1197 Chapter 12 Static Equilibrium and Elasticity Conceptual Problems 1 • [SSM]True or false: (a) r F ii∑=0 is sufficient for static equilibrium to exist. (b) r F ii∑=0 is necessary for static equilibrium to exist. (c) In static equilibrium, the net torque about any point is zero. (d) An object in equilibrium cannot be moving. (a) False. The conditions ∑=0Frand 0=∑τrmust be satisfied. (b) True. The necessary and sufficient conditions for static equilibrium are ∑=0Frand 0=∑r. (c) True. The conditions ∑=0Frand 0=∑rmust be satisfied. (d) False. An object can be moving with constant speed (translational or rotational) when the conditions ∑=0Frand 0=∑rare satisfied. 2 •True or false: (a) The center of gravity is always at the geometric center of a body. (b) The center of gravity must be located inside an object. (c) The center of gravity of a baton is located between the two ends. (d) The torque produced by the force of gravity about the center of gravity is always zero. (a) False. The location of the center of gravity depends on how an object’s mass is distributed. (b) False. An example of an object for which the center of gravity is outside the object is a donut. (c) True. The structure of a baton and the definition of the center of gravity guarantee that the center of gravity of a baton is located between the two ends. (d) True. Because the force of gravity acting on an object acts through the center of gravity of the object, its lever (or moment) arm is always zero.
Chapter 12 1198 3 •The horizontal bar in Figure 12-27 will remain horizontal if (a) L1= L2and R1= R2, (b) M1R1= M2R2, (c) M2R1= R2M1, (d) L1M1= L2M2, (e) R1L1= R2L2. Determine the Concept The condition that the bar is in rotational equilibrium is that the net torque acting on it equal zero; i.e., R1M1−R2M2= 0. )(bis correct. 4 • Sit in a chair with your back straight. Now try to stand up without leaning forward. Explain why you cannot do it. Determine the Concept You cannot stand up because your body’s center of gravity must be above your feet.5• You have a job digging holes for posts to support signs for a Louisiana restaurant (called Mosca’s). Explain why the higher above the ground a sign is mounted, the farther the posts should extend into the ground. Determine the ConceptThe higher the sign, the greater the torque about the horizontal axis through the lowest extremes of the posts for a given wind speed. In addition, the deeper the post holes the greater the maximum opposing torque about the same axis for a given consistency of the dirt. Thus, higher signs require deeper holes for the signposts.6 • A father (mass M) and his son, (mass m) begin walking out towards opposite ends of a balanced see-saw. As they walk, the see-saw stays exactly horizontal. What can be said about the relationship between the father’s speed Vand the son’s speed v?
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