Block A in FIGURE EX7.4 is sliding down the incline. The rope is ...

Question

Block A in FIGURE EX7.4 is sliding down the incline. The rope is massless, and the massless pulley turns on frictionless bearings, but the surface is not frictionless. The rope and the pulley are among the interacting objects, but you'll have to decide if they're part of the system. (c) Draw a free-body diagram for each object in the system. Use dashed lines to connect members of an action/reaction pair.

Accepted Answer

Hey, everyone in this problem, we're given a figure that shows two wooden blocks connected through a massless and frictionless pulley using a massless chain block two is sliding down the incline whose surface is not frictionless and some of the interacting objects are the pulley in the chain. But we need to decide what to include in the system. OK. So we're asked to draw a free body diagram or the objects in the system. We're gonna use dotted lines to connect objects that form action reaction pairs. And when we do this, we're asked to consider the positive X axis in the upward direction along the incline planes. All right. So we're given four answer choices a through D that detail what forces we have acting on block one and block two. As well as whether we have any action reaction pairs, we're gonna come back to these as we work through the problem. So let's start with our free body diagram and we're gonna start with block two, which is on the left hand side and on the incline. So we're gonna draw it on the left hand side. Now, block two is resting on a surface. So there will be a normal force pointing perpendicular to that surface. We're gonna call this normal force N two. We also know that the force of gravity is gonna be acting on this block just like any object. Um And it's gonna point straight downwards. And so we're gonna call that FG two. Now, the other thing we can see in the diagram is attention OK. The string is pointing straight to the right. So our attention force is gonna point straight to the right along that incline. And there's one other force that we have to think about. This block is on a surface that is not frictionless. That means we have friction active. Now, in this case, we're told that the block is sliding down, the incline, friction is gonna oppose that motion. And so the friction force is gonna act to the right upwards of that incline. OK. So it's gonna act in the same direction as the tension. So we have our force of friction, we'll call it F and it's gonna be FK it's kinetic friction because this block is moving. OK. So this is our free body diagram and we're asked to take the direction up the incline plane as a positive X direction. So we have and of our positive X and Y directions on this tilted incline pointing up into the right. OK. So that's for block two. And then we have to do the same for block one. So for block one, we're again gonna have a normal force acting, it's gonna act perpendicular to the surface and we have a force of gravity acting, it's gonna act straight down. We have the force of tension acting. We can see that in our diagram, it's gonna act along that incline in the upwards direction. Hi, this is our attention tea and then we also have friction here. Now if block two is sliding down the incline on the left and these are connected by a massless rope or massless chain. OK. So in order for that chain not to break, that means that block one is gonna be moving up its side of the incline. And so if it's moving upwards, kinetic friction is gonna pose the motion. So it's gonna point down along the incline. So we have FK one. Now let me label this as T one and we'll label the other tension as T two. Now these tensions T one and T two, this is the same chain. It's the same chain. And so we're gonna have an action reaction pair for these tensions. So we're gonna draw a dotted line between those two. Now, for block one, if we think about our positive direction, we're saying that upwards, the incline is positive. So that's to the left along that incline. OK. So these are free body diagrams and now we need to look at these answer choices and think about what forces we have act All right. So let's start by eliminating some of these that don't make sense. And we're gonna start with C and D. Hey, because the very first thing in option C and D says that we have tension along the negative X direction. If we're looking at our diagram, we're taking up the incline as our positive direction, the tension act up the incline. And so those tension that tension force is going to be positive in a positive X direction. What that means is that answer C and answer D are not correct. So we can eliminate those right off the app. And we're left with option A and option B. And what you'll see is that they actually mention the same forces. So for both of them, we have tension in the positive X axis, the normal force in the positive Y direction, kinetic friction in the negative extraction gravity downwards. OK. For block one and for block two, we have tension in the positive X direction, the normal force in the positive Y direction, kinetic friction in the positive X direction gravity downwards. Now how they differ is that in option A? It says that we have action reaction between the chains in option B, it says that there is no action reaction pair. Now, what we know from our diagrams is that we do have this action reaction pair between those chains between those two tensions in block one and block two because we have that same chain A and so what we have is that option A is gonna be the correct answer. In this case, we have all of those forces that we drew in our free body diagram in the correct directions and we have that action reaction here. That's it for this one. Thanks everyone for watching. I hope this video helped.

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