A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0-N force at the end of the handle at 37° with the handle (Fig. E10.7).

(a) What torque does the machinist exert about the center of the nut?

Video transcript

Hi everyone today, we are going to actually determine the amount of torque that the worker is exerting on this range relative to the center of the bowl itself, which is the pivot point. So this worker actually pushes the ranch with a force of newton. So we can write that down as what we know which is the force is going to be 19 newton right here At a distance of cm from the center of the bowl itself or the pivot point. So we want to indicate distance to be our which is just going to be cm and in as a unit it is going to be 0. m. And then the force actually makes an angle of 30° with the handles, which is indicated right here As shown in the image. So the angle that is known is going to be 30° now to start calculating the torque. What we have to do is to actually determine what information pieces do we need to do. So. So the torque itself represented by cow is actually going to be calculated by multiplying our or the distance from the pivot point to the point where the force is exerted on it, multiplied by the force or the amount or the magnitude of force itself that is exerted on the thing. This to have to actually be perpendicular to one another or at a 90° angle. So if not we want to add an angle correction or a correction angle, which is just going to be a sign of data. Right? So, so in this particular example, we know that the force exerted is actually not perpendicular to the radius itself, which is indicated right here. So if it is perpendicular to the radius, we will have this angle right here and the force will actually be exerted in this direction right here. However, it is not the case here. So what we have to do is to actually do a projection of this force right here to do so we want to actually use this angle here and this component right here is just going to be the force multiplied by the sine Of the angle opposite to the component itself. So this is going to be signed off 30° like so, so then we actually will have all the information needed to calculate the torque and we can just plug everything into this formula right here. So these are the earlier we have determined that it is going to be 0.2 m in S I unit. Remember that we have to use all SA units or all the units have to match up and then the force is going to be 19 newton right here, which is indicated 19 newton And then sign data is going to be signed 30 right here. And if you look closely, this last two part right here is going to actually be this projected part right here. So this 19 Newton multiplied by sign 30° is the same thing as I have multiplied by sine of 30°. So we can then determine that the tao by multiplying all these three is going to be nine newton times meter, which is going to be option A, Which is nine newtons times meter. So there you have it. Let me know if you guys have any questions.