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The 4.00 kg block in the figure is attached to a vertical rod by means of two strings.When the system rotates about the axis of the rod, the strings are extended as shown in Figure 6.31 and the tension Figer cord? Start with a free (b) What is the speed of the block?

See solution.

Physics 101 Mechanics

Chapter 6

Circular Motion and Gravitatio

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

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Okay, so the block moves around this rod and ah, this block makes a circle while rotating around the rod. So let's say the radios that a block makes is our And if you wanna draw everybody, diagram ofthe this system on What we'll do is we'll draw you a diagram on the block. So let's mark the Y an X axis first. So this is our wide the vertical direction and exist the horizontal direction now their toe strings that's attached to the block. So that means there will be a tensile force along this way and along that way. So let's call the upper one Stu. That means that string are the tensile force that's acting on. And dude under blood due to this chain will be team you. And then there will be a component along the extraction and there'll be another component along the wind direction. So it's Jordan those right? And let's call this angle angle, Tita. So if this is angle data, so the component off this tension on why access will be see you cause I ain't Ada on dawn exacts is it would be to you signed data now. Similarly, we have another string. That's Ah, attaching on this area. So we call it T n. So let's call it T end There and again there will be two components. One is along the extraction and won is along the wind direction, so we call the wider component. So again, if we want to look at the angle that it's making, ah will see that this angle right here is angles, Ada. So the component will be TL co sign data, and this will be ta a scientist. So it's TL science data right on DH again, since the since we have gravitation force that's acting downwards will have a component for that as well. So we'll have empty hands acting downward and due to all the forces that's combined together, we'll have Redl acceleration towards the center off the circle, and we call it a radiant right now, a few things that we need to compute before we move on to our parts. First of all, we need to know the radios that the block is making while it's rotating around the rod. We see that here this angle is 90 degree and this is half off this total length so the length from here to here will be one meter and ah if and we know that this length is 1.25 meters. So if we use Pythagorean theorem there we can solve for this distance are so are will be ah, this length squared minus the other one. So it's 1.25 squared minus one, neither squared and that gives us 0.7 meters. So we know that the radius off that block is the readers of the servant this 0.75 meters. Now, if we wanna calculate the angle that it's making, ah will do the similar approach here. So it's going to be one meter, which is the base, which is Ah, this guy right here and then the distance are the length of the string is 1.25 meters. So base overhype witness gives us co signed data and from there we solve for theta we get 37.9 degrees. So this to anguish idea there are 36.9 degrees and the reason he strangles or similar is because the length of the string is same for the lower and the upper half. So that means whatever angle it's making over here or whatever angle it's making over here should be equal to bang. Let's make that's created here, right? So now let's look at the parts that we need. So for part A, we need to find out the attention due to the lower half of the string on the lower strain. So again we do this everywhere diagram over here so that we can understand what's going on. So as we mentioned that we have all the components along X and y axis, if we consider the Y access on, did you consider all the forces that's acting on the Y axis? We see that we have tea. You co signed data which is, ah, upwards in direction. And then we have two forces that better downwards. Ah, wanna steal consented and one is the one is m times c. Diff. We considered the upward motion as positive direction. So we'll have positive to you co signed it and then we'll have negative teal co sign for the downward more downforce and similarly will have md as negative. And from there we can solve for TL. We know that t u is 18 mutants and then masses. For Katie, gravity is 9.8 and we already calculated to cause Cinta, which is 36.9. So they raise their 6.9. So free. Take those and data we get 31 newness. So notice one thing that this attention is actually smaller than the tension. That's Ah, on top of the upper part of the tension. A cz we see that upper part of the tension is 80 Newton's, although TL is 31 mutants. And the reason for that is because there's an extra force that is acting down, were due to the weight of the block. So that force and the lower part of the tension our counterbalanced by the upper part of the tension. That's why the upper part of the tension is higher than the lower part, right? And for the second part, we need to find the speed of the book. So for that, we can use the X direction and motion and we see that in extraction we have this radial acceleration. So we know that the radiant acceleration is equal to the square over our If we use that value on DH, we multiply that by am we get the force that's acting on the extraction, and that should be equal to the forces due to the tension off the two strings. So we have to use scientist Antti L scientist and they're all acting in same direction. So we considered this way as positive we can put. So that's why these two guys are positive here. So we have to you plus TL scientific data, which is equal to the acceleration times mass. And from there it's all for V. We get this fall expression on. We know are We know t u t I and stayed on m so rry plug in the numbers. We see that the velocity is 3.53 meters per second. Thank you.

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