The Maths and Science Thread - Collection of Problems and Facts

[AngryPixel]

Thats because light has dual nature: particle as well as wave. A particle must have some mass.

AngryPixel added 3 Minutes and 0 Seconds later...

Light doesn't have a rest mass but it does have a effective mass

AngryPixel added 5 Minutes and 38 Seconds later...

Some people might say that light bends around sun so it must have a mass. Truth is, sun does have enormous gravitational pull but it doesn't attract the light or bends it. It changes the shape of space-time around it.light just follows its path in the space, so when it travels from that bent space time near sun, it gives a illusion that sun's gravity is bending the light

 

[ZoraxDoom]

Wave particle duality.

Sometimes it's a wave, sometimes it's mass.

As E=mc^2 shows, since Energy is constant, as the speed increases, the mass decreases, which means if light were to slow down to regular speeds, it would have a pretty large mass.

But it doesn't. Light travels at the speed of light. That's why it is light. Photons are light. And so they have mass which is virtually 0.

Best explanation I can give ATM.

Although I can be wrong - there is some way of explaining it which explains why when you accelerate a particle in an accelerator, the faster it becomes, the heavier it becomes, and therefore more energy is needed to keep it accelerating at the required speed.

 

[ste_mc_efc]

But if photons have mass, then the speed of light in a vacuum isn't quite the universal constant for maximum speed. Again due to e=mc^2.

 

[ZoraxDoom]

Something in math has me stumped.

You have a sequence (aq)^n-1

You have to find if it is convergent as n approaches Infinity.

It's simple enough. If q is a decimal it approaches 0, if q=1 it approaches a, q=0 it approaches 0, q any integer but not 1 or -1 it approaches Infinity, and if q is negative it alternates.

Then it gets annoying. They're saying that if q is -1, it'll alternate between a and -a. That's correct. But then they say this if q=-1, and a=0 it diverges. Why? Doesn't it converge to 0? Apparently it's convergent if a is anything but 0, which is wrong as well as it's supposed to be alternating...

 

[Varun]

Could somebody help me with this one -

A cell with a given emf is connected to wire as to form a circuit (no resistors, no anything except the cell and wires). When current passes from positive to negative (electrons movement), it develops a voltage A and current B passes in the circuit. When current passes from negative to positive terminal (positron movement?), it develops voltage C and current D passes in the circuit.

How can we find the internal resistance of the cell?

 

[Chewie]

You're doing homework on Christmas Day?

 

[Varun]

Nah, just a problem my friend gave me day before yesterday. Forgot to put it yesterday, so I posted it today.

Of course, I am enjoying my day.

 

[Varun]

I got the idea on how to do that one. So if somebody is willing to know, do tell me.

 

[sachin_rocks]

This is what I think regarding Akshay's question.

Sorry for spelling and grammatical errors. Realized today that typing in photoshop sucks.

this is wrong.
but if you dig through the earth like this there will be two bodies and there will be a separate center of gravity for both bodies and for calculating the center of gravity for semi-circles see this .

and it will depend where EXACTLY is the person to predict the result if the person is in the center the force exerted by both the bodies will be equal and the net force acting will be 0 so the person will move in as people move in vaccum .

 

[Varun]

Two bodies? Earth is a sphere and we aren't cutting it in half. We're just digging through it.

 

[sachin_rocks]

Two bodies? Earth is a sphere and we aren't cutting it in half. We're just digging through it.

if we dig from one end to another it will divide the earth .

 

[AbhishekS]

Not necessary. If you dig a hole, it won't get separated.
Take a sponge ball and a pencil, insert the pencil from any point on its surface, and try to remove it from another point, diametrically opposite to the point of insertion.

The ball which you now have will be how the earth would be if we dig it.

 

[sachin_rocks]

Not necessary. If you dig a hole, it won't get separated.
Take a sponge ball and a pencil, insert the pencil from any point on its surface, and try to remove it from another point, diametrically opposite to the point of insertion.

The ball which you now have will be how the earth would be if we dig it.

got you point .
what confused me was the illustration by you since it was 2d it looked like it was cut into 2 bodies.

 

[AbhishekS]

what confused me was the illustration by you since it was 2d it looked like it was cut into 2 bodies.

That was the best I could do. I am not an expert in graphics to produce 3D illustrations.

 

[6ry4nj]

I would think that the strength of the force of gravity in the 'downward' direction would diminish as you fell through the earth. When you have fallen say 90% of the way to the centre, nearly half of the Earth's mass is now 'above' (behind) you. It will be exerting a gravitational pull on you in the 'upward' direction. If this pull was (for example) .4 of 1G, and the residual downward force was .6G, the net force relating to the downward vector is 1/5th of what it was at the surface, and still decreasing. For this reason (plus air resistance which continues to limit you to an ever-decreasing 'terminal velocity') I don't think you would fall through the centre at all - or certainly not very far.