Problem Solving Strategies

It's a famous result that if you consider an isolated electron being struck by a photon the isolated electron cannot completely absorb the photon. That's because when you write down the equations for conservation of energy and momentum they cannot both be satisfied.

That's why in the Compton effect the photon hits the electron and is remitted as a second lower energy photon rather than being completely absorbed.

In the photoelectric effect the electron is in a solid so momentum can be exchanged with the material surrounding the electron, and that's why the photon can be completely absorbed.

But then of course the electron doesn't get all the momentum of the photon.

psa

6:55 AM

ah I see

user586228

7:06 AM

Ff/ Fm =EfVf/EmVm (All with subscipts f denote fibre and m denote matrix?)

How to solve this for longitudinal loading

user8718165

7:42 AM

@JohnRennie okay sir...thank you so much.

Intellex

9:04 AM

@JohnRennie, Hi sir. If possible kindly clarify this doubt - If we take ultra clean blocks of copper and place them in contact they stick with each other (that is what given in my book). Doubts: (1) Why do they stick together? Is that because of transfer of electrons from one block to another or something else? (2) Is it possible to see sparks due to electron transfer from one block to another when they are separated by very less distance as we use to see when electric train's pantograph

touch the high voltage line?

John Rennie

@Intellex it's called cold welding:

Cold welding

Cold welding or contact welding is a solid-state welding process in which joining takes place without fusion/heating at the interface of the two parts to be welded. Unlike in the fusion-welding processes, no liquid or molten phase is present in the joint. Cold welding was first recognized as a general materials phenomenon in the 1940s. It was then discovered that two clean, flat surfaces of similar metal would strongly adhere if brought into contact under vacuum. Newly discovered micro- and nano-scale cold welding has already shown great potential in the latest nanofabrication processes. The reason...

Intellex

10:00 AM

@JohnRennie Thank you sir :) I was reading about friction and it wasn't given in my book! So that solved (1), what about (2) sir?

John Rennie

I'm not sure what you are asking in (2).

The sparks you see if you brush electrical contacts against each other are electrical arcs (small arcs)

Intellex

@JohnRennie Is it possible to see the same if we do this experiment in the dark sir?

John Rennie

Yes, if you connect two wires to a large battery, and brush the wires together in the day you'll see the sparks. But then you can probably see them in daylight as well.

Intellex

@JohnRennie Fine sir. But not during cold welding right, sir?

John Rennie

Cold welding is nothing to do with a current flowing between the two surfaces.

Intellex

10:07 AM

@JohnRennie Ok sir. May I ask another doubt?

John Rennie

Yes, of course.

Intellex

Thank you. Are plane mirrors smooth for reflection for visible light but rough for reflection for light of lesser wavelengths?

John Rennie

It depends on how well the mirror has been made.

But in any case once you get past the UV and into X-ray wavelengths they don't reflect well from mirrors because they go stright through the mirror.

Intellex

@JohnRennie If it reflects well in the visible range, it means it will for light of higher wavelengths but not necessarily for lower wavelengths, am I right sir?

@JohnRennie Can we say it will be diffused reflection in case of lower wavelengths?

John Rennie

@Intellex with lower wavelengths the light tends to be absorbed in the metal rather than being reflected.

Intellex

10:19 AM

@JohnRennie Ok sir. Is it possible to reflect them or simply they will penetrate always?

John Rennie

This isn't really my area, but I believe that metals will reflect X-rays provided the X-ray strikes the surface almost parallel to the surface i.e. the angle of incidence is nearly 90°.

The X-ray telescopes used in satellites work like this. The mirrors they use to focus the X-rays are designed so the X-rays strike them at a glancing angle.

Intellex

Ok @JohnRennie sir. Thank you for the information :) I'll ask further after I learn about X-rays in my book. Currently in mechanics part only.

John Rennie

@Intellex this assumes the metal is smooth on length scales comparable to the wavelength.

If the metal is rough on lengths scales smaller than visible light then it will reflect visible light well but it will scatter lower wavelength light to give a diffuse reflection.

Intellex

@JohnRennie It will also reflect well radio waves automatically right sir?

John Rennie

@Intellex yes, because if it's smooth on visible wavelength scales it's also smooth at larger wavelength scales.

Intellex

10:52 AM

@JohnRennie Thank you for clarifying sir :)

John Rennie

@Intellex :-)

Intellex

11:22 AM

Sir, I read the following questions about rolling friction (rolling resistance) and it's relation with static and kinetic friction:

2

Q: Rolling resistance and static friction

I am a bit confused about the relation between rolling resistance and static friction. I have often heard that it is the static friction that lets the wheel roll. Consider the following two cases: a) A tire of a car of mass $m$ moving with positive acceleration $a$ on a street b) A wheel of a ...

20

Q: What is the cause of rolling friction? & why is it less than sliding friction?

Rolling friction is the resistance to motion experienced by a body when it rolls upon another. It is much less than sliding friction for same pair of bodies. When one body rolls upon another, there is theoretically no sliding or slip between them. And if both are perfectly rigid, there is no s...

newtonian-mechanics friction

But still, I'm unable to understand why is rolling friction not same as static friction.

And, why is it lesser than static friction.

Could you please clarify this (^) doubt briefly @JohnRennie sir?

First confusion is because, in rolling it is said the point of contact of a wheel with the ground is at rest, no relative motion, so static friction as discussed in the following answer:

6

Q: Static as opposed to Kinetic Friction in Rolling Motion

During analysis of rolling motion, why do we consider coefficient of friction as that of static friction and not kinetic friction?

newtonian-mechanics rotational-dynamics friction

John Rennie

We need to be clear about what we are discussing.

Typically these sorts of questions are asking about the energy lost i.e. why is the energy lost in rolling much less than the energy lost in sliding.

Is that what you are thinking about?

Intellex

@JohnRennie No sir. I am asking about the difference between rolling friction and static (not kinetic friction), and why is it lesser than static?

Will it be easier for you if I frame it as a question on Phy.SE?

John Rennie

Static friction is the force between two surfaces that are not sliding across each other. Yes?

Intellex

@JohnRennie Of course yes.

John Rennie

And when something rolls across a surface, at the point of contact between the rolling object and the surface the two surfaces are stationary with respect to each other.

Intellex

11:31 AM

@JohnRennie Yes sir. I understood this. Please proceed.

John Rennie

So since the two surfaces are in contact the friction is approximately the same as the static friction.

Intellex

The friction in your last message refers to rolling right sir? If yes, my book says rolling friction is lesser than static/kinetic friction. And this is why ball bearings are used (acc. to my book)

And that's why I'm confused

Both arguments are equally reasonable here sir

John Rennie

@Intellex this is exactly the confusion I was referring to earlier. What your book means is that less energy is dissipated in rolling than in sliding.

Intellex

@JohnRennie But we don't have slipping (sliding) anywhere here right sir?

John Rennie

@Intellex correct, so what you should be asking yourself is what is the mechanism for energy loss during rolling?

Intellex

11:40 AM

@JohnRennie Yes sir. I know. In non ideal cases, the surface becomes deformed and the forward portion exerts a normal force opposing the translation of the rolling body.

This is what causes energy loss during rolling

But how can this be lesser than static and kinetic sir?

John Rennie

Yes the energy is lost due to deformation, and that's a completely different mechanism to energy loss in sliding.

Intellex

An intermediate doubt. Could you please clarify this before the main doubt as it's related. ----- During non ideal case, is the friction acting on a rolling body static, kinetic or combination of both or altogether a different type sir?

John Rennie

It is altogether a different type.

Intellex

@JohnRennie Fine sir. Is that the rolling friction we are talking about ?

John Rennie

Yes. The term rolling friction is rather misleading. It should really be rolling resistance or something like that because the energy loss isn't due to friction.

Intellex

11:46 AM

@JohnRennie Ok sir. So in short my book refers to rolling resistance rather than rolling friction. Am I right sir?

John Rennie

Yes

Intellex

Thank you. Now, why is rolling resistance lesser than static or kinetic sir?

@JohnRennie sir, are you busy?

John Rennie

@Intellex I'm doing something else, but I can still answer if you don't mind the answers taking a while sometimes.

Rolling resistance happens because when you deform an elastic object and then let it return to its original shape some energy is always lost.

The exact mechanism of energy loss can be complicated, but basically some of the work you put into deforming the object gets lost as heat and the work you get back as the deformed object returns to its original shape is less than the work you put in.

yuvraj singh

@JohnRennie hi can I see you in our room.

John Rennie

Soft squishy objects tend to lost a lot of energy when they are deformed while very rigid obejcts typically lose much less energy.

@yuvrajsingh give me a moment to join the room.

yuvraj singh

11:58 AM

If you are free.

OK.

Intellex

@JohnRennie ok sir. So it is an experimental fact, which we must accept and there are no general reasons, right sir?

@JohnRennie Understood this point sir.

John Rennie

It's going a bit far to say there are no rules. It's just that the meachism for the enrgy loss will be different in a soft piece of rubber and a hard piece of steel.

Intellex

@JohnRennie But I didn't still get why the energy lost in rolling is less than the static friction and kinetic friction case (whatever be the material soft or hard). Sorry for this sir :(

John Rennie

It's a completely different mechanism. Why should the energy losses be comparable?

Intellex

@JohnRennie I don't have a valid reason for that. It was given in my book that rolling friction (resistance) is lesser than static/kinetic. This is how the author explained why ball bearings are used. Else, could you please explain how ball bearings are useful?

John Rennie

12:04 PM

If you roll a ball made of very rigid steel then it hardly deforms at all as it rolls, and because it hardly deforms at all very little energy is lost because of the deformation. OK so far?

Intellex

Yes. But here the friction is static right sir?

Energy is lost not only due to deformation but also due to friction right sir?

John Rennie

No, why would any energy be lost to friction? No sliding is occurring and energy is lost to friction only when surfaces slide over each other.

Intellex

@JohnRennie Ok sir. Is there any energy losses when bonds form and break at the surface when the ball rolls?

John Rennie

In most cases bonds do not make and break at the contact point. I guess this could happen e.g. with perfectly clean and smooth surfaces rolling in a vacuum, but that isn't a realistic scenario.

Intellex

@JohnRennie Fine sir. Then please proceed with the ball bearing :)

John Rennie

12:11 PM

A ball bearing is just a very rigid ball rolling between two surfaces.

Intellex

@JohnRennie So very negligible deformation, very less loss in energy and so we use it.

John Rennie

And the energy lost as the ball rolls is tiny because there is no sliding happening.

Intellex

@JohnRennie Thank you sir. I'll think this for a while and ask you further if I've any doubts.

Advil Sell

Hey @JohnRennie !

Intellex

Thanks a lot sir :-) Bye.

John Rennie

12:13 PM

@AdvilSell hi :-)

Advil Sell

@JohnRennie I have a doubt in QM

John Rennie

@AdvilSell what's the problem?

Advil Sell

We are being taught solving the Schrodinger , tiday we were taught the case of a particle in a box

The box wall would take infinity energy to cross

John Rennie

OK ... ?

Advil Sell

So , we found that the energy that the particle can have is quantized

I hav the doubt if everything is perfect in our world there is no way of loosing energy

A electron with a little higher energy than what we found at n=1 , how would it disipate the energy ?

John Rennie

12:19 PM

@AdvilSell typically the excess energy would be lost by creating a photon. That is, suppose an electron starts in the $n=2$ state then it can emit a photon to carry away the excess energy and fall into the $n=1$ state as a result.

Advil Sell

@JohnRennie i know that accelerating charges can emit photon , where is the electron accelerating here ?

John Rennie

@AdvilSell this seems like a simple question, but it turns out to be surprisingly complicated. It's because the electron oscillates between the $n=1$ and $n=2$ states, and there is an oscillating acceleration associated with the oscillation between the states.

And this oscillating acceleration is what causes the photon to be emitted,

Advil Sell

@JohnRennie (☉｡☉)!

John Rennie

If you're interested Emilio Pisanty wrote an amazingly good answer explaining this. Do you want me to search for it?

Advil Sell

@JohnRennie Yeah that would be great

John Rennie

12:24 PM

63

A: Is there oscillating charge in a hydrogen atom?

In this specific instance you are correct. If you have a hydrogen atom that is completely isolated from the environment, and which has been prepared in a pure quantum state given by a superposition of the $1s$ and $2p$ states, then yes, the charge density of the electron (defined as the electron ...

Advil Sell

Also if I replace the electron with a neutral uncharged particle how will it dissipate energy ?

@JohnRennie thanks !

John Rennie

@AdvilSell how would a neutral particle be bound by electrostatic forces?

Advil Sell

@JohnRennie it won't I just threw the particle in a box with energy a little higher than that at n=1 there's ain't any gravity .

John Rennie

You can't throw the particle into the box at an energy a little higher than n=1. If the particle starts outside the box then its energy starts at zero (assuming we take the energy at infinity to be zero).

Advil Sell

@JohnRennie this is a bit over my head for now

John Rennie

12:31 PM

So to get the particle into the box there has to be some mechanism for the particle to lose some of its energy and settle into a ower energy state inside the box.

@AdvilSell yes, that's quite a complicated treatment, although you don't need that much more QM to understand it.

Advil Sell

@JohnRennie ah okay , I have to think about it for a while . Thanks !!

PolarBear

1:22 PM

@JohnRennie Are you here?

Transcript for

Problem Solving Strategies