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10. kg object has the following acceleration components:ax=Josz %+(oss a,= (t9 4-|os7nat is the magnitude of the net force acting on the object at lime t = 4.07 s?N...

Question

10. kg object has the following acceleration components:ax=Josz %+(oss a,= (t9 4-|os7nat is the magnitude of the net force acting on the object at lime t = 4.07 s?NumberFnetWhat is the direction of the net force at this same time? Give your answer as number of degrees counter-clockwise from the +x axisNumber

10. kg object has the following acceleration components: ax= Josz %+(oss a,= (t9 4-|os7 nat is the magnitude of the net force acting on the object at lime t = 4.07 s? Number Fnet What is the direction of the net force at this same time? Give your answer as number of degrees counter-clockwise from the +x axis Number



Answers

Find the magnitude and direction of the net force on the object in each of the FBDs for this problem. In the FBDs, the forces are labeled with their magnitudes.

We have true forces acting on our body and the body is accelerating in a fixed direction. And given that we know the acceleration and one of the magnitude is off the force, we want to know the other one. So we have the acceleration. The composing components in the X and y direction is a cool sign. Data in the eye direction was a sine theta j direction and now we have the magnitude of the acceleration is given us 5.48 meters per second cube and the angle is 38 degrees. And now we used the the Newton's second law to find the I met force. So we know that the net force is equal to the mass times the acceleration and the net forest in this case is f one bless have to is you going to mass time the separation and then we know what fun we need to find that too. So this over factor, So after we can just pass to the other side is and a minus four in Vector. So now we can visit the dividers for this. So let's go to the other board. So I have to Miss Ukraine so and a minus. That's one. So this is a photo. Three points 25. This is the mass in kilograms times as moderns of deceleration 5.48 and then the Acceleration Factories School Sign off 38 I plus sign off 38 j minus. So now minus the force There is only on there I direction minus 8.63 new toes in the my direction and this gives us the result off the force US 5.4 noodles in the eye direction waas 11 New toes in the Why direction. So we want to know the magnitude and they ago So we have the vector. The magnitude is just the square root off the square off each component. So we have the magnitude have to is square root off 5.4 square plus 11 swear And there's this so healthy point two noodles and the angle is just the in verse. 10 agents off If why divided by F packs. So this is 11 divided by 5.4. The Anglo is 63 like a day in Greece. These angle is measured clockwise. From there I direction

So this is the graph I drew for his questions. So the two blue arrows here, other two forces act on the objects and the red arrows. Here is the direction off the path and the direction of the Net force on any object. So now we know that now force came in with the F one class after two, which is evil F one I plus two x i plus up to Why, Jay. So now I can take a vector together and j vector together to have everyone plus at two extends I plus after why J is a good on air force. So we know after axe was just the X component off the force to is you go to after co Santa and the Wycombe from components off the force to is you go to have to Santa. So now we can use have to call Santa substitute for F two acts and have to silently their substitute for up to why so half f neck, which is an effort is go f one plus absolute call Santa has I plus have to sign data test J and we also know that in efforts can we go to mast has acceleration and the acceleration in his case also have X y components. So therefore, if you do sound random here, eventually you have the net force is equal to m a x I plus m a y j. And we know ass is the axe component of the acceleration which is equal to a close eye in Terry degree in his eagle, it goes to our school 3/2 a and in one component over the acceleration issue to a sign very degree, which is you do have a So now we have a century question here. So the Air Force Comey, you go to m a square 3/2 i plus m a over to J, which is equal to F one us after Cassandra I Plus after Santa J now have have long plus after co Santa Ucom way Times Square or three over to em through Santa is real. Anyway, over to it's now have f to call Santa is, um way score 3/2 minus F one and F does. Santa is evil and way over to so have to square. Should we go to have to call Santa to a power to us after Santa to the power to, and it's a sequel to M A. Score 3/2 minutes, everyone to the power to plus and way over to To a Park too. If expending question, we have ah, essential question here. We know the mass off the objects is given to 1.5 kilograms and acceleration is 7.3 meters per sentence. Where and we know the horizontal force is six point Newton. So now that's plugging these values back into the equation to determine the square of the other force, which is after here. And this is you goto 37.2 Newton to a far too so therefore the other force after is able to 6.1 Newton. So now I can determine the direction which is the ah angle fade out here. Since the direction off the force depends on the angle data, so we know after Santa is you go to any way over to therefore who have. Fada is with the inverse time function and may over to have to you plug in the values back into the equation and we'll have any angle. Data is go to 64 degrees in this diagram here. Show the direction for the other force. Have to. And these are the answers. What his question.

I'm just just going to record this because I believe the answer in the back of the book is wrong. I have no idea where that came from, So I'm thinking you're you're gonna think the same thing if they'd A is 60 degrees and the forces 450. Newt. So I'm gonna draw this can. There we go. Um, 60 degrees, 415 Newtons. What's the magnitude of the resultant force? Well, there's only one force here, so it's 450 news and its direction. Well, I already have the direction on there, so it's 60 degrees. I have no idea where the answer in the back of the book came from. Especially 100 55 degrees. I don't know how you get 155 out of, um 60. So I hope you're thinking the same thing

It took me the longest time to figure out what was meant by problem number one. Because I didn't realize that this book puts the diagrams down below. Would have thought it would put it like in between the two questions. All right. Nevertheless, I finally figured it out. Um, actually went through, like, seven questions. And then I realized Oh, wait a minute. Now I get what it meant. Okay, So here's data and years F uh, f We're told that f is 450 and fada is 60 degrees. Okay, We also have 700 Newtons here, and we have an angle here, which is 15 degrees. And what we're supposed to do is determine the magnitude of the resultant force and its direction measured from the X axis. Okay, so the some of the forces in the X direction Oh, are, um f times the co sign of Fada minus 700 Newtons, times the co sign of 15. All right, the some of the forces in the why direction are, um ass, because the sign of data, by the way, F sign theater would be this. Ah, and then 700. These air in opposite directions also. Oh, man. I wanted that to be blue, and then that's the co sign. No, it's not the co sign. It's also the sign. All right, so we need the resultant force and the direction. Um, so I'm not gonna write some here race that I was gonna call that f sub x and f sub y. So the resultant is going to be using the Pythagorean theorem. It's gonna be the square root of the force in the X direction squared, plus the force in the Y direction squared and the angle the tangent of the angle is going to be the opposite, which will be force in the Y direction over the adjacent, which is the force of the X direction. So let me show you how I figured this. If this is f sub X, and this is f sub y, and this is I guess I can't call it fate because I already have a fada. This is fi angle in Here is fi than the tangent is F y over FX. All right, let's just put this into a calculator. Does most dot com is what I'm using. Square it of F X squared, but F x is I'm gonna put in parentheses 450 times the co sign of 60 degrees, minus 700 under the co sign of 15 degrees. And then I want to square that plus 450 and the sign of 60 degrees minus 700 times being sign of 15 degrees. And I want to square that also that gives me 497 Newtons. Our angle is going to be the inverse tangent of F. Why over f x. So I could just copy and paste here of why it's 4 50 Sign 60 0 minus 700 Signed 15 FX is copy and paste also go. I got negative 20 five degrees. So we think about what that means because the book got 155 degrees. So let's look at what we're doing here. Measured clockwise from under no measured counterclockwise from the positive X axis. All right. Usually we measure clockwise. So what I'm saying is that it would be negative 25 degrees, so that would be here. No, that doesn't seem right, because if we add these two up, we're going to get a parallelogram and it's gonna be like this, so it's not gonna be down here. So is it reasonable? The reasonable. But believe that would be 20 night would be 25 degrees. All right, Now, I'm a little confused. So I've got a go back through this again, the force in the X direction and the force in the Y direction. Let me think about whether it measured counterclockwise from the X axis. And I don't see how 155 could be right either. Ah, so I would normally measure room clockwise. All right, so I didn't draw it very nicely. So I'm gonna draw this again. When I calculate this, I get negative 451. So that would be 451 in this direction. And when I calculate this, I get 209. Okay, those would result in this, and so I'm going t o change it so that, um my X value is positive. So I'm just gonna multiply by negative one, and that gives me 24.8. Right? So what I'm saying is that this is 24.8 or 25 degrees, and so this is gonna be 100 80 minus 25 which would be the 155 degrees. And that's our answer.


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