a-wrench-30-cm-long-lies-along-the-positive-y-axis-and-grips-a-bolt-at-the-origin-a-force-is-applied

Name: a wrench 30 cm long lies along the positive y axis and grips a bolt at the origin a force is applied
Uploaded: 2021-03-23
Duration: 2 min 53 s
Channel: Numerade
Description: A wrench 30 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction $ \langle 0, 3, -4 \rangle $ at the end of the wrench. Find the magnitude of the force needed to supply $ 100 N \cdot m $ of torque to the bolt.

Question

A wrench 30 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction $ \langle 0, 3, -4 \rangle $ at the end of the wrench. Find the magnitude of the force needed to supply $ 100 N \cdot m $ of torque to the bolt.

Carson Merrill · Accepted Answer

so we know an important equation, which is that torque is equal to R cross F, Um, and ar is the vector drawn from the bolt to the point where the force is applied and we know the magnitude of the Turk would just be this, which is also our times f times signed data we&#x27;re theta is the angle between r and F. So we note that, um, this is just gonna be the length of the wrench, which is just 30 centimeters. And then because the wrench lies on the positive y axis, we see that our equals 30 j or given that X f wise along the vector 03 negative four. So now what we have is our cross, um, or rather r dot 03 negative four. And that&#x27;s going to give us 90. But another thing that we have is that a dot B is the same as the magnitude of eight times the magnitude of the times cosine theta. So this is going to be equal to 30 times five times co sign data, so 90 equals 150 coarsened data, which means that data is equal to, um in this case Co ST Data. Actually, coastline data is equal to 3/5 but we want sin data, so we end up getting the same data equals 4/5. We want to find the magnitude of the torque now. So we see that 100 Newton meters is equal to 30 times the magnitude of F the Force times for fifth, which is the sign of data we saw for the force. The magnitude of force, that is, and we end up getting that. It&#x27;s 12 50 over three, which is approximately 417 unions.

Vikash Ranjan · Answer

so this you wouldn&#x27;t bother us. F And this is given as, uh, more on this scientist. Therefore, we are zero three and minus four. This is given as 0 30 0 The 03 minus four. This is even as 19. And we have 19.24 off 30 Squire, you don&#x27;t know of nine plus 16 Gostigian. So it is 91 13 5 Boss There. Four days. She starts this two times. So it is. We&#x27;re gonna find past teacher and a sign TJ will hold upon. No, we have to find you. Don&#x27;t? Yeah. Four talk is even as one up demand have do a science teacher authorities. Andre, you 10 meter is even in the question. What is your 100.30 and Dumanis defaulted on five. So these over 100 of this answer this father always 5000 or to have So this is even more. Our is given us 417 This is that, sir. Don&#x27;t give in

Vikash Ranjan · Answer

in the problem. Fourth equal, £40. Atlantico, 18 inches and Tito papers by bantering, therefore, topic FL Science teacher. But if people do 40 into aiding or toe feet, sign by a tree. This sequence, too. Here are three on here, too. Or discuss this train to 20 times with people 60 into design my tree&#x27;s root tree upon to which is equal to 33. Feed bounds, so we have dark sequence to a T into a tree. Fiji Pass. This is the answer to be given.

Vikash Ranjan · Answer

in the great problem. Four sleepers T Lenti. Whoa, INGE&#x27;s and he goes to buy a battery. So we have If a sign teacher which is given us touchy bass into age or 12 feet, sign three minutes 20 into rood tree. Want to which is equal to en route three feet past. Therefore top equals 10 room, three feet. So this is the answer to give in.

Darshan Maheshwari · Answer

question were given that a force of 20 Newton is getting a flight on that long range, which is attached to a board. So let&#x27;s suppose this is the board on. This is the range on the length of the wrenches given us 0.5 m and the apply force on this range, uh, which is at an angle of 45 degrees to the range. So it does something like this the magnitude of this forces to continue. Then we&#x27;re supposed to find the magnitude of the talk. We know that the talk is f cross deep. The value off fs 20 The D is the distance, which is 0.25 on sign off angle between them, which is 45. So this will become 20 times 1/4 times want Oh, do so the answer will be five over on the unities nuclear meter.

Kara Merfeld · Answer

writes. This problem asks us if we have a 100 pound force and its 1000.3 meters from a point of rotation was the torque on that? So would say we have some some rotating object here and we&#x27;re exerting a force right here on that force is gonna be 100 Newtons. So that&#x27;s 100 doings. Don&#x27;t say the point of rotation is right here. That point of rotation, it&#x27;s gonna rotate around that and then that distance there, um, this 0.3 meters, this problem. So basically, we have the equation. Um, torque is that That&#x27;s the force times. This is right. So force is the 100 Nunes in the distance from the point of rotation. That&#x27;s the 0.3 meters. In this case, um, you know, 100 times 1000.3 would be 30. We&#x27;re gonna be careful of the units. We have a force times the distance, uh, Newton&#x27;s tens meters, and that&#x27;s definitively what we call Jules. It&#x27;s a unit of energy. Won&#x27;t work

Carson Merrill · Answer

a ranch thirty cents and mentors long last long the past y axis and drips out and read it force as applied in direction bureau threatening war at the end of the rich, finding the magnitude of the force needed to spy a handwritten Newton meters torque to you about. So first, go back to our this leak. Accio we used laughter. So here, this is Ciro zero point three meters and you miss the direction of R as a lot of positive y axes. Now what is that? We do know magnitude two outs of force, but we know it&#x27;s a direction off the force. Yes, you know, threatening war. So I should be a scanner. Arms this direction zero very next year for thiss zero three Hey, make you for it now through magnitudes after torque as they cut you the love of our cross. I&#x27;ve So let&#x27;s see First, though we compute our cross This isn&#x27;t about you. That nation this isthe syrup on three you know, three a next year for a Have I minus zero zero zero Your boy Here Los zero zero point three. You know three, eh? Hey, this is cultural negative one point two a half hour. This is love off our trust. If they go to one point two hams, we know this is difficult to watch behind you. So pain. It&#x27;s the culture while you&#x27;re over one point two. So I have as the cultural Cyril and one hundred over one point two times three thiss Ahhh! Andrew off one point two Time three and negative. Ah, hand good one point re times Or this&#x27;LL easily, can&#x27;t you? Zero Two hundred and fifty on here this connective one thousand over three So I&#x27;ve as they caught you a magnitude of off and the country roots Two hundred and fifteen squared plus Conectiv one thousand over three score So let&#x27;s see what it is This number is this is the culture Teo six to, uh zero zero us nine. And this this one thousand It&#x27;s going This&#x27;s a cultural can arms turn over three terms. Good stuff, Juan. Thanks to our you can computed this number by yourself

Carson Merrill · Answer

Hello. I have a question. It is given that Parents 30 Centim long. So uh length is 30 centimetre lies along the positive Y axis. And groups boy at the origin force is applied in the direction zero comma three for minus four at the end of the range. So we have to find the marriage of the force needed to supply and then you to meter. So dark is being given as handed. Newton meters and rent will be the radius definitely it will be the radius of the rotation therapies and images. That is 0.30 m. And force the applied in the direction zero comma three comma. Mine is full. So it is just like this is why here is the board and wrenches lying like this. This is our and the forces applied in the direction zero comma three comma minus four. Remember this is only the direction not the force. So let&#x27;s suppose in any direction this force is being applied. Okay. Our accent why both are positive solid is supposed forces being applied in this direction. Okay. We know that dark equal to ask victor&#x27;s cross affected. Okay. Darkies are victor across affected and if we just take the magnitude it becomes equal to talk equal tours that affected as magnitude of ours are let us say into earth and scientists. So basically we need to find the value tita for that we&#x27;ll be using the fact that the direction of this are victor is direction of this. Our victories zero comma one comma zero as it is lying along the y exist. Okay. And little camera And not 10 comma are because it is a lentil, Alexis are 0.3 m. Why is 0.3 m and zero. And we know that the direction of force is being given as zero comma £3 minus four zero comma three comma minus four. So if we make it dot product that it got ripped off victor expected it becomes equal to magnitude of our victors, magnitude of a vector cost. Uh Cause teacher Okay so this is we are doing for the only for the direction, we are doing only for the direction these things after it&#x27;s not actual force. What direction is it will be corporate of these two which will become zero plus 3 to 0.3. Place zero This magnitude will be zero, press zero point 09 into nine plus 16. And car seat to Okay this is three and 2 0.3 Equal to 0.3. Mhm Little pointy Into this will be 25. So five cost data. These two will get cancelled out. So course it is three x 5 and of course it a three x 5 according to Pythagorean identity. Scientists will be one nine x 25. Before by five. Now let us plug in over here in the formula formula for talk. So talk will be asked f scientist to which is followed by a file. So f will be equal to five and 2 Talk by foreign to us. So five into targets 100 m m by four into, uh, is 30 cm, so 0.30. This will be 25, so 125 by 0. 1 Thing, you know, 25 416 points 67 million. So they should be required force. Thank you.

Problem

Let $ v = 5j $ and let $ u $ be a vector with len…

Problem 41 Hard Difficulty

A wrench 30 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction $ \langle 0, 3, -4 \rangle $ at the end of the wrench. Find the magnitude of the force needed to supply $ 100 N \cdot m $ of torque to the bolt.

Answer

$|\mathbf{F}|=\frac{1250}{3} \approx 417$

More Answers

Related Courses

Calculus

Related Topics

Discussion

Top Calculus 3 Educators

Lily A.

Kristen K.

Samuel H.

Michael J.

Calculus 3 Courses

Vectors Intro

Vector Basics - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 12

Video Transcript

James Stewart

Calculus

Lily A.

Kristen K.

Samuel H.

Michael J.

Vectors Intro

Vector Basics - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$|\mathbf{F}|=\frac{1250}{3} \approx 417$

Calculus

Lily A.

Kristen K.

Samuel H.

Michael J.

Vectors Intro

Vector Basics - Example 1

James StewartCalculus

Lily A.

Kristen K.

Samuel H.

Michael J.

James Stewart

Calculus