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Three blocks (m1 85 kg, m2 20 kg; and ms 15 kg) are arranged as shown in the diagram below . Blocks 1 and are connected by light piece of rope that runS acrOSs a ma...

Question

Three blocks (m1 85 kg, m2 20 kg; and ms 15 kg) are arranged as shown in the diagram below . Blocks 1 and are connected by light piece of rope that runS acrOSs a massless; frictionless pulley Blocks 2 and 3 are connected by separate piece of light rope: The inelined plane has an angle of 0 = 349 and its surface is frietionless. Determine the acceleration of the system of blocks Note: the two pieces of rope will not have the same tension_mzm1mz

Three blocks (m1 85 kg, m2 20 kg; and ms 15 kg) are arranged as shown in the diagram below . Blocks 1 and are connected by light piece of rope that runS acrOSs a massless; frictionless pulley Blocks 2 and 3 are connected by separate piece of light rope: The inelined plane has an angle of 0 = 349 and its surface is frietionless. Determine the acceleration of the system of blocks Note: the two pieces of rope will not have the same tension_ mz m1 mz



Answers

Two blocks are connected by a string over a frictionless, massless pulley such that one is resting on an inclined plane and the other is hanging over the top edge of the plane, as shown in Figure $5-21 .$ The hanging block has a mass of $16.0 \mathrm{kg},$ and the one on the plane has a mass of 8.0 kg. The coefficient of kinetic friction between the block and the inclined plane is $0.23 .$ The blocks are released from rest. (FIGURE CAN'T COPY) a. What is the acceleration of the blocks? b. What is the tension in the string connecting the blocks?

Okay, let's take a look at the $35 for each block. So they freed by government for the hanging block is something like this. Which means that the hang of hope or experience a graph to you from the Earth and the ground, these evil MSG images a massive hanging Bob, and you also experience attention. It was going upward in the direction of an air force on the hanging block. Should be going downward is because the hanging block is trying to move down. Okay. And the everybody that was full of block on inclined plane should be something that is, and the angle between the inclined plane and the grounds. 45 degree. Any block yourself experience of gravity from the Earth, which is, um a g m I am eyes the mass of a block from inclined plane, and it experienced attention that was, uh, moving upward. But along the direction of the inclined plane and only, uh, political direction, you each friends a normal force there was moving upward and which is perpendicular to the inclined plane. And lastly, you also experienced the friction. There was allow the inclined plane, but in opposite direction when compared with the direction of attention and in the air Force off the block on an incline plan should be moving upward, but a long incline play. Okay, so you've reconsidered. Okay, Upward direction on an incline plan is the deposit X axis and the direction that is perpendicular to the incline planes in upward direction is the Y axis. So therefore can decompose the gravity which you will have the s component of the gravity and the y component with gravity. OK, As you can tell, no more force is equal to the gravity times cause I'm 45 degree which is equal to oh, I m i g because I 45 degree. And we also know the friction in his case sixties kinetic friction. So it Ziegel Toby coefficient of kinetic friction passed a normal force, which is you go to meal times M I. G cause I 45 degree and an air force only vertical direction that was perpendicular to the incline plants is equal. Zero is because it blocked in the moving up or down. He only moved along the inclined plane. Okay, so therefore we can say that the net force equation for the block on in climb were just net. I is equal to the tension minus the friction. An M minus name. Ask component over the gravity. OK, which is going which is also going to the opposite direction when you compare with that direction of attention, which is, um, Jane sign for inviting me, which is you go to is the question we put the t minus mu n minus McGee. Sign for my degree. If we expend it will have t minus mule m i g because I 45 degree minus MRG sigh or if I'd agree. And we also know that the net force off the block on Inclined Plan is equal to the mass off the block on an inclined plane has the acceleration A and is or you go to t minus. Um, I gee, because I 45 degree, the I minus MRG sign 45 degrees. So it seems that we don't know how much tension is. Remember, the block on incline plan was connected. Ah, with uh, hanging block to real strength. Okay. Which means that if we take a look at everybody that were funny hanging block, we can have the therefore see questionable hanging ball. Is there definite H music? Green pencil? I have no h. You see? You go to T minus t. OK, because it's going Donald were okay, This is equal to Mohd finest he and then we'll have attention. T is equal to MSG minus f in their age. Which is he going to MSG minus, um age eight. Okay, because then their force on hanging glass is equal to the mass of the hanging above has the acceleration and attention finally hanging Block is you go to the tension on a block off inclined play. Okay, is because they're connected with each other and there in the sand. Sister. Therefore Okay. Along these inclusion here, back into here and we'll have and my a equal to m h g minus. Um, my j Yeah. Minus mule. Am I G cause I 45 degree and then minus am I signed 45 degrees. Okay, I am convinced of the m e J two left side. No have. And my a plus I m a j is able to msg minus you. Am I Jane? Course I 45 degree minus. Am I sigh 45 degree. Okay, So now I can determine acceleration off this system, which is you can take a out. We'll have eight times in my plus image is equal to MSG minus, um, I g cause I 45 degree minus. Am I signed for by degree, you know, have a which is the acceleration. So you go to MSG minus, Um, I oh, j cause I 45 degree minus. And why so everybody me divided by and my plus a mate And from the question we know the Mbai, which is, uh, mass of the block on an inclined plane is 2.0, kilograms. And the mess overhanging block image is able to three point. I'll kill where a coefficient of a kinetic friction is given a 0.1 I and we know the acceleration of gravity, you see, go to 9.8 meter a second square. We know, cause I'm 45 degree and signed 45 degrees right now. So cause I or if I agree, is you go to So for if I'd agree, which is square to over to. Okay, So if you're plugging these values back into the equation here we'll have. Acceleration is equal to, um three point. Oh, you were kinds nine point a meter per second square minus Joe 0.1 I times 2.0 killer worms times Now I'm going eight meter per second square and end Times Square to over to minus to a bono kilograms times 9.8 meters per second square 10 times square to over to and it's holding here, divided by 2.1 kilograms plus 3.1 kilograms and this will give us acceleration is equal to 2.6 meter But seconds were okay Simple question Be things when we know the acceleration of on a question A Now we can determine attention on us on a string OK, was his tea is equal to remember Fun question a worry Uh, this the equation pretension which is right here. Attention is evil toe msg minus Emma Jay Gray. That's right down. So its able to msg minus amazing A Which can we go toe image G minus a. We know the mass overhanging block image is 3.1 kilograms 10 times G minus eight, which is the XRs on ground D minus the acceleration off the block, which is not going a university square minus 2.6 University Square. And this will give us attention is about 21. Only six new times. If we run into the tens digit, we'll have 22 newshounds. I'm sorry. No intense digits. Integer here. So is about 22 new times. Okay, so this is the answer for this question. Thank you.

In this problem for part A. We're trying to find the free body diagram for both the same block in the block of the table. This is how I set up my system with the positive extraction being to the left in the positive direction, being downward. So if we draw the hanging block here as a point source, then downward it is mg and a board. We have the tension of the rope and those were the only two forces on the pain block. Now, as far as the block on the table goes, we have it won't force on a force down equals for G because the mass of the block on the tables, four kilograms, we're attention to the left. Well, for part B, our goal is to find the acceleration by the block and to do it. So I'm going to apply some of the forces in the ex direction physical mass times acceleration, the extraction for the table block. And so the sum of the forces is equal to attention, which is positive because to the left, and that's how I could find my coordinate system. And then that's the only horizontal force is just equal to mass times acceleration the extraction this yields a is equal to t over for at this point, I'm just taking the magnitude of the vectors here. And then we're given T as fifteen. So the suffice to three point seven five meters per second squared in part. See, our goal is to find the mass of the hanging block. And to start by doing this, we're going to write out Newton's second law in the wind direction for the hanging block. This implies that positive MG because it's downward and that's hard to find. My coordinates system, minus tension, cause tensions upward, and this is equal to the massive pain block. Times acceleration him block. And this acceleration was the same as three point seven five because when one block six sellers, the other follows its lead. And so we can solve this for the Mass and we do that we get the mass is equal to the tension over G minus a and then playing in the values for G and T, we get that this is two point forty eight kilograms. No for party. We need to figure out how the weight of the hanging block compares with attention and so the weight of the hanging block is equal to and ten G where it was the massive hanging block. We found that in the previous part to be two point four eight kilograms. So we're gonna multiply this by nine point eight to get twenty four point three. Nunes attention was given to us as fifteen Nunes, so the weight close pain block is greater than attention, meaning that the block oil faults of floor and I see into the problem.

Hello, everyone in this problem, we're going to find what the acceleration of two blocks connected in such a way as shown in this diagram is. And then we're going to find the missing mass that we don't know in this problem. So we're told that to masses, a big mask with 4 kg is resting on a horizontal surface that has no friction. And two, it would tie a massless rope or approximately massless trope. That then goes over a pulley and attach is to a smaller mess. Ma'am, we're told that once the blocks are released, the tension on the rope is 15 buttons, and so we are asked to first draw a free body diagrams. So for the big mass, we just have that there is a force of gravity. So the weight of this mass acting on the object and the normal force that's in the Y direction but in the X direction, we also have the tension acting on this mass. There is no, um, friction force because, as we were sold the tabletop or the surface as friction. Less so. This is the frequent diagram for the big mass for the small mass. Uh, we only have the force of gravity. So the weight of the small mass and the force of tension coming from the road acting outwards. So that's the frequent diagram for, uh, for these two objects. We've got this for big mess and this for the small mess. Uh, and the part of the river has defined with the acceleration of the blocks are now the acceleration of the blocks are the same for both blocks because the length of the rope is fixed. So if this mass moves that amount or a distance, D, then this mass must follow distance the so the acceleration of the two is going to be the same. And this acceleration can find from the equations for from the equation for for the big mass, because for the big mass in the X direction we have that the mass times acceleration. So the net force is equal to just attention. And so, using that, we can find that a is equal to detention divided by the big mass, which works out to be 3.8 m per second squared. So now that we have this acceleration, we can actually find what the small masses. So if you look at the we look at the free body diagram for the small mass, we noticed that in the Y direction this mess is going to be moving, so it's going to have some acceleration. So the Net Force is going to be, um, time is equal is going to be equal to its mass times acceleration. And the net force in this direction is, um w m So the weight of the small mass minus attention. So here we've chosen, we know that the block is going to be falling. So we chose to we choose the downward direction to be positive. And so we've made respected the downward direction. The weight is positive and the tension is negative. So that's how we arrive at this exploration. And then we just plug in the values So we know that w, uh, answer that wait is mass times the gradation accelerations about mg and then rearrange this equation for little M, which works out to be detention divided by the difference between the gravitational and the and the acceleration of, uh of mass began and putting in the values we find that this mass is 2.5 kg. Okay. And then in part D were asked to find how were asked to compare the force attention with the gravitational force of the of the little mess. So the weight of the mass, and we find that that ratio is 0.62 which if this ratio is greater than one, then that would mean that the, um tension is greater if it's smaller, that means that energy is greater than teeth. And so here we have this number 0.62 is smaller than one. So we have detention is smaller than the weight of the of the little mess.

In this problem, we have to blacks. One weighs 2 kg and the other weighs 3 kg. Tied together with masks rule. The rope is blown over a massive resistance free holy blocks of released rest. When we want to find the tension in the cable here and the acceleration of the blocks Thank you. So we can cable here Gruff three by diagrams of me to be blocks for this block. You have attention. I'm gonna call this positive. With this block we have the tension minus the weight equals the mass, its mass times, its acceleration for this block. I'm gonna call this positive because we know because this this table where sermon doesn't stretch, that the displacement of this block down must be equal to the displacement of this block. So for this, but we have the weight minus attention equals its mass times the same acceleration that we have here. Obviously, I could have put minus minus plus and that would have just said if I would have made this positive, I would have had to say that the acceleration of this block was the negative of acceleration of this. So either way, we can just make sure was consistent with signs. So what I did is even eliminate a from these two equations by multiplying this equation by m to look playing this one by m one and then subtracting too. And this is what you get. So that gives us leaves us with our only unknown Well, only there are only unknown being key we can solve for t plug in our values for m one of them to get t equals five, not 12. 50 She so 12 50 is what we get for attention in this cable A little over, you know, But what is that? That's two on a 2.4 G. Now for the acceleration. We could just take one of these equations. I guess I took first one here. And since we know T now it's all for a and we complex. What? He is been substitute for TV from here. And we get this and then doing some, um, algebra. You get that? And what the A. He was the difference in the masses times g divided by the sum of the masses. And that one's that being t over five. So it's, you know, point to


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