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E Calculate the forces in cables AC and AB needed to hold the 2rb-kg ball D in equilibrium: Take F100*4 and d 0.8*b m [25 pts)12*amFoam...

Question

E Calculate the forces in cables AC and AB needed to hold the 2rb-kg ball D in equilibrium: Take F100*4 and d 0.8*b m [25 pts)12*amFoam

E Calculate the forces in cables AC and AB needed to hold the 2rb-kg ball D in equilibrium: Take F100*4 and d 0.8*b m [25 pts) 12*am Foam



Answers

Determine the forces in cables $A C$ and $A B$ needed to hold the 20 -kg ball $D$ in equilibrium. Take $F=300 \mathrm{N}$ and $d=1 \mathrm{m}$.

In this problem we have given at £2200 wrecking ball is held in static equilibrium by two cables, one horizontal and one at the angle of 40 degree from vertical on were asked to find the magnitude of tension. Victor, T and H. First of all, let's read rather given figure. So this is the diagram of the given situation, and we can solve for the magnitude for the normal force and other force. So this is the diagram which represent the given situation here. We have given the weight off freaking ball that is £2200. It can solve for the magnitude for the normal force on for the other force by using the engine on person function that is engine 40 degree is equals toe magnitude off age upon 2200 it would be equals toe engine 40 degree is 0.839 which is equals toe magnitude off upon 2200. From here, we get magnitude off. Age is equals toe 1846 found Now we have who signed 40 degree is equals toe 2200 upon magnitude off. P, who signed 40 degree is 0.766 is equals to 2200 upon magnitude off key. From here, we get magnitude off. He is equals to £2876. Therefore, the magnitude of P as equals to £2876 on the magnitude off age is equals to £1846.

For the first one. In the figure. We can say now see that the force F. G. Acting downward is equal to this weight of the ball. So if she is a girl to M. G. Given the mass of people lives one g. Or Moss is 1:30 one grand. All we can say the point is a little one catchy. And the expiration due to gravity is 9.8 m/s square. So uh At a point that a little one Kg Multiplied by 9.8 metre for 2nd square. So if she will win 9.8 into 10 to the power three. Newton does the force the force as G Is 9.18- 10. 20. Power three. Yeah. 10 to the Power -3 Newton. No, for the second one, let us first draw the force diagram showing the forces that are acting monday right? Most bit more mm. Uh huh. This is the 4th f. E. Because theater S. F. P. Anger is data. They forced. Mhm. Fine insist their fourth MG angle list it again. And here we have the was Ngos saying they don't in this figure. We can see that F. E. Costa is a girl. Sorry. African sitter is in opposite direction. Two MG scientist to which are equal in magnitude and opposite in direction. So happy cause theta is equal to MG. Scientific. Ah here we need to find the electrostatic force. Ft So let us rearrange this equation A physical MG Scientific one. Because paper this little bit energy then Peta. No, we have a misery .01 Kg. She is 9.8 m. for a second square 10 ties 13°.. That will be equal to 5.65 to 10 to the power minus train. You can does the electrostatic fourth doing the charges this 5.65- 10 to the Power -3. Need to Now for the third one we need to find the charges of each bus. Let Q. BD judge of each voice. Uh No, we'll apply the columns law equation to find the formula for Q. That is a physical too. Okay, Q. A. You be upon our square Here. K represents the columns constant efforts. The force between the two charges and our representative distance between the 22. Um, Judges. So let us replace Q. A. And Q. B. With queues. Okay, sequel. I think going to cuba you upon our square. That will be KQ square upon our square. So Q will see have odd uh fun. Okay, so we have um the force we have forces by point 65-10 to the Power Ministry Newton Are given 0.03 m. So this is square. So square upon columns constant is 19 to 10 to depart 19 new 10 m square per column square. So you will be 2.4 into 10 to the Power -13. Cool. Um, and therefore josh on each ball is 2.4 and 210 to the power 13 Cool.

Okay, so this is the free body diagram. True for the charge court ball. So issue experience. Three different forces once the gravity and I want to see a lot of force that review and the attention from the spring. Okay, so, again, those on decomposing here so the natural force can be decomposed to ask what components sample attention. So we have every X and you want, which is the ex wife components that reports and tst wise. The extra components for attention and angle here is 37 degrees. So there for the white components off the ability forces go to charge. That's the wild components off that review. And the X component of the national is equal to a charge density as a component of the electric view. We know you actually, different question was given its three I pacify j can stand apart fire and you turned piccolo. Therefore, the X components will be that refuses three times 10 to power our find new timber cool. And why component is five times 10 to the power bi. Uh, news and book will. So therefore, we know the X component off the attention can just people tea time sign three Santa degree. Okay. And the white components of attention is equal to teach. High school signed 3 70 So we know that t signed 37 degree has the same Magan to as the axe components off the alleged reports. Okay, so they have same magnitude by ops direction. Okay, so they're broken, set out and eagle to each other, which is gonna kill yaks, and we know t call sanitary some degree. Plus, uh, the white components off the electric force. We'll have the same man to as a gravity. OK, as you can see here. So therefore we'll have tea for sign. 37 degrees people. Two mg wish to the gravity minus the white components off the that your force, which is equal. MGI minus cure you. Why now? We can't say that such a question Here was this t signed signed 37. Nobody calls out themselves degree. Are you seeking a cure? Reax over energy mines. Cool. You are well, now we have tension. 37 degrees able to cure yaks over MP minus cure. You are so eventually we'll have charge Q physical mg tension. 37 degree over the white engine 37 degree plus yaks. And we know the mass of the boys One grand, which is potential power of three killed way and exploration. Grab these 9.8 meters per second squared. You know, you I ax from the, uh, the question here and fill in the information here as well. Okay, so then we can plenty. All these values bring to the question to determine the among the charge Que O K. Which is equal to mg times and 37 which is 01 times potential apartment name three killed were oak times 9.8 meters per second square in times attention 37 degree over you. Why? Attention 37 degree, Which is, uh, five point hello Times potential up Or if I knew Turnbull Cool. And sometimes engine 37 degree. And then plus DX, which is plus, um, three point alot times 10 to the power. If I neutron for cooler and this will give us your money charges about Okay, one point 09 times 10 to the power of Meghni eight cooler. Simple question being he was asking us attention. So from the previous question we know t sign three Some degree, which is the X components about tension as the same man to as the S components off the air Force, which secure yaks. So therefore have tension is just simply able to cure yaks over science 3 73 And we know charge is 1.1910 cents on a a column in the axe is three point all The times tend to power. Find your temper. Quell. So therefore attention is equal to one point. You and I times potential apartment a cooler and sometimes, um, three point low times to tend to qualify New temple. Cool over a sign 37 degree, and this will give us the tension is about five point for three times 10 to the power off. Negatory you don, and he's out answers for this question.

So we're going to denote the tension in the upper left string so t prime This would be upper left string attention uh, essentially the segment BC and then the tension. She would be the lower right string attention. This would be segment A B. We can then say that the supported Wait w would be equal to M times G. This would be 2.0 kilograms multiplied by 9.8 meters per second square. This is equaling 19.6 Newton's. So then we can use the ah some of forces in the essentially applying Newton's second law in the horizontal direction and the vertical direction So we can say T Prime Co sign of 60 degrees. This would equal t co sign of 20 degrees. This would be the ex direction and then for the ah Wai direction we have tea prime sign of 60 degrees would equal the weight plus T sign of 20 degrees. This would of course, be the wind direction. So for part A, we can say that we're going to solve the some above the solve the simultaneous tiny uh, my policy sign solved the equations simultaneously and say that the tension T would be equal to the weight divided by tangent of 60 degrees Times Co. Sign of 20 degrees, minus sign of 20 degrees. This is equaling simply, just plugging in for W 19.6. Newton's divided by tangent of 60 degrees Co. Sign of 20 degrees minus sign of 20 degrees, and we find that attention t in the ah lower right string would be 15 Newtons and then for part B, this would be answered for per day. For part B. A t Prime was equaling T co signed 20 degrees divided by co sign of 60 degrees. We're plugging in for tea, equaling 15 Nunes and so this is equaling 29 noons. This would be the tension in the upper left string for part B. That is the end of the solution. Thank you for what?


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