s of orbits at least to hit the earth... maybe more, I'm not sure how high the ISS is.

[JellyBean]

Big Crunch is right. Berzerker, the brick displaces less water when it's submerged because then it's only displacing its own volume. When it was in the boat, it was causing the boat to displace an additional quantity of water with the same mass as the brick.

If you throw something towards the Earth from a space station, the orbit it ends up in won't even be entirely inside the one you started in. If you want it to hit the Earth, you're better off throwing it in the opposite direction to your velocity, back along your orbit. If you throw it at your orbital speed, it will simply drop from your altitude. If you throw it more slowly, then at least it'll end up in an elliptical orbit that's entirely inside yours, it's greatest distance from the Earth occurring at the point where you threw it.

[Sheik]

Are these too easy, too hard or what?

These questions are perfect. If all of us are formulating ideas and spending this much time reasoning them then they are good questions. For High School it is probably more important to have a discussion about different ideas then to actually get the right answer. I would say these questions will do the trick.

[Berzerker]

Big Crunch is right. Berzerker, the brick displaces less water when it's submerged because then it's only displacing its own volume. When it was in the boat, it was causing the boat to displace an additional quantity of water with the same mass as the brick.

When the brick is tossed overboard, the boat no longer displaces the same amount of water, but the difference is now under water. I'm not getting this, oh well...

[Rogan Josh]

Thanks for your help guys

[Kuciwalker]

Originally posted by Sirotnikov
Isn't a pendulum's T (time of erm.. period] equal : 2*pi*sqrt(length / gravitational pull) ?

If so, then when the gravitational pull is nearing 0 (in orbit) the period lengt would strive to infinity? Meaning it would never return?

Actually, the period would disappear, which is pretty much the same thing.

But would it move at all?

Yes, it would spin forever.

[MrWhereItsAt]

If they're too tough for the first years (read: College Freshmen) I tutor, then they're too tough. They couldn't get this.

These are too tough for your average "high school" student.

[Kuciwalker]

I didn't realize that the pendulum one was sort of a trick question until today when I was telling my dad about this thread (he started laughing when I told him about that one, and I asked why). He said that students who had just been studying relativity would immediately start working out the time dialation on the ISS. I didn't even realize that was an issue

[KrazyHorse]

Originally posted by skywalker


Actually no. It just has a slightly higher velocity than necessary to stay in orbit, thus it spirals away (slowly).

Uh uh. Two ideal spherical bodies interacting will orbit their centre of mass in a conic section. If the net energy of the system is negative the conic section will be an ellipse. If zero it will be a parabola. If positive it will be a hyperbola. This is known as the two-body problem and is easily solvable (every physics student sees it solved at least once).

The spiralling outward effect is a result of angular momentum transfer from the earth to moon as a result of the tides. As time goes on, the stretching of the earth caused by the gravitational gradient (~10 meters, IIRC) tends to transfer angular momentum from the earth's rotation to the moon and earth's revolution about each other. The net effect is that in a couple of billion years the earth and moon ought to become tidally locked so that each only faces one side to the other (i.e. the period of revolution of the two bodies will become equal to the periods of revolution of each). The moon has already become tidally locked to the earth, which is why we only ever see one face. IIRC, the final system will have a period of ~50 days, as opposed to today's 28.

I'm not sure what the effect on the final solution will be if you include the sun as a perturbing force. I would guess that the end solution would look like a permanent solar eclipse, although I'm guessing it would take trillions rather than billions of years to manifest itself.

[KrazyHorse]

Originally posted by Big Crunch
2 is easy. Just use common sense. You don't even need numbers.

Yes you do.

Put the moon twice as close to the earth as it is and see what the answer is...

The way I figured it out I used the period of rotation of the moon about the earth and about the sun, as well as the mean radius of rotation of each body. Then I applied a=w^2*r

The moon has an angular velocity about the earth ~13 times what it has around the sun (since it rotates about the earth in 28 days and the sun in 365). It also has a radius of rotation about the sun of ~400 times that of its distance from the earth.

400/13^2 = 2.5 or so.

Not too much different so far as I can see.

[KrazyHorse]

Originally posted by Berzerker
dannubis -

If you jump in the air, does the earth move in your direction as much as you move toward the earth when landing? If you were right, we'd be floating along the surface waiting to hit a bump and bounce off into space.

His statement has nothing to do with the question (he seems to have misread it) but it is quite true. Force and acceleration are not the same thing.

[KrazyHorse]

Originally posted by Starchild
In the space station, there is no gravity drawing the pendulum downwards. So there is no potential energy, just the kinetic energy. So when a pendulum is started off, it will swing around and around.

Bastard. Stop confusing people. The ISS is in almost as strong a gravitational field as we are (~95% or so). The difference is that they're a freely-falling frame and we're not...

[KrazyHorse]

Originally posted by Rogan Josh
2. The sun has more effect on the moon. This one is probably easiest to think of in terms of the energies involved. The energy of a rotating body goes like w^2*r where w is the angular velocity and r is the radius. w is 12 times larger for the moon round the Earth than for the moon round the sun (a year^-1 compared to a month^-1), but the Earth-moon distance is much less than a twelfth* of the moon-sun distance. So w^2*r is greater for the moon-sun and they must therefore have more gravitational energy.

a) You're mixing terms, rogan. Gravitational energy and gravitational force are quite different. Getting sloppy...

b) You've forgotten that the w is squared. The forces are on the same order of magnitude (only different by a factor of 2.5, if you see above) Unless the kids are supposed to remember the relative orbital disatances of the earth-moon and earth-moon-sun systems fairly accurately then the question is impossible. BC's statement that the answer is self-evident from application of common sense is completely untrue. The answer is rather counterintuitive, actually. Most natural satellites in the solar system are held in a stronger gravitational field by their primary than by the sun. Although, to be fair, I'm pretty sure all natural satellites in the solar system are given a greater gravitational potential by the sun than by their primary...

[KrazyHorse]

Originally posted by Rogan Josh
The reason for the tides being caused by the moon is because the orbit of the moon around the Earth is not circular. The same effect in the Earth around the Sun is what causes the seasons.

This is untrue. The tides of the moon on the earth are caused by the moon's gravitational gradient across the earth, not by the moon's orbital eccentricity. In other words the moon pulls harder at the points on the earth nearest it. As the earth rotates underneath it, this point changes, causing periodic stretching of the earth's shape.

The seasons are caused by the earth's tilt, not by its eccentricity. As a matter of fact, the earth's perihelion occurs at around Jan. 20, in the depths of the Northern hemisphere's winter...