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Chapter 9: Q2 CQ (page 314)
Under what conditions can a rotating body be in equilibrium? Give an example.
The total torque is zero and the angular acceleration will be zero and angular velocity remains constant.
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Question: Even when the head is held erect, as inFigure 9.41, its center of mass is not directly over the principal point of support (the atlantooccipital joint). The muscles at the back of the neck should therefore exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. (a) Calculate the force exerted by these muscles using the information in the figure. (b) What is the force exerted by the pivot on the head?
Two children of mass \({\rm{20}}\;{\rm{kg}}\)and \({\rm{30}}\;{\rm{kg}}\) sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of \({\rm{3}}\;{\rm{m}}\), at what distance from the pivot point is the small child sitting in order to maintain the balance?
Figure \({\rm{9}}{\rm{.1}}\)
Suppose we replace the 4.0kg book inExercise 9.31of the biceps muscle with an elastic exercise rope that obeys Hooke’s Law. Assume its force constant k = 600N/m. (a) How much is the rope stretched (past equilibrium) to provide the same force FB as in this example? Assume the rope is held in the hand at the same location as the book. (b) What force is on the biceps muscle if the exercise rope is pulled straight up so that the forearm makes an angle of 25owith the horizontal? Assume the biceps muscle is still perpendicular to the forearm.
(a) What is the mechanical advantage of a wheelbarrow, such as the one inFigure\({\rm{9}}{\rm{.24}}\), if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of \({\rm{5}}{\rm{.50}}\;{\rm{cm}}\), while the hands have a perpendicular lever arm of \({\rm{1}}{\rm{.02}}\;{\rm{m}}\)? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is\({\rm{55}}{\rm{.0}}\;{\rm{kg}}\)? (c) What force does the wheel exert on the ground?
What minimum coefficient of friction is needed between the legs and the ground to keep the sign inFigure 9.35in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?
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