Recent content by haruspex

No, it's the maximum value of P before A slips on B if B were fixed. Since B can move, the max value may be greater. Just write down the forces and accelerations for each block separately. If the blocks are moving together, they have the same acceleration, a, and the horizontal force between...

The best strategy I can find gives them a mere one in ##^{100}C_{50}## chance, but at least that’s better than the ##2^{-100}## chance without a strategy. It does not use @.Scott's hint, and I confess I do not see how any particular arrangement of the numbers gives a better chance than any other...

I don’t know if it can be formalised, but I once stumbled on this: We know all the roots of sin(x), so write it as a factorised polynomial. We also know the series expansion. Equate the two and pair up the powers of x.

As I indicated in post #22, the answer is predicated on those assumptions. What odds one ascribes to them is another matter.

Not at all. I am suggesting that while microbial life only examples might be ten million times as common as advanced civilisations it could also be that the distance at which we might be able to detect the latter could be a thousand times the distance at which we could detect the former. That...

My basis is the string theory landscape of around ##10^500## equally possible universes. Amongst those, I feel sure b would vastly outnumber c.

True, but coupled with the anthropic principle it has the advantage of solving the "goldilocks universe" puzzle. I don't know why you mention that. It has nothing to do with my post.

In each of those, starting with the first denominator, the terms on the left follow an arithmetic sequence while the numerators on the right follow a quadratic one.

I think you are overlooking the detection requirement. There may be vastly more places where there is just primordial life than anything more advanced, but an industrialised intelligent life would be detectable from a lot further way. As to the Fermi paradox, one answer is based on the...

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...