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Unformatted text preview: 8-1 EQUILIBRIUM AND ELASTICITY8Q8.1. Reason: Because the definition of equilibrium includes !!=0 as well as!!F=!0,an object that experiences exactly two forces that are equal in magnitude and opposite in direction may still not be in equilibrium because the forces could cause a net torque even though the sum of the forces is zero. See Figure 8.1. Furthermore, an object could even have!"=as well as!!F=!(and therefore be in equilibrium) but still not be in staticequilibrium if it is moving at a constant velocity. Assess: Think carefully about the definition of equilibrium, especially what it doesntsay. Q8.2. Reason: See the figure below for a few possible forces. Calculate torques about the pivot point. The moment arm for forces exerted at point P is smaller than that for the force at the end of the rod, so the component of the force at point P perpendicular to the radial line must be larger than that of the force at the tip of the rod. As long as the force has the appropriate magnitude component perpendicular to the radial line, the net torque will be zero. Assess: Note that the pivot provides an additional force that keeps the rod in static equilibrium in the horizontal and vertical direction. Q8.3. Reason: The ladder could notbe in static equilibrium. Consider the forces in the horizontal direction. There is a normal force exerted by the wall on the top of the ladder, but no other object (in the absence of friction) exerts a counterbalancing force on the ladder in the opposite direction. Examine Figure 8.9. Assess: This makes sense from a common sense standpoint. If a ladder is about to slip out one tries to increase the friction at the point of contact with the floor, or to produce a horizontal component of a normal force by wedging it. Q8.4. Reason: As you move out farther on the branch the torque on the branch increases. The support torque provided by the branch must increase for the branch to remain in equilibrium. When the force that provides this torque exceeds the bending strength of the material making up the branch, the branch will break. Assess: The thickness of the branch decreases as you move farther out. This also increases the chance of the branch breaking. Q8.5. Reason: For divers to be stable on the board before the dive their center of gravity must be over an area of support, that is, over the board. Extending their arms moves the center of gravity over the board. Assess: If the arms are not extended, then the center of gravity would be over the edge of the diving board when they stand on their toes with heels extended out. They would not be in static equilibrium and would topple over before getting off a good clean dive. The other option to get the center of gravity over the board (besides extending arms) is to lean forward slightly toward the board. 8-2 Chapter 8Q8.6. Reason: In order to be stable, the centers of gravity of the people must lie over their base of support....
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- Fall '10