Mhm. Okay. So in this video we're trying to we're looking at this apparatus so we have object on a friction full, there is friction on this uh ramp, So that someone attached to a string over a pulley attached to another mass. M2, that is just dangling over the edge uh the box. And we want to know three things. First, we want to know the mass of em too. That is necessary to move M. one up the plane at a constant speed. Mm. Then we want to know em to to move M. One down the plane at a constant speed. And then what range of M. Two S. Will the blocks remain at rest? So, first let's draw our FDD. So for and one. So just to make a little bit easier drawing until ting it. Yeah, So, into the ramp actually, let's keep it keep it. Let's withdraw that, sorry. So and one we got F. G. Straight down towards the center of the earth. Yeah, we got normal force perpendicular, we've got tension, pulling it up the ramp and we got the force of friction opposite motion. That's what's sliding up the ramp towards the frictions opposite. Now, here we have a problem F. G. We really can't use like that because it's in between directions. So we have to break F. G up. So let's get rid of this. We're gonna break it up into its components and we're gonna do that is figure out the perpendicular component, which is just gonna be MG coast data and the parallel components, which is M. G. Side potato. And let's also draw our fPd for our other box. That's too this means a lot easier. We got M two G. Let's actually go back and let's make sure we put in those ones and tubes. These are both, and one's in our previous equations. This one We're going to be right. The force of gravity or in other words, mass to gravity and tension. So essentially, you know, everything is moving at a constant velocity. That means that all of the forces have to be balanced. So for our M two we can write T equals M two G. And for our other box for M one we can write two equations. T equals M one G. Sign. Alfa. You go back and correct that earlier. Yeah. Right. Mhm. We're using alphas instead of fears of the culture. So M one G sine alpha plus force of friction. And we also know that normal force is equal to M one G co sign outside. Okay, we're getting somewhere and one more thing you need, the force of friction when it's moving is equal to mute. Okay? Yeah. Times. FN which in this case are force of friction is going to be um U. K. Times M1G face alpha. Mhm. So if we mash this all together, I'm going to substitute the M2G in for attention. I'm gonna substitute this expression for force of friction. So I'm gonna end up with and to keep Equals M1G sign Alison bus. You okay? M one G coats house? Thanks. So now we can get rid of Gs. So let's cancel those out, be cancels out everywhere and I'm left with and two equals and one side alpha plus UK and one looks oh yeah, especially. Okay, so we got our first part done. Mhm. Yeah. In part B now we're looking at the box sliding down the plane at a constant velocity. So let's redraw our F Bds. So the FBD for M. two, okay, hasn't changed. So you got M two G and T. And they are still equal to each other and for one this time I would have brought the components in already. So we got Tennessee and yeah, yeah. Yeah, force of friction up the plane. Mhm. Yeah. And one she signed alpha. So here we go. Normal force and And one G coats. Yeah. Already. So now let's write our equation for are in one box. Now I'm gonna skip the F N. And M one G close alpha part because that's already gonna be baked into the force of friction. So now we have M1G sign alpha equals T plus UK M one G Coast Alfa. And a little bit room. Let's re write that down alone. I got M one G sign up for equals T plus UK. M Y G cooks. No, mm no we gotta get now we got a substitute in for tea. So that's M1G sign alpha equals. And to G what in the UK? Yeah. M one G coast alpha. Yeah. Again we can get rid of all of our G's. Each one is a G. Some common factor cancels out. So you must subtract the UK and one goes out to the other side. So now I have I am too because and one side alpha minus UK. M one coats. No. Yes. So notice the only thing that changed was in sliding up the ramp. It's N one side Alpha plus U K. M one coast alpha. And in the slide down the ramp it's minus. Yeah. And the real nice thing about going to static friction. This is our last part part seat. What is the conditions for the blocks term made at rest? Two things change. We switch the equal sign to less than or right. Less than or equal Tucson. And we also switch arm us or our location for you guys. So for static friction it only balances out less than or equal to. So the only thing that changes from our two expressions earlier is that I am too has to be less than or equal to and one sign also plus U. S. M one coast Elsa and M two has to be greater than or equal to the reason that is is any lighter then it's going to accelerate down the ramp heavier so it keeps it from sliding down the ramp right? Everyone is almost winning here and trust we agree with an equal to M one side. Alpha made this us 10 1 pulse Alfa. Yeah.