Recent content by haruspex

No, as I posted, you just need to assume the objects are arbitrarily rigid. That does not conflict with assuming the collision to be perfectly elastic.

True, but then we have to start worrying about friction and rotation of the ball, so we have to take the materials to be elastic but arbitrarily rigid.

Looks to me that @putongren has been consistent in using h for the cliff height.

So why do you quote Relevant Equations: K=1/2 m v^2 ? (But you also need to assume the package does not slide off!)

First, let’s tidy the question up. The impact is given as elastic. The impact takes some time. The force the two bodies exert on each other varies over that time, reaching a maximum at the half way point. So maybe you are asking how the maximum force depends on impact location, but it would...

I read post #8 before I posted on the thread. The point of post #49 is to show that that starting value produces a lower bound. Post #8 did not show that. This, in principle, has nothing to do with rates of convergence, whether merely observed or proven. If a mathematician wants to claim the...

Yes, yes, I know all of that as you do. But I have come across people who have read the oversimplified "heat flows from a hotter body to a colder, not the other way", from sites that ought to get it right, and come away with the belief that it is all one way, not merely one way on balance. I...

I did not understand that bit. What is a "radiant temperature"? Isn’t that anything above absolute zero? And do you mean more heat or a higher temperature? Do you just mean the flow of heat is slower if radiation is the only mechanism?

Who are "they" here? Google "second law heat flow" and you will find plenty of apparently authoritative sources that say such as "heat always flows spontaneously from a hot object to a cooler object, and never in reverse on its own"...

No, post #8 observed that it gave the fastest convergence seen. My posts on this thread are all primarily concerned with bounds. These are not the same thing. Unless proved otherwise, it could be that the sequence generated by starting with 9 * 10n oscillates around the limit. I showed that...

That’s not what I suggested. If you take all the "horizontal" resistors (I am taking the ladder to be horizontal, as in post #1, so the rungs are vertical) to be zero after n, the vertical resistors thereafter are all in parallel and can be evaluated to ##9*10^n##. That gives a lower bound for...

A lower bound for the resistance in the infinite case. The OP's original way of starting with a finite ladder, taking all vertical resistances to the right to be open circuit, gave an upper bound for the resistance of the infinite ladder.

That gives an upper bound. Since the horizontal resistances are so small beyond n=20, how about taking them as zero, giving an initial ##r_n=9*10^n## to get a lower bound?

Yes, I only discussed radiation. So what is the full expression for the rate of loss of heat at the air surface… ##A(T_{block}-T_{air})+\epsilon(T_{block}^4-T_{air}^4)##? How so? Isn't it just a matter of two different equations within the blocks with a common boundary value? Why do we care...

It is in principle unless the near and far faces are perfectly insulated. The time it takes T2 to reach a particular temperature will depend on the transfer through the composite. You have to model that too.