00:01
And that's probably, we're given, basically, well, we're given three different situations.
00:08
But we have a two thing, a rope over a pulley here.
00:15
First case, we have a mass here and a mass here.
00:17
And in that case, this weighs 200 pounds, this weighs 100 pounds.
00:21
In the second case, we don't have a mass here, but we just have a force, just a force on this rope.
00:29
A force of 100 pounds, this still weighs 200 pounds.
00:31
And in the last case, and in the first case, there's no force here.
00:36
And in the last case, there's also no force, but now this one weighs 2 ,200 pounds, and this one weighs 2 ,100 pounds.
00:44
So in the first, from the first and the third case, there's a difference in 100 pounds.
00:50
But we'll see that there's quite a bit of difference in the results.
00:54
Now, what i did is we know that if i said this was positive for this, this was positive for that, so we know because this is inextensible, we know that the acceleration of this block has equal this acceleration of this block.
01:09
Looking at this, we have minus wa plus t equals the mass of this block times a.
01:17
Looking at this block, we have, again, positive is down for this block.
01:21
So we have p plus wb minus t equals the mass times the acceleration of that block.
01:27
And i use p here because what i want to do is that, you know, for the problem where there's just a force here, i'm just going to call the weight of this block 0.
01:36
So that basically means this is zero, and then, you know, this tension in the rope is just then p.
01:45
So in that case, you all set, you know, wb to 0 and p to 100 pounds.
01:51
So then they ask, we can solve for the acceleration of b.
01:59
And that wise which is also an acceleration of a of course which is g times you know this this ratio here wb minus w a did i have a yes i need a i need a yeah i'm happy that wrong and this should be a plus sign down here so we have wb minus w a plus p all over wb plus w a plus w a so this is is basically a nondimensional thing and it's kind of a multiplier of g.
02:38
And then they ask us for, let's see, they ask us what for how fast it's going after, after it drops after it changes height 10 feet and then how long it takes to get up to a velocity of 20 feet per second.
02:59
So again, in all cases this thing is going to be dropping because it's heavier or it has more force than what's being applied over here.
03:07
So this one is going to drop in all cases.
03:10
So the first thing they ask us for is, you know, what are the accelerations? well, let's see here.
03:18
I said this was positive for this block.
03:21
So we wind up, we just plug into here, we plug all these values.
03:24
W .a is 200 pounds...