Block A has a mass of 10 kg , and blocks B and C have masses...

Block $A$ has a mass of 10 kg , and blocks $B$ and $C$ have masses of 5 kg each. Knowing that the blocks are initially at rest and that $B$ moves through 3 m in 2 s , determine (a) the magnitude of the force $\mathbf{P},(b)$ the tension in the cord $A D$. Neglect the masses of the pulleys and axle friction.

Transcript

00:01 Here we have this little contraption of three polies and three hanging masses or blocks.

00:10 And so we have one, two cables.

00:12 This cable comes over these pulleys and attaches to the center of this pulley, and then there's another cable rolling over that pulley.

00:18 So we need to do a little bit of kinematics analysis here, but that's not too difficult.

00:27 We know that, let's see here.

00:31 Call it positive down and so i have you know the forces acting on all of our blocks and on here so we'll go through that so let's say we know they're told that this block weighs 10 kilograms and these each way five we know that that this block here drops uh three meters um i think i should need that should be a plus let's see here um yeah that should be a plus because we have um because i said positive was down i think uh let me look up the problem make sure that it said it was it didn't could raise up yeah it could rise up but so let's take a look and see what the problem actually says let's see here, number 28.

01:42 Let's see here.

01:46 28.

01:48 Moves through meter.

01:49 Okay, it just says it moves through three meters in two seconds.

01:56 So it doesn't say, well, we got a load.

02:00 I forgot about this extra load acting on it.

02:04 So we're assuming that it's probably going to move down.

02:06 So i'm going to say it's plus three meters.

02:11 So let's see here.

02:13 We can write newton's laws for each of these guys.

02:17 And so for this guy, we just have the weight minus the t1 equals the mass times its acceleration.

02:25 And we know since this cable doesn't change the length, we know that ad is minus a -a.