Problem Solving Strategies

Kavin Ishwaran

05:22

@JohnRennie the setup..

John Rennie

That's the antique camera presumably?

Kavin Ishwaran

yes...

John Rennie

Is this to do with the spring?

Kavin Ishwaran

yes

it is partially working

but there is a small spring that supports a timer is not good

so I decided to make one

John Rennie

Ah, I see. The spring we were talking about is for the camera?

Kavin Ishwaran

05:28

yes :)

My father took this cam and asked me if it can work as it used to

John Rennie

I had misunderstood what you were trying to do. It sounds as if you're just trying to make a regular spring.

Kavin Ishwaran

@JohnRennie The camera is not useful today, There is a time inside which can be used for physics experiments, as soon as I make the spring I will detach that timer

you can see that timer below that lens

I can precisely measure time up to 1/300th of a second

it*

John Rennie

I don't think I can help. I don't know anything about repairing cameras.

Kavin Ishwaran

thats fine :)

but your explanation on the springs helped me a lot !

Arjun

06:16

@JohnRennie hi, can you help me with this?

whenever you're free...

John Rennie

@Arjun Hi :-)

Arjun

hi

John Rennie

The way we do this is to conserve both linear and angular momentum.

Initially the total momentum is mv. Yes?

Arjun

yes

John Rennie

After the collision the joined mass and rod have a momentum of 2mu, where u is the velocity (of the centre of mass), and this has to be equal to the initial momentum mv, so the speed after the collision is u = v/2.

OK so far?

Arjun

06:21

@JohnRennie yep

John Rennie

Now, after the collision the rod+mass will be rotating about their combined centre of mass, so we have to find where this centre of mass is.

Arjun

at L/4 from A?

John Rennie

Yes.

The rod will be rotating clockwise at angular velocity ω about the point 𝓁/4 below A, and at the same time it is moving right at linear velocity v/2.

Arjun

@JohnRennie so far so good

John Rennie

Consider a point on the rod a distance x from the COM. In the rest frame of the rod the speed of this point is xω. This is just using the equation v = rω. Yes?

Arjun

06:27

yes

John Rennie

If the point is above the COM, i.e. near A, then the clockwise rotation is making it move right, and the linear velocity is to the right, so the total velocity is v/2 + xω.

Conversely, if the point x is below the COM, i.e. near B, then the rotation makes this point move to the left, so the total velocity of the point is v/2 - xω.

OK so far?

Arjun

@JohnRennie ah yes

John Rennie

You can probably see where this is going now.

Arjun

i can and i got the ans now

John Rennie

@Arjun OK :-)

Arjun

06:31

demn this was easier than expected :/
i feel dumb

@Wolgwang you might wanna give this a read too

John Rennie

Questions like these are easy if you've done them before

Arjun

@JohnRennie well now i have

tnx for the help!

John Rennie

If I made it seem easy that's because I've done questions like this 100000000000 times! :-)

Arjun

@JohnRennie i bet you have ;-)

pi-π

@JohnRennie Hello

John Rennie

06:39

Hi :-)

pi-π

When we call a member function as:
obj_name.function_name();
Then does this function name also act as pointer?

John Rennie

Yes. If effect function_name is a member variable of the object of type "pointer to function" and its value is the address of the memory where the code for the function is stored.

pi-π

So basically the thing is if we have a class with some data members and member functions and if we call a member function by creating an object of that class then the function name will be a pointer to the function that is in the data section in the memory. Yes?
Or is the function loaded in the stack as well?

TonyPhysicslover

question - Why work is not instantaneous ?

Arjun

@TonyPhysicslover how do you define work?

TonyPhysicslover

06:49

Doubt - i read that work is done in an INTERVAL and 'instant' is also a very small interval ... So , Why Instantaneous Work is not defined ?

Work done by a force is product of displacement and component of force in the direction of displacement

Dot Product

John Rennie

@pi-π The code for the functions is not on the stack. It is in the static memory for the process.

Arjun

@TonyPhysicslover that is correct at a elementary level

pi-π

@JohnRennie Okay

TonyPhysicslover

@Arjun So ?

Arjun

i prefer to define it as
work is done by a body when it either transforms energy or transfers it

TonyPhysicslover

06:56

yeah i mean when force is applied , and displacement occur there is a measure of energy transfer.......that is nothing but work

my question is not that though

John Rennie

@TonyPhysicslover are you thinking of situations like collisions, where we assume the collision is instantaneous?

Or do you mean the rate at which work is done i.e. dW/dt ?

TonyPhysicslover

@JohnRennie nope just a simple situation in which mass m is being displaced by the action of force f

@JohnRennie yep

I was reading a textbook and found the statement that said that there is no such term as instantaneous work, however the textbook does not give a reason as to why it cannot be defined.

John Rennie

I suspect it means that work cannot be done in zero time. e.g. in collision one body does work on the other body, but the collision always takes some finite time t > 0 and the collision cannot be instantaneous.

TonyPhysicslover

but instant = small interval of time ..........so Time in this case is not 0

and does it mean that a graph between work done and time is not possible ?

John Rennie

The word "instantaneous" is a little ill defined. It's like the way we define dt in calculus.

TonyPhysicslover

07:06

yeah

John Rennie

When we write a derivative dy/dt the dt is a limit dt ⟶ 0 so it's kind of zero and not zero at the same time.

TonyPhysicslover

yeah it is very small like 0.0000000000000000000000000000000000000000000000000......1

or even smaller

but still there is an interval or passage of time

John Rennie

Suppose the work is some function of time W(t). Then we can define dW/dt and this is just the power i.e. the work per unit time. Yes?

TonyPhysicslover

yes

John Rennie

Just like if we have position as a function of time, x(t), we define velocity as dx/dt.

TonyPhysicslover

07:12

yeah

John Rennie

I think what your book means is that for work to be instantaneous we would need dW/dt = ∞ i.e. the power would have to be infinite.

It would be like saying that for your position to change instantly the velocity would have to be infinite.

TonyPhysicslover

hmmm

Kavin Ishwaran

08:10

@JohnRennie how the time will be when we travel faster than light

John Rennie

You cannot travel faster than light so the question never arises!

Kavin Ishwaran

I know we will never know, but what about the hypothetical tachyonic anti-telephone ?

John Rennie

Physicists often get asked questions like this. The problem is that the laws of physics say you cannot travel faster than light, so if you want to allow FTL travel you have to invent new laws.

But if you are inventing new laws you can invent any new laws you want.

So the answer to your question depends on what random new laws you choose to invent.

Different people may invent diffrent laws and therefore get different answers.

Kavin Ishwaran

so the present laws of physics cannot explain this ?

John Rennie

You say "present laws" as if you expect the laws of physics might change in the future, but the "present laws" that forbid FTL travel are based on a fundamental symmetry of the universe called general covariance. The only way FTL travel could be possible is if this symmetry doesn't apply.

But if general covariance is wrong then all the laws of physics would break down and the universe would be a very strange place.

So I suspect most physicists, me included, have the view that FTL travel is fundamentally impossible and will never be done.

Kavin Ishwaran

08:22

Ohhh

John Rennie

Sorry to disappoint you :-)

Kavin Ishwaran

haha :)

user157860

09:35

@JohnRennie, I John, could you vote to reopen this question?:physics.stackexchange.com/questions/688998/…

John Rennie

@user157860 Hi :-)

user157860

do you think it'ss worth reopening?

John Rennie

The problem is that the electromagnetic mass is a concept that doesn't make sense now we understand that the motion of charged bodies is described by special relativity. The question was closed because it's about history, and I have to say I agree with that.

It would be worth asking the question on the history of science stack exchange as it would be on topic there.

user157860

I just want to learn how how he measured it, the instruments available, It's just an experiment, like MMX or other

the concept, the name has changed, but the increase is there anyway

@JohnRennie, why mass increase is related to relativity?

John Rennie

@user157860 If you apply a force to an object then its momentum changes, and the momentum change is related to the force by the equation:

user157860

09:45

they say it concerns the speed of light and spacetime, hoe does that regard mass increase

John Rennie

F = dp/dt

OK so far?

user157860

ok

John Rennie

In Newtonian mechanics p = mv, where the mass m is constant so dp/dt = m dv/dt = ma

So we get the usual Newton's second law F = ma

But it turns out that for speeds approaching the speed of light p ≠ mv. The equation p = mv is an approximation that only works well for low speeds.

The correct equation is:

p = mv × 1/ √(1 - v²/c²)

Ok so far?

user157860

ok

John Rennie

We usually write the expression 1/√(1 - v²/c²) as the symbol γ and then we write the momentum as:

p = γmv

user157860

09:49

ok

John Rennie

Now, in the early days of relativity it was common to combine γm into a single symbol M so the momentum could be written as:

p = Mv

where M = γm is called the relativistic mass.

The mass m is a constant, but γ depends on the velocity, and that means the relativistic mass changes with velocity. Specifically it increases with velocity and indeed it goes to infinity as v ⟶ c.

This is why sometimes people say the mass increases with speed. This actually isn't correct because they should say the relativistic mass, i.e. γm, increases with speed.

user157860

an electron at near C has, say 1000, rest masses, what does actually increase? the mass of the electron or the mass of KE?

John Rennie

Generations of students have been confused by misunderstanding the difference between mass and relativistic mass, and as a result these days physicists do not use the term relativistic mass at all.

user157860

does the mass of the electron change?

John Rennie

@user157860 what happens is that the equation KE = ¹⁄₂mv² is only an approximation and it breaks down at high speed. The mass of the electron does not change.

user157860

09:55

then the mass in excess is due to KE

John Rennie

The correct equation is KE = mc²(γ - 1)

You can easily show this approximates to ¹⁄₂mv² when v << c.

user157860

999 electron mass

is the the mass of KE?

or what?

John Rennie

An electron near c does not have 1000 rest masses.

It has a mass of me.

You probably know Einstein's famous equation E = mc². Yes?

user157860

just a sec, just consider the speed at which mass is 1000 me, -1 is 999, it means we have accelerated it by 999 x energy of an electron, right?

John Rennie

If you see it written that the energy of an electron is 1000 rest masses what it means is that the total energy of the electron is 1000 mc², where m is the mass of the electron.

The energy of a stationary electron is mc², because for a stationary object E = mc², so that means the KE is equal to 999 mc².

user157860

10:03

right, so the nass in axcess can ony belong to KE, right?

John Rennie

Yes

user157860

to wrap it up, if we give an electron mc2 KE its mass will be equal to 2 mc2, OK?

John Rennie

No

It's mass will be 9.11 × 10⁻³¹ kg i.e. one electron mass.

The mass does not change.

user157860

i did not mean the mass of the electron, but the total mass

John Rennie

The total energy of the electron would be numerically equal to 2mc², but that just means it has an energy mc² due to its mass plus it has a KE numerically equal to mc².

user157860

10:08

but we said that mc2 KE has the equivalent of one electron mass, right?

e=mc2

John Rennie

Right, but that isn't the same as increasing the mass of the electron.

user157860

NO, the total mass

Now I'll try to say something really complicated, can you try to follow me?

John Rennie

But you are just making up the phrase total mass to mean the total energy divided by c². No such concept exists in physics. The total energy is just the total energy - mass doesn't come into it.

user157860

is the total energy different from total mass? we read at LHC that a proton has xxx masses

e0mc2

John Rennie

There is no such thing as total mass. If you read that somewhere it wasn't written by a physicist.

We only talk about total energy.

If you're interested, the equation for the total energy is:
E² = p²c² + m²c⁴

where you should note note that p = γmv.

user157860

10:15

that's Dirac's right?

John Rennie

I don't know who first wrote down that equation. I doubt it was Dirac.

user157860

"This is why sometimes people say the mass increases with speed. This actually isn't correct because they should say the relativistic mass, i.e. γm, increases with speed." Can I refer to relativistic mass?

John Rennie

No, all physicists will run away screaming if you start talking about relativistic mass.

user157860

but mass does indeed increase, and a proton weighs also more at LHS, howshould I refer to it?

John Rennie

Mass does not indeed increase.

A proton does not weigh more at the LHC.

satan 29

10:19

@user157860 mass does not increase

user157860

you mean the proton's mass does not increase?

we settled that

@j

@JohnRennie, to the proton's mass we must add the mass of the KE, right

John Rennie

"the mass of the KE" is a meaningless phrase. KE is not mass.

user157860

you said:"This is why sometimes people say the mass increases with speed. This actually isn't correct because they should say the relativistic mass, i.e. γm, increases with speed" then you added the term is desuete, but the increase is still there?

John Rennie

Sometimes people say the mass increases with speed but they are wrong and they shouldn't say this because it is misleading. If you could somehow weigh a proton as it zoomed past in the LHC (how you could actually do this I don't know) you'd find the weight you measured was just the weight of a stationary proton.

user157860

if the electron mass does not increase and KE has no (relativistic) mass, why the increase? to what is it due? relativity doese not explain that

John Rennie

10:28

I guess you could measure the gravitational field of the proton and get its mass that way. If you did this you'd find the mass is just the regular proton mass.

user157860

maybe it is not affected by gravity ( I read to the contrary, though, I'lltry to trace that) but anyway inertial mass does increase, else we would not need so great force to accelerate it to near c

John Rennie

> inertial mass does increase

As long as you keep insisting on this there is little point in continuing the discussion.

user157860

and what do you call that increase? to what is it due?

John Rennie

The force needed to accelerate near c increases because F = dp/dt and p = γmv.

F increases because γ increases.

user157860

i'll check my reading about LHC and find the right terminology

John Rennie

10:35

OK, but note that if you are reading popular science articles or any articles not written by physicists they may well use the wrong terminology.

user157860

sorry I cannot espress myself,

before you go, can you tell me if it is possible to use the transcript searching for a certain date?

John Rennie

Searching the chat doesn't work very well, and I don't think there is any way to search by date. What are you looking for?

user157860

we had dozens of chats in the past 5 years, very interesting ones, so I'd like to read them over

If I come back from data from the LHC official site will tou accept the wording?

John Rennie

Try this: chat.stackexchange.com/search?user=286498&q=johnrennie

user157860

I am searching the site, but all has changes, I can't find the experiment with 7TV KE

John Rennie

10:43

The LHC site contains some articles written for the general public, and they may also use incorrect terms as explaining the correct terms to non-physicists is hard. As you are finding out :-)

user157860

thanks for the link, it's great

If LHC site is not good, then I have no hope of communicating to you,

but you are so bright, surely know what I am talking about, try to translate my inadequate language

John Rennie

I'm not sure what concept you are asking about.

We've been talking about kinetic energy, and for relativistic speeds the KE is not given by ¹⁄₂mv² but by the more complicated expression mc²(γ - 1). But this has nothing to do with mass.

user157860

this is from wiki, is it rubbish? " The conservation of mass holds even as some types of particles are converted to others. Matter particles may be converted to non-matter particles (such as photons of light), but this does not affect the total amount of mass or energy. Although things like heat may not be matter, all types of energy still continue to exhibit mass.

Thus, mass and energy do not change into one another in relativity; rather, both are names for the same thing, and neither mass nor energy appear without the other."

John Rennie

Can you post the link to the page on Wikipedia?

user157860

Mass

Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration (change of velocity) when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower...

Mass

Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration (change of velocity) when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower...

Thus, mass and energy do not change into one another in relativity; rather, both are names for the same thing, and neither mass nor energy appear without the other."

@JohnRennie, I have to go, leave me your answer , I'll get back sometime

John Rennie

11:31

@user157860 Sorry, my other phoned so I had to break off to chat to her.

@user157860 that bit of the article is talking about a stationary object i.e. it is saying the rest mass of a stationary object is equivalent to the energy of the stationary object, which is quite true.

It is not saying the kinetic energy of a moving object is equivalent to mass.

Transcript for

Problem Solving Strategies