Fisica

12
Static Equilibrium and Elasticity
CHAPTER OUTLINE
12.1 12.2 12.3 12.4 The Conditions for Equilibrium More on the Center of Gravity Examples of Rigid Objects in Static Equilibrium Elastic Properties of Solids

ANSWERS TO QUESTIONS
*Q12.1 The force exerts counterclockwise torque about pivot D. The line of action of the force passes through C, so the torque about this axis is zero. In orderof increasing negative (clockwise) values come the torques about F, E and B essentially together, and A. The answer is then τD > τC > τF > τE = τB > τA Q12.2 When you bend over, your center of gravity shifts forward. Once your CG is no longer over your feet, gravity contributes to a nonzero net torque on your body and you begin to rotate. Yes, it can. Consider an object on a spring oscillatingback and forth. In the center of the motion both the sum of the torques and the sum of the forces acting on the object are (separately) zero. Again, a meteoroid flying freely through interstellar space feels essentially no forces and keeps moving with constant velocity.

Q12.3

Q12.4

(a)

Consider pushing up with one hand on one side of a steering wheel and pulling down equally hard with theother hand on the other side. A pair of equal-magnitude oppositelydirected forces applied at different points is called a couple. An object in free fall has a non-zero net force acting on it, but a net torque of zero about its center of mass.

(b)

*Q12.5 Answer (a). Our theory of rotational motion does not contradict our previous theory of translational motion. The center of mass of theobject moves as if the object were a particle, with all of the forces applied there. This is true whether the object is starting to rotate or not. Q12.6 A V-shaped boomerang, a barstool, an empty coffee cup, a satellite dish, and a curving plastic slide at the edge of a swimming pool each have a center of mass that is not within the bulk of the object. Suspend the plywood from the nail, and hang theplumb bob from the nail. Trace on the plywood along the string of the plumb bob. Now suspend the plywood with the nail through a different point on the plywood, not along the first line you drew. Again hang the plumb bob from the nail and trace along the string. The center of gravity is located halfway through the thickness of the plywood under the intersection of the two lines you drew.

Q12.7*Q12.8 In cases (a) and (c) the center of gravity is above the base by one-half the height of the can. So (b) is the answer. In this case the center of gravity is above the base by only a bit more than one-quarter of the height of the can.

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*Q12.9 Answer (b). The skyscraper is about 300 m tall. Thegravitational field (acceleration) is weaker at the top by about 900 parts in ten million, by on the order of 10−4 times. The top half of the uniform building is lighter than the bottom half by about (1 2)(10−4) times. Relative to the center of mass at the geometric center, this effect moves the center of gravity down, by about (1 2)(10−4)(150 m) ∼10 mm. Q12.10 She can be correct. If the dog stands on arelatively thick scale, the dog’s legs on the ground might support more of its weight than its legs on the scale. She can check for and if necessary correct for this error by having the dog stand like a bridge with two legs on the scale and two on a book of equal thickness—a physics textbook is a good choice. *Q12.11 Answer (b). Visualize the hatchet as like a balanced playground seesaw with onelarge-mass person on one side, close to the fulcrum, and a small-mass person far from the fulcrum on the other side. Different masses are on the two sides of the center of mass. The mean position of mass is not the median position. Q12.12 The free body diagram demonstrates that it is necessary to have friction on the ground to counterbalance the normal force of the wall and to keep the base of the...