Recent content by Sourabh N

@bcrowell - I cannot say anything about the WP conformal diagram (it looks flat out wrong at first glance, but I'll get back to you). As for the diagram in #3, it is common practice to draw the center as a vertical line (since the center is supposed to be timelike). But if you actually perform a...

I'm not sure what is part of Calculus II (Non-US bachelors, sorry). But in any case, if using Cartesian coordinates, having your origin at the top of the spherical cap (the north pole of the sphere) gives the bounds as x = 0 to r, y = 0 to r and z = 0 to -h, with the constraint that x2 + y2 + z2...

The integration (whose bounds you are speaking of, presumably) would be considerably simpler if done in spherical polar coordinates.

Magnitude is the absolute value, so, yes, it will always be increasing. If your answer was "it depends on relativity, being as its a vector quantity (i.e. up can be negative or down can be negative)", it's absolutely right. But if instead your answer was "it depends on relativity, being as its...

Yes, that is correct. It's possible that your teacher was thinking about the magnitude of the velocity (also known as speed) which does increase as the object starts falling downwards.

Define a new variable, say, j. How should j and k be related so that j goes from 1 to 6 when k goes from 3 to 8?

The boldface part is not right. What you have in the first line is V_{1} = \frac{1}{T_{1}-10} - 4.5 and the second line doesn't agree with this. It should read \frac{1}{T_{1}} = \frac{1}{T_{1}-10} - 4.5

Yes, that is correct. I think instead of ft/s, you should stick with miles per hour. Then, you will have two equations in two variables! Do you see it?

Yes, here you can use velocity and speed interchangeably. Notice how the question says "When you increase your speed by 4.5 mi/h" ... it means V2 = V1 + 4.5. How do the equations look now?

Look at the line I have boldfaced. The question says the speed increases by 4.5 mph, but you're increasing your distance D by 4.5 :eek:

Ah! That's enlightening. Can you draw the forces on the "object" and the "tube", possibly in two separate figures (to avoid confusion)?

Trying to understand the point you're making - are you suggesting a levitating mechanism using magnetic fields?

It seems a popular assumption -- "Consider a black hole that forms from collapse of some pure state" (quoted from the AMPS paper). I don't see an obvious reason for this though. Can someone explain this or direct me to one?

Step 0: G\frac{m_{earth}m_{ spacecraft }}{r^2} = G\frac{m_{moon}m_{ spacecraft }}{(r_{earth-moon}-r)^2} Step 1: \frac{(r_{earth-moon}-r)^2}{r^2} = G\frac{m_{moon}m_{ spacecraft }}{Gm_{earth}m_{ spacecraft }} Step 2: \frac{(r_{earth-moon}-r)}{r} = \frac{\sqrt{m_{moon}m_{ spacecraft...

Exchange LHS numerator and RHS denominator. Take square root. Do you see it now?