Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

Video transcript

Hey everyone in this problem, we have straps used to manage forces on body parts with injury. Okay. So in this case we have a patient with a jaw injury that needs a net upward force of eight newtons applied to the chin using a strap, we were told that the strap has uniform tension throughout its length and that the angle between T. One and T. Two is 65 degrees. Okay? We're asked what tension should be set in the strap to provide that upward force. And we're giving this diagram here. So let's just draw this out like this. Okay, so we have T. one over here and we have T. two over here. Alright. And we can imagine here, let me just erase this and same thing here. We can break these tensions into their components. Okay? So we have the X component of T. Two. We have the X. Component of T. One. And similarly we have the Y. Component of T. Two and the Y component of T. One. Okay. And if we consider the middle here, of these two tensions we're going to find is that we have T. One, Y plus T. Two, Y. Okay. The sum of the two. Now the angle between T. one and this vertical vector. Okay, we're gonna call this data one in between the vertical vector and T. two. We'll call this data to and then down here between T. One and T. One. X. We're gonna call this phi one And similarly on the other side we'll call it 5 to. Okay, so this is what we have, what we want to find is the tension in these straps. T. one and T. two. Okay. Alright. So let's start working with what we know Now we're told we want a net upward force. Okay? If we want a net upward force, this means That we need T. one and T. 2 to cancel each other. Okay? So we need them to be the same magnitude. They're in opposite directions but we need them to be the same magnitude. Okay? So when we add T. one, X. And T. Two X. Together, we want to get zero. All right. So now we know some information about T. One, X. T. Two X. Let's also recall that we're told we have uniform tension. Okay, what does uniform tension mean? Well that means that the tension T. One is going to be equal to the tension T. Two. And with our X. Components being the same. And our tension being uniform. What we know is that so uniform tension. And this information implies that we're gonna have feta one equals two. Theta two. Okay X. Components are the same uniform tension. So those angles are going to be the same. Now we can find some information out about those angles because we know that the distance between yet the angle between T. One and T. Two is 65 degrees. Well, that's going to be theTA one plus data to Okay, so now we know that data one plus data to equal to 65 degrees. But theta one is just equal to Theta two. Okay, so we can replace it. We get to theta one is equal to 65 degrees. And actually let's do this, let's call theta one equals Theta two. Let's just call it theta. Okay, so now we know that two, data is equal to 65 degrees. So data is going to be equal to 32. degrees. Okay, and that's going to be those angles Data one and data to They're both gonna be 32.5 degrees. Okay, so We know some information about the angle now. Okay, and let's just relate this to five, we know that we have a 90° angle here. So if we're going that theta is going to be 32. then five. Okay. And if data one and data to our equal this means that 51 and 52 are also equal. Okay. Based off of symmetry. And so five is just going to be equal to 90° -32.5° which is 57.5 degrees. Okay. Alright. So now we know all of the angles on our diagram, we know some information about the X components. What can we say about the Y components? Well, if the X components are equal and the angles are equal, this means from symmetry that we must have the Y components equal as well. Alright, so we know the Y components are equal. Well let's go ahead and think about what we want. Okay. We want the net upward force To be equal to eight Newton's. Well the net upward force is just gonna be the sum of R. Two Y components. Okay? So we're gonna have T. One Y plus T. Two Y. And we want this equal to eight newtons. Well we know these two are equal. So let's just call this T. Y. The tension of Y. And so this is just going to be two times detention of Y. Is equal to eight Nunes and divided by two. We get the tension and Y. Is going to be four Nunes. Alright now we have the tension in the Y. Direction and we know the angle so we can go ahead and find what we want. The actual tension force in the um strap that we're using. Okay so we have the fallen, we have this which is T The tension T. Okay, it's gonna be the same. T. one and T2 are the same because we have a uniform tension and all of the components are the same. Okay we have this extension, we don't know exactly what it equals but we have this white tension, we know this is for Nunes. Okay and we know that this is our angle five Which is 57.5°. Well how do we find T T. Is going to be equal to the tension And why divided by sign of the angle. Bye. This is gonna be four. Newton's divided by sine of 57.5° Which is going to be four 0.74. Okay, so that is attention. That needs to be applied to that strap. 4.74 Newtons. Okay. That's going to correspond with answer B. Thanks everyone for watching. I hope this video helped see you in the next one.