Commons

ProblemsKey√∫⋆A computerized answer check is available online.A problem that requires calculus.A difficult problem.1 You are trying to loosen a stuck bolt on your RV using a bigwrench that is 50 cm long. If you hang from the wrench, and yourmass is 55 kg, what is the maximum torque you can exert on the√bolt?2 A physical therapist wants her patient to rehabilitate his injuredelbow by laying his arm flat on a table, and then lifting a 2.1kg mass by bending his elbow. In this situation, the weight is 33cm from his elbow. He calls her back, complaining that it hurts himto grasp the weight. He asks if he can strap a bigger weight ontohis arm, only 17 cm from his elbow. How much mass should shetell him to use so that he will be exerting the same torque? (He is√raising his forearm itself, as well as the weight.)3 An object is observed to have constant angular momentum.Can you conclude that no torques are acting on it? Explain. [Basedon a problem by Serway and Faughn.]4 The figure shows scale drawing of a pair of pliers beingused to crack a nut, with an appropriately reduced centimeter grid.Warning: do not attempt this at home; it is bad manners. If theforce required to crack the nut is 300 N, estimate the force requiredof the person’s hand. ⊲ Solution, p. 1825 Two horizontal tree branches on the same tree have equaldiameters, but one branch is twice as long as the other. Give aquantitative comparison of the torques where the branches join thetrunk. [Thanks to Bong Kang.]6 (a) Alice says Cathy’s body has zero momentum, but Bobsays Cathy’s momentum is nonzero. Nobody is lying or making amistake. How is this possible? Give a concrete example.(b) Alice and Bob agree that Dong’s body has nonzero momentum,but disagree about Dong’s angular momentum, which Alice says iszero, and Bob says is nonzero. Explain.7 A person of weight W stands on the ball of one foot. Findthe tension in the calf muscle and the force exerted by the shinboneson the bones of the foot, in terms of W , a, and b. (The tension is ameasure of how tight the calf muscle has been pulled; it has unitsof newtons, and equals the amount of force applied by the musclewhere it attaches to the heel.) For simplicity, assume that all theforces are at 90-degree angles to the foot. Suggestion: Write downan equation that says the total force on the foot is zero, and anotherequation saying that the total torque on the foot is zero; solve theProblem 4.Problem 7.Problems 71