Clculate the torque (magnitude and dirertion) about point Ihe force Fin each &f the Cs sketched in the figure: each case; the fone and the rod both lie in the p...

Calculate the torque (magnitude and direction) about point $O$ due to the force $F$ in each of the cases sketched in $\textbf{Fig. E10.1.}$ In each case, both the force $F$ and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude $F =$ 10.0 N.

On this problem. We are looking at the torques applied by various forces on a 4 m long bar. Uh, that is attached to a pivot at one end. Ah, the force being applied in each case is 10 Newtons, and we're supposed to find the torque. In each case, we know that torque is equal to R F. Sign of fee. Uh, so all we didn't do is plug in our numbers and we should be able to figure out pretty quick here, Uh, our is in. It's at the end of ours. This before f is 10 and sign of fee. Uh, sign of 90 is, of course, one. So one and that will be equal to 40 Newton meters next. This one, it looks more like a J T. Uh, this is 120 degrees. Once again, it's at the end of the bar, 4 m away from the pivot. So that will be four times 10 times the sign of 1 20 which is going to be a 0.0 point 866 Yeah, and that will come out to 34.6 Newton meters. Uh, next once again, at the end of the bar. Uh, so that's 4 m. 10 Newtons. Same for each one times thesis. Ein of 30 is one half. So 10.5 and that will give us a total of 20 Newton meters. Uh Ah. This one is a little different. It is 60 degrees, but it's only halfway down the bars or 2 m away from the pivot. So the turkey will be equal to only two for the distance times the same 10 Newtons times the sign of 60 which is once again 0.86 six, which will get us a total of 17.3 Newton meters. Squeeze that in there. Okay, this one is directly on the pivot. So the eso the distance will be zero times 10 times are sign of 60 again is 0.866 But none of this matters because it's all being multiplied by zero. So this will be zero and then finally this one it is being, uh, directed at the end of the bar. So that will be again four times 10 and this. But the sign of 1 80 is zero. So once again, none of this matters. It will just be zero. So if you apply a force at the center of the pivot point or going toward the pivot point, no torque will be created.

Hello. We're going to calculate on problem number one the torque of magnitude and direction. Um, about this point. O thes point owes six different scenarios here. All three of them are going to be using the same rod of length four meters. So in all cases, here are this our length here is four meters. You know when we're done rotating here and then all of them are forced. That's being applied. Is 10 millions difference years that the force is applied a little differently, depending on the situation. So let's go to our definition of what torque is. Work is force times, lever, arm and by lever arm. I mean, it's the perpendicular distance from the force to the pivot point and a. It's pretty simple because this is the perpendicular distance. So our torque here would be four times 10 and that's 14 8 meters now for direction. Okay, counter clockwise torque is considered positive and clockwise. Twerk. He's considered negative. This is a positive counterclockwise to work good. Our next Hunde we actually want need to extend out our lever arm kind of set up a little bit, but putting it a little too high here But the perpendicular distance would go to this point here. And since this is 1 20 be 60 so are perpendicular distance. Here, calculate artwork is four sign of 60 times that 10 that, if you calculate that out, is there before 0.6 meters again. This produces a counterclockwise Twerk, right? See now the same way looking for lever arm the force here or would be this perpendicular distance? The torque here would be four sign 30 times the 10 that calculates too. 20 meters again. This is also producing a counterclockwise tour. Hey, Difference Years or LeBron gives a tad shorter because our forces being applied at the midpoint instead of four here we're going to use to Torque is to interview. Lived here of the perfect distance again would be the sign of 60 times that force of 10 calculates, too. 17.3 ends. Yeah, you know, it's just time still. Well, now this somewhere, actually producing that clockwise tour Hey e and F for a little unique trying to find a perpendicular distance from the force to this pivot point. Well, you actually can't because it's lever arm here is zero. So it's torque is actually zero times that, Tim, Which gives us his zero torque. Actually, same thing's gonna happen here. Finding a perpendicular distance to the pivot point isn't gonna happen. So again, artwork is that zero times 10 cheese. Zero Newton meters. Thank you for learning with me today.

Before getting into solving this problem. It is very important to define directions. So let's say that a rotation in the clockwise direction will be positive and rotation and the counter clockwise direction will be negative. Okay, so now let's begin solving the problem. We have these two vectors force acting on this rock and we know that the rod. We want to calculate the talk about this part, This arch. So let's begin with this one, fourth one. 1st 1 is going to share it pork one, and that is going to be equal to the force times its distance from the center of rotation. So that will be eight mutants times two plus five m. So that is five m. So we have 40 mutants. I'm sweeter. Now let's talk about torque number two. Okay, well that one is heading in the opposite direction so that means that it will result in counterclockwise rotation. So we will have negative force two times distance of course, to the center of rotation, times sign of the end. Because the only component that results in rotation is the vertical component. This other component is simply pushing the rod to the left. It is not rotating it, so that is why we only account for the opposite component of force. Over here, we didn't have to do that because 100% of the force was on the vertical axis. But over here we have 30°. So we have to write negative 12 newtons times two m Times sine of 30°. Thank you. And it turns out that sign of 30.5. So 3.5 times two is 1. So we simply have negative. So new things. Now, it is a coincidence that 12 neutrons times meters is the same as the magnitude of the factory. In all cases, you should always take into account if you have an angle. Now let's find the net pork. Well, the network will be the some of these forks, so that is 40 minus 12, which is 20 eight Newtons. current splitters Remember that this is positive, so that is clock once and that is our final answer.