In our first example we will see that we can use a lever arm to greatly increase

Question

In our first example we will see that we can use a lever arm to greatly increase the torque without having to provide more force. Suppose, for instance, that an amateur plumber, unable to loosen a pipe fitting, slips a piece of scrap pipe (sometimes called a "cheater") over the handle of his wrench. He then applies his full weight of 900 N to the end of the cheater by standing on it. The distance from the center of the fitting to the point where the weight acts is 0.80 m, and the wrench handle and cheater make an angle of 19 degree with the horizontal (Figure 1). Find the magnitude and direction of the torque of his weight about the center of the pipe fitting. SOLUTION SET UP (Figure 2) diagrams the position of the force exerted by the plumber in relation to the axis of rotation at point O. SOLVE We have a choice of methods for solving this problem. From (Figure 2), the angle pi between the vectors r and F vector is 109 degree, and the moment arm I is I = (0.80 m)(sin 109 degree) = (0.80 m)(sin 71 degree) = 0.76 m We can find the magnitude of the torque from either r = FI or tau = rF sin pi. From tau = FI, tau = FI = (900 N)(0.76 m) = 680 N m Or, from tau = tau Fsin pi, tau = tauF sin pi = (0.80 m)(900 N)(sin 109 degree) = 680 N m ALTERNATIVE SOLUTION Alternatively, we can start with the components of F vector. From (Figure 2), we see that the component of force F vector perpendicular to r vector (which we call F_tan) is F_tan = F(cos 19 degree) = (900 N)(cos 19 degree) = 850 N Then the torque is tau = F_tan tau = (850 N)(0.80 m) = 680 N m REFLECT The force tends to produce a counterclockwise rotation about O, so with the convention described above, this torque is +680 N. m, not -680 N. m. Also, please don't try to use this plumbing technique at home; you're very likely to break a pipe. If the pipe fitting under consideration can withstand a maximum torque of 698 N. m without breaking, what is the smallest angle at which our amateur plumber can safely stand on the end of the cheater and apply his full weight without breaking the pipe fitting?

Explanation / Answer

torque = rfsintheta

sintheta = 698/900*0.8

sintheta = 0.969

theta = 90- 75.79 degrees = 14.21 degrees

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