HW7_Sol_F10 - Oct 11 2010 PHYS 2101 HW#7 WileyPlus Problem...

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Oct. 11, 2010 PHYS 2101 HW#7 WileyPlus Problem Solutions 1 HW #7 Solutions – or at least most of them… (USING BOOK VALUES 9 th Edition in problems; problem # indicated by []) 2) [12-3] 3. Three forces act on the sphere: the tension force of the rope (acting along the rope), the force of the wall (acting horizontally away from the wall), and the force of gravity (acting downward). Since the sphere is in equilibrium they sum to zero. Let θ be the angle between the rope and the vertical. Then Newton’s second law gives vertical component : T cos θ mg = 0 horizontal component: F N T sin θ = 0. (a) We solve the first equation for the tension and obtain T = mg / cos θ . We then substitute : . (b) We solve the second equation for the normal force and obtain . Using , we have 3) [12-5] The object exerts a downward force of magnitude F = 3160 N at the midpoint of the rope, causing a “kink” similar to that shown for problem 10 (see the figure that accompanies that problem in the text). By analyzing the forces at the “kink” where is exerted, we find (since the acceleration is zero) 2 T sin θ = F , where θ is the angle (taken positive) between each segment of the string and its “relaxed” position (when the two segments are collinear). In this problem, we have Therefore, T = F /(2sin θ ) = 7.92 × 10 3 N. 4) [12-11] We take the force of the left pedestal to be F 1 at x = 0, where the x axis is along the diving board. We take the force of the right pedestal to be F 2 and denote its position as x = d . W is the weight of the diver, located at x = L . The following two equations result from setting the sum of forces equal to zero (with upward positive), and the sum of torques (about x 2 ) equal to zero: (a) The second equation gives which should be rounded off to . Thus, (b) F 1 is negative, indicating that this force is downward.
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Oct. 11, 2010 PHYS 2101 HW#7 WileyPlus Problem Solutions 2 (c) The first equation gives which should be rounded off to . Thus, (d) The result is positive, indicating that this force is upward. (e) The force of the diving board on the left pedestal is upward (opposite to the force of the pedestal on the diving board), so this pedestal is being stretched. (f) The force of the diving board on the right pedestal is downward, so this pedestal is being compressed.
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