The math help thread

Two blocks are sliding towards each other, and hit with one far side hitting the mother in the middle.
A Picture.

 Spoiler

Using math(what ever variables you'd need), how would you predict the movement of the blocks after impact? Include friction, and assume the blocks are identical in all characteristics that would affect the situation, and that equal forces are pushing the blocks together.

Use Newton's 3. law:


By that, divide the blocks into two.



Furthermore, we now assume that the left part of the black block has zero mass, and that the right part of the red block has zero mass. What would happen then? They would simply have the same effect depending if the collision's elastic, inelastic or plastic.

That's the very basic part which you will go and use. But what should be assumed? I need more data. Does the blocks have the exactly same mass at any given point? What kind of collision-type is it? (Mostly this.)

New problem that for some reason I can't get the right answer to.

Find the product of inertia of the triangle bounded by the x-axis, -b, and y = -(h/b)*x.

Product of inertia = ∫xy*dA

Are you speaking of the moment of inertia? I assume that. However, there's no possibility to calculate the moment of inertia if you only have that data. At any given x, how heigh is the triangle at that position? You need a function for the triangle. y = ??

I was going to make a whole new thread about this here, but then I saw this thread so I suppose it goes in here (even though it has nothing to do with homework).

It's about clean slate scrolls. I was thinking about what scroll would have the highest possibility of getting you a slot back. I tried to solving the problem but didn't knew where to start.

So, the problem is as follows: Say you have an infinite amount of 1,5 and 20% clean slate scrolls, what is the chance to success? Which has the highest chance of success?


If I should guess, it would be best to use the 20% scroll, because, suppose there are other clean slate scrolls at x% with x in (0,0.5], so 0.5 having a 100% destroy rate at fail. Then the scroll with 50% has 50% chance of success. Which is definately more than the 1% scroll. (You have success after on average 100 tries, while it gets destroyed after ~50.5 tries. If it were also 50% chance, the chances would be the same.)


It looks like I just answered my own question but what I'm really interested in is the exact chance of the 1,5 and 20% scrolls.

GL

The exact chance? Do you mean the scroll with the highest chance of succeeding in recovering a slot, given you have unlimited amounts of the scroll?

For 1, 3 and 5% slates, there's twice the chance of destroying the item. For the 20% one, there's 50% chance of destroying the item.

Assume p is the chance of working the clean slate, and 2p is the chance of destroying the item. Then, the chance of no effect is (1 - 3p). We have then that



This is the chance for 1, 3 and 5% slates.

For 20% one, we have something else:
The chance of working a clean slate is still p, but the chance of destroying the item is increased to 2.5 instead of 2 only. Then, the chance of no effect is (1 - 3.5p). We have that



And yeah, 2/7 is a lower chance than 1/3, so it follows that the slates with the highest probability of working, assuming you have infinite of them, are the 1, 3 and 5% slates.

Noah