How to deal with conceptual Physics after learning advanced math?

[leo.]

Hi all,

I've started the course of Physics at college last year and I need some advice right now. My main areas of interest are General Relativity and Quantum Mechanics, and these theories as well as every math needed to understand them wouldn't be covered in the course in detail (General Relativity wouldn't even been explained a little), so I've gone to the course of Mathematical Physics. Right now I'm studying advance linear algebra, complex analysis, analysis over Rⁿ and differential geometry of manifolds.

The only problem is that all of this in some way made me "forget" how to deal with basic conceptual physics. When I was on high school I understood well about forces, energy, motions, in general I had a good understanding of the phenomena itself rather than the underlying math. Today I simply can't understand the phenomena.

A very good physicist I know told me to read Feynman's Lectures on Physics, but it's not helping. I try to read that, and it seems like impossible to get this kind of reasoning. I lost much of the intuition I had before and this is really bad, because if I get an advance physics book the author supposes that I know how to think about energy, momentum, colisions and all of that. It's also hard to deal with these basic books because the author supposes that the reader knows nothing of math.

I've thought on studying Spivak's Physics for Mathematicians, but I don't really like this idea because it's an approach for mathematicians, and well, I'm trying to be a physicist rather than a mathematician.

Does anyone know how to deal with this kind of situaton? I'm really needing to solve this, because I'm already finishing the second year of course and I still don't understand basic concepts of Physics. Next year I'll have advanced mechanics, advanced electrodynamics, and things like that, and without knowing how to reason with basic concepts I'll be in trouble.

Any kind of help is appreciated! Thanks very much in advance!

 

[Turion]

Honestly, the conceptual side of Newtonian physics isn't very hard. With some review, you should be able to re-understand it. Start with the basics.

Do you understand Newton's 3 laws of motion?

You are on a bus that is traveling at a constant 20 km/h North and you have a small ball under your seat. Relative to the bus, you and the ball are not in motion. The bus suddenly stops. What will happen to the ball relative to the bus? What will happen to the ball relative to the ground? What will happen to you relative to the bus? What will happen to you relative to the ground? Assume you are wearing a seat belt. Draw a diagram with the forces that are applied to yourself, to the ball, and to the bus.

What will hit the ground faster? A 40 kg bowling ball or a 10 kg bowling ball? Assume they're the same volume.

 

[leo.]

Thanks for the aid Turion. I thought I understood Newton's law, but the first questions I really don't know how to answer properly. I have some ideas, but a little confused, in the sense that I have a vague notion but don't know how to justify properly. Your second question about what will hit the ground faster I know that if we are not considering air resistance, then by the principle of equivalence, they would hit the ground at the same time.

Where you recommend to get a review about those basic concepts? I was looking for some book shorter than Feynman's Lectures on Physics, just to re-understand the basic notions to be able then to move to a more advanced book. Feynman's book was the only book I've found aimed at physicists really and it is very interesting, but for the moment I was just trying to get a quick review just to understand basic concepts and move forward. The others I've found are mainly interested in practical applications rather than concepts of Physics, so they didn't help too much. Is there any other book than Feynman's that I can use for that matter?

Thanks a lot for your help.

 

[verty]

The second question about what will hit the ground faster I know that if we are not considering air resistance, then by the principle of equivalence, they would hit the ground at the same time.

You should think of it in this way. A bowling ball is a sphere, so if the volume is the same, the cross-sectional area is the same. So both bowling balls meet the same number of air molecules that they need to displace. Work done by the bowling balls to displace the air is presumably the same, but the heavier ball has more kinetic energy, so the average speed must be higher for the heavier ball.

I think Turion's point is, you don't need to have a special feel, you can apply what you have learned.

 

[Turion]

Thanks for the aid Turion. I thought I understood Newton's law, but the first questions I really don't know how to answer properly. I have some ideas, but a little confused, in the sense that I have a vague notion but don't know how to justify properly. Your second question about what will hit the ground faster I know that if we are not considering air resistance, then by the principle of equivalence, they would hit the ground at the same time.

The key to both questions is to think of Newton's first law: inertia. Objects resist changes to their motion. If a ball is in motion, then it will always remain in motion until a force such as friction is applied to it. If a ball is at rest, then it will always remain at rest until a force is applied to it.

You are on a bus that is traveling at a constant 20 km/h North and you have a small ball under your seat. Relative to the bus, you and the ball are not in motion.

At t=0, the bus's velocity is 20 km/h North relative to the ground, your velocity is 20 km/h North relative to the ground, and the ball's velocity is 20 km/h North relative to the ground.

The bus suddenly stops.

The bus's new velocity is 0 km/h relative to the ground. Your velocity and the ball's velocity is still 20 km/h North relative to the ground.

Assume you are wearing a seat belt. What will happen to you relative to the ground?

If you weren't wearing a seat belt, then your velocity would continue to be 20 km/h North relative to the ground until you hit the bus's windshield. The reason why your speed doesn't change is because of inertia and because no force would be applied to you.

However, you are wearing a seatbelt. This means that when the bus decelerates, the seat belt pushes you back and you also slow down with the bus. That means that a force is applied to you by the seat belt until you also slow down to 0 km/h relative to the ground.

What will happen to you relative to the bus?

Assuming you aren't wearing a seat belt, before the bus stops, your velocity relative to the bus is 0 km/h. After the bus stops, your velocity relative to the bus would be 20 km/h North.

Assuming you are wearing a seat belt, you were traveling at 0 km/h relative to the bus before it stopped and you remain at 0 km/h relative to the bus after it stopped.

What will happen to the ball relative to the bus? What will happen to the ball relative to the ground?

After the bus stops, the ball will continue to move 20 km/h North relative to the ground because of inertia and because there is no force applied to stop it. Relative to the bus, that velocity is 20 km/h North too because the bus is at rest.

Where you recommend to get a review about those basic concepts? I was looking for some book shorter than Feynman's Lectures on Physics, just to re-understand the basic notions to be able then to move to a more advanced book. Feynman's book was the only book I've found aimed at physicists really and it is very interesting, but for the moment I was just trying to get a quick review just to understand basic concepts and move forward. The others I've found are mainly interested in practical applications rather than concepts of Physics, so they didn't help too much. Is there any other book than Feynman's that I can use for that matter?

Thanks a lot for your help.

Honestly, I'm just a second-year computer engineering undergrad so I wouldn't know too much on Physics books. My grade 12 physics textbook "Nelson Physics 12" had a "Understanding Concepts" section for each concept that asked thought-provoking questions like the one I've given you. Actually, the questions I've given you I think are from that textbook. If you're interested, I suppose I can send you the https://dl.dropboxusercontent.com/u/98686624/Physics%2012/Nelson%20Physics%2012.pdf + solutions. Just control + F "Understanding Concepts" and skip the ones that are too easy.

You should think of it in this way. A bowling ball is a sphere, so if the volume is the same, the cross-sectional area is the same. So both bowling balls meet the same number of air molecules that they need to displace. Work done by the bowling balls to displace the air is presumably the same, but the heavier ball has more kinetic energy, so the average speed must be higher for the heavier ball.

I think Turion's point is, you don't need to have a special feel, you can apply what you have learned.

The heavier ball might have more kinetic energy, but that doesn't mean it has a higher average speed. Assuming that both start at the same height and are at rest at t=0, they will hit the ground at the same exact time. The acceleration is 9.8 m/s² and is the same for both balls.

$${ F }_{ 40kg }=ma\\ =40*9.8\\ =392\quad N\\ \\ { F }_{ 10kg }=ma\\ =10*9.8\\ =98\quad N$$

As shown, the force applied to the 40 kg ball is larger. Recall however, that the 40 kg ball has more inertia, and thus requires a larger force to accelerate it.

 

[verty]

The heavier ball might have more kinetic energy, but that doesn't mean it has a higher average speed. Assuming that both start at the same height and are at rest at t=0, they will hit the ground at the same exact time. The acceleration is 9.8 m/s² and is the same for both balls.

$${ F }_{ 40kg }=ma\\ =40*9.8\\ =392\quad N\\ \\ { F }_{ 10kg }=ma\\ =10*9.8\\ =98\quad N$$

As shown, the force applied to the 40 kg ball is larger. Recall however, that the 40 kg ball has more inertia, and thus requires a larger force to accelerate it.

Sorry, I thought you meant for air resistance to be taken into account. If we ignore any friction, what you say is of course true.

 

[Turion]

Sorry, I thought you meant for air resistance to be taken into account. If we ignore any friction, what you say is of course true.

Oh yeah, I forgot to include that. Yeah, you're right if we take air resistance into account.