Conceptual Physics: Understanding Velocity of Rain Drops Hitting Car Window

[Gale]

Ok, I'm in a calc based physics course. I'm thinking i should have taken conceptual physics first... we did a problem with the velocity of rain drops hitting a car window. The math i could do ok, but i didn't even semi understand the problem. In my mind the rain was going wicked wicked slow... when really it was going fast... took me a while to grasp the idea that the rain was bouncing off the windows and i was only seeing tons of tiny bits of the rain drops... didn't matter for the math i did, i still added the velocities or whatever... but my answer didn't mean i thing to me since i didn't even understand the situation right.

So... I'm wondering if maybe we could have a bit of just conceptual phyics in here. Mainly math free, unless someone needs proof or something. But i could really use some help understanding just the general idealology behind how everything works.

 

[chroot]

Conceptual physics is very much welcome here. It'd be easiest for us to help if you posted some specific problems that are causing you difficulty -- then we can help you understand the concepts involved in finding the solution.

- Warren

 

[Gale]

ok well let's see... i guess i could try and make this congruent with my physics course... but screw it... i really don't get energy at all... I've asked questions here before.. but really doesn't make sense to me. This stuff makes things happen... that's all I've figured out...

So maybe work? or uh, energy conservation? or anything that'd help me understand the stuff at all... or we could try again with the what is energy? or gravity, we can talk about how that all works? understanding gravity would probably be most helpful with my phyics right now i guess... But really any topic is a-ok with me. if i finally understood something in physics i'd be pleased.

 

[chroot]

Sorry Gale, I'm afraid your questions are probably far too general to be answered by anything less than a textbook. (Have you tried critically reading your textbook?)

Try posting some of the problems you don't understand, and we'll help you understand them.

- Warren

 

[Gale]

yes I've read my textbook, and really it doesn't make sense. I don't think right or something. energy makes no sense to me. i know i said it a long time ago, but in my mind energy is pretty much the same to me as the idea of 'god.' and my physics book hasn't changed that idea in me.

but ok, let's just talk about gravity, conceptually. my physics b ook hasn't gotten into it really at all. I get that its some attraction thing. And the more mass something has the more gravity it has. So how much do we know about how gravity works? what do we know? things like that.

 

[lavalamp]

Gravity was mentioned. I can help out with that.

Gravity is one of the four forces, the other three are the strong nuclear force, the weak nuclear force and the electrostatic force. Gravity is the least well understood of these forces, it is a force that mysteriously arises as a result of a body having mass, although mass is pretty mysterious and there are a few theories floating around about that. Anyway, you probably don't want to know all this so let's jump into the physics of it.

Gravity is always an attractive force (although I've just created a thread in this very forum where it suggests to me that it isn't). To fit in with electrostatics we say that an attractive force is always negative. The reason for this is because protons and electrons attract, if you multiply the charges +1 * -1 you get -1, therefore the attractive force is negative.
If you have a 1000Kg car, the Earth pulls down on it with a force of 1000g N where g is the graviational field strength, this is just what the acceleration due to gravity would be if the ground suddenly weren't there. g can also be thought of as the force in Newtons that acts vertically downwards on a body of 1Kg.

There are some more complicated equations to deal with the forces of attraction between two masses for a certain separation of their centres and the change in gravitational potential when moving from one point in a gravitational filed to another. The equations for the two I've just mentioned are:

F = - G*m[sub]1[/sub]*m[sub]2[/sub]
    --------
       r[sup]2[/sup]

V = - G*m[sub]1[/sub]
    ------
      r

Where G is the gravitational constant 6.67*10^-11

If you are dealing with stuff near the Earth's surface then not much of this will have helped yet, I'm very sorry but there isn't really much to do about gravity near the Earth's surface other than constant acceleration and potential energy changes.
Since you did mention energy, I thought that I might show the equation for potential energy changes near the Earth:

E = mg[del]h

It's considerably simpler that the other formulae and the mass of the Earth doesn't need to be included in the formula as it is assumed that g will stay constant.

My description of gravity and the laws thereof has probably been a little bit patchy because I don't have anything to bo specific about, so like chroot said, if you want better explanations then you're going to need to post an example of the kind of question that you're having problems with.

 

[Ambitwistor]

Originally posted by Gale17
or uh, energy conservation?

For energy and energy conservation, Feynman had a really good lecture on that. It's in Six Easy Pieces, and also the Feynman Lectures (vol. I). I can't explain it better than him.

 

[Ambitwistor]

Originally posted by Gale17
I get that [gravity is] some attraction thing. And the more mass something has the more gravity it has. So how much do we know about how gravity works? what do we know? things like that.

lavalamp gave you the complete Newtonian theory of gravity (if you note that the direction of the force is directly the line between the centers of mass of the two bodies, which lavalamp implied but did not state). From that force law, you can derive orbits/trajectories, the whole works. An important point is that the motion of a body under the influence of gravity alone is independent of the body's mass; you can see that from the force law.

It's beyond the scope of your course, but we also know that Newton's theory of gravity is wrong; it was replaced by Einstein's theory of general relativity. In that theory, there is no gravitational force: bodies under the influence of gravity alone experience no external force and thus move in straight lines, just like Newton said. It's just that in Einstein's theory, spacetime is curved, so a "straight line" in spacetime can look curved to us. (This is like how the equator is a "straight line" on the curved surface of the Earth: if you start out there and always walk due east, you will trace out the great circle that is the equator.) Whereas Newton's force law describes how much force there is at a point, due to some mass, Einstein's theory describes the geometry of spacetime (and thus its curvature) at a point, due to some mass.

 

[bandonrun]

It is my understanding that Gale is looking for some sort of 3D rendition of a gravitational field. I.E. Something you can sink yer teeth into. Unfortunately this will not be forthcoming, and will lead to the questioning about the validity of anything in the book. In essence the understanding is woefully incomplete.

 

[Ambitwistor]

Originally posted by bandonrun
It is my understanding that Gale is looking for some sort of 3D rendition of a gravitational field. I.E. Something you can sink yer teeth into. Unfortunately this will not be forthcoming, and will lead to the questioning about the validity of anything in the book. In essence the understanding is woefully incomplete.

I don't know what you're talking about, but it's possible to make a 3D rendition of the gravitational field.

 

[bandonrun]

but it's possible to make a 3D rendition of the gravitational field.

I can't wait! Let's see it!

 

[Ambitwistor]

Originally posted by bandonrun
I can't wait! Let's see it!

It's not possible to make a truly 3D picture and have you view it on a 2D screen, without stereoscopic glasses or something. Would you accept a 2D projection of a 3D plot (as you see when you view "3D" pictures on TV)?

If so, just get a graphing program like Mathematica to calculate the gravitational field for some system, and plot the force vectors.

If not, you'll have to build your own 3D depiction. (Toothpicks and wire?)

Or are you talking about general relativity's model of gravity? It's not possible to visualize a 4D curved space embedded within a 3D space, so you can't visualize all aspects of the gravitational field at once. (You can visualize separate projections of it, though.)

 

[Gale]

ok thanks, this is helpful. All of it. I can't really ask for anything specific... cause i don't really want to know the specifics i guess. I just have difficulty understanding really general ideas and concepts.

The straight line gravity thing is interesting. I'll have to think about that somemore, but it makes sense how spacetime changes our perception of it.

Or are you talking about general relativity's model of gravity? It's not possible to visualize a 4D curved space embedded within a 3D space, so you can't visualize all aspects of the gravitational field at once. (You can visualize separate projections of it, though.)

i'd like to know what that's all about. Where that idea came from or whatever. Just a theory?

Something I'm not sure if i understand right... the idea that the further from the center of the Earth you are, the less the gravity has effect. I think actually, this is something about forces in general I'm a bit shady on. Why is the effect less? Does gravity still work on a molecular level? or does it just have no effect and that's when the other forces kick in?

 

[Ambitwistor]

Originally posted by Gale17
ok thanks, this is helpful. All of it. I can't really ask for anything specific... cause i don't really want to know the specifics i guess. I just have difficulty understanding really general ideas and concepts.

Kind of ironically, I've found that a good way to understand general ideas and concepts is to work through a lot of specific, detailed examples ... (of course, if you're really lost you can't get that far..)

i'd like to know what that's all about. Where that idea came from or whatever. Just a theory?

What are you referring to? The idea of 4D curved spacetime? Or the idea that you can't directly visualize a 4D curved space?

Something I'm not sure if i understand right... the idea that the further from the center of the Earth you are, the less the gravity has effect. I think actually, this is something about forces in general I'm a bit shady on. Why is the effect less?

Well, forces don't always have to decrease with distance. In the confining phase of quantum chromodynamics, the strong force between two particles is constant with distance --- that's why you never see free quarks. But the gravitatational force doesn't happen to have that property. If a force didn't decrease with distance, we probably wouldn't call it "gravity" just by definition.

Does gravity still work on a molecular level? or does it just have no effect and that's when the other forces kick in?

We believe that gravity works on all distance scales, but we have no experimental verification of that below about 100 micrometers. (Gravity is so weak it's hard to measure on small scales.)

 

[barcat]

It sounds like maybe we got off track a little bit. More times than not, when I ask a question about something (not necessarily here), the two or three Physics’s types go off on a tangent and leave me standing there listening to jargon argumentation that I have know idea about what is been said. I can empathize with the one who started this thread. I’m 45, a little math heavy, and am taking a “Conceptual Physics 101” course for the first time. I thank my lucky stars that I did. I’m finally beginning to internalize some of what I have heard other (more intellectually gifted) say. To the poster, you go and ask any question you want, as many times as you want until it makes sense to YOU.

 

[zoobyshoe]

Originally posted by barcat
It sounds like maybe we got off track a little bit. More times than not, when I ask a question about something (not necessarily here), the two or three Physics’s types go off on a tangent and leave me standing there listening to jargon argumentation that I have know idea about what is been said. I can empathize with the one who started this thread.

This has happened to poor Gale so many times I think we should start calling it "The Gale Effect".

 

[chroot]

Originally posted by zoobyshoe
This has happened to poor Gale so many times I think we should start calling it "The Gale Effect".

This is an unfortunate consequence of the free-form nature of this communication medium. Many people teach with little structure to begin with, and adding several more posters just makes topics go awry quickly sometimes. The "Gale effect" is perhaps one of the biggest obstacles to effective learning here. As a moderator, I'm interested in hearing people's opinions on how to curb/control the Gale effect. I'm going to make a thread about it...

- Warren

 

[Ambitwistor]

Originally posted by chroot
The "Gale effect" is perhaps one of the biggest obstacles to effective learning here.

The "Gale effect" is how I learned about almost all of the interesting physics I know; people bringing up issues and ideas and subtle aspects of my questions that I didn't even know existed.

 

[Gale]

Hahaha... the Gale effect... no comment...

Anyways... so gravity by definition weakens with distance? and its the only force that works that way? noo... electromagnetism... so is the strong force the only force that isn't that way?

New sort of random question, potential energy? is that just like... its not real... hmm... i mean, its pretty much just gravity's effect on that object or something right?

i had a bunch more questions, but they'll wait. I have a lab i need to pretend to do...

 

[Ambitwistor]

Originally posted by Gale17
Anyways... so gravity by definition weakens with distance?

It's kind of philosophical whether this is by definition, or by observation, or what ... the end result is that the interaction in our universe that we choose to call "gravity" has the property that it weakens with distance.

(Well, until you add in dark energy, which causes a repulsive -- instead of attractive -- gravitational effect that starts becoming significant at cosmologically large distances.)

and its the only force that works that way? noo... electromagnetism... so is the strong force the only force that isn't that way?

Yes, it's just the strong force which has that weird confining property.

New sort of random question, potential energy? is that just like... its not real... hmm... i mean, its pretty much just gravity's effect on that object or something right?

Well, we can't really measure potential energy directly; we infer it, usually through the work it does. And yes, gravity (as well as other forces) has a potential energy; the force acts along the gradient (direction) of decreasing potential energy.

(Well, gravity doesn't have a potential energy in Einstein's theory, but that's a whole new can of worms ... don't worry about it.)

 

[lavalamp]

Aha, potential energy. Looks like I can help out again here.
Gravitational potential energy is always regarded as negative. If you just consider the Earth for now and you are at the surface, let's say that you have -x J of gpe. If you move away from the surface of the Earth you gain gpe and so you may now have -x+y J of gpe, if you move an infinite distance away you would have 0 J of gpe (where x = y).
Because the maximum gpe you can have is 0 J, and you can put a value on your current gpe, this means that you can calculate the energy needed to propel yourself (or a space shuttle) to an infinite distance away and just stop when you get there. This means that you know how much kinetic energy you will initially need, since you also know your mass, from this you can calculate the initial speed that you would need to have to get an infinite distance away and stop. This is called the escape velocity.

 

[Gale]

gravitational potential energy? gravity has potential energy? what? I'm actually more familiar with einstiends theories... my dad always taught bout them. I have no clue what you mean though. i thought objects had potential energy because of gravity? no? I'm confused...

 

[lavalamp]

Potential energy is the potential that something has to do work. Gravitational potential energy is just the abilty to do work due to gravity. For instance, if you stepped off the edge at the top of the mine shaft, you would lose GPE but gain KE, (until you hit the bottom). Generally all bodies want to lose energy, which is why if you throw a ball up in the air, it won't stay there, instead it falls back down.
This may not be the best description of GPE floating around but I can't think of a better one right now.
I can't help you out with hardly any of Einsteins laws, because we simply haven't done those in class yet, unfortunately I don't think that we ever will either.

 

[Ambitwistor]

Originally posted by Gale17
gravitational potential energy? gravity has potential energy? what? I'm actually more familiar with einstiends theories... my dad always taught bout them. I have no clue what you mean though. i thought objects had potential energy because of gravity? no? I'm confused...

Yes, this can be subtle. Objects within a gravitational field are imbued with potential energy due to that field. It is possible to speak of the energy of a field itself, but it's a different concept than the concept of the potential energy of a body that you're learning now.

 

[lavalamp]

The following was dictated to us in class (not long ago), now I'm copying straight of my book:

Gravitational Potential

The potential energy of a mass in a gravitational field depends on the size of the mass and on its position in the gravitational field. To compare the effect on different masses, for the purpose o a definitionwe choose a unit mass, ie: 1 Kg.
If the mass were taken to infinity, the gravitaional force on it would be 0. Therefore it could be moved around without doing any work on it. A point at infinity is therefore a logical choice for choosing the potential energy 0. It follows that the potential energy decreases from 0 as it moves towards the Earth.

The gravitational potential V of a point in a gravitational field is the work done per unit time mass by an externalagent in moving the mass from infinity to the point.

I hope that painted I better picture than my previous definition that I recounted from memory.