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. (a) Draw an interaction diagram

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Accepted Answer

Hey, everyone in this problem, two metallic boxes are connected to a massless and frictionless pulley by a massless cable as shown in the diagram below. So we have block one sliding down the incline. And we're told that the incline plane is not frictionless. We have some of the objects interacting, we have the pulley, we have the cable. And what we're asked to do is decide whether or not they're part of the system and to present an interaction diagram of the system. All right. So we have block one sliding downwards and it's connected through this massless rope in this pulley to block two. So block two is then going to slide upwards and these surfaces we're told are not frictionless. So let's start with our interaction diagram. OK. And the first thing we're gonna start with is our two blocks. And we know that we have these two boxes and those are gonna be part of our system. So we have block two and we have block one A and we draw them as circles because we're drawing an interaction diagram and those are our objects. Now, these also interact with a pulley. And so we have our pulley and they interact with the pulley through some tension and there's tension on this rope that goes around the pulley. And so the interaction between each of our boxes and the pulley is gonna be through tension and we're gonna call that t and the tension is the same from both of those blocks because it's the same rope that's connected. OK. So that's everything going on with these boxes and the pulley. Now we have to think about what else they're interacting with and they're interacting with the surface. OK. So we're gonna draw the surface and we know that there are a couple of interactions with the surface. OK. So we know that we have friction. In this case, we're told this is not frictionless. So we're gonna have some friction acting between each of the blocks and the surface through friction. OK? And because these blocks are partially resting on the surface, that means there will also be a normal force acting between the surface and the block. So between each of these are also gonna have a normal force and that normal force will be different. In each case, we're gonna call it. Now, the last thing we have to remember to do in our interaction diagram is to think about the entire earth, if we think about the entire earth and we know that there is a force of gravity acting between these blocks and the entire. And so we have our force of gravity FG in both cases. OK. Now, if we think about our system, we know that we don't want to include the external environment. OK. So the entire earth and the surface are not included in our system. So that leaves the blocks, the boxes and the pulley. Right now, the pulley, in this case, just changes the direction of the forces rather than actually participating in the force interaction. OK. It's just changing that direction of the rope, changing the direction of that tension force, but it's not creating tension or anything like that. So that's actually going to be excluded from our system as well. So if we think about our system, in this case, it's actually just going to be these two boxes and the cable because the cable is creating that tension, our system is gonna be inside of this dotted blue box. And if we look at the answer, choices, we were given a option A is that the system is composed of two metallic boxes in the pulley. And so that's not the correct answer. We've eliminated the pulley from our system. Option B, the system is comprised of the two metallic boxes in the cable. And that sounds like what we found. Option C we have the two metallic boxes, the pulley in the cable. Again, we can eliminate that because we've eliminated the pulley. And option D, the system is comprised of the two metallic boxes and the entire earth we know that we don't include the entire earth in our system. OK. That is an external environment so we can eliminate that. And so B is the correct answer here. This matches with the diagram we drew. We have our system comprised of those two metallic boxes and the cable. Thanks everyone for watching. I hope this video helped see you in the next one.

Verified Solution

Key Concepts

Free Body Diagram

Newton's Second Law

System Boundaries