Physics 41 HW Set 1 Chapter 15

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39. An 10.6-kg object oscillates at the end of a vertical spring which has a spring constant of 2.05 10 4 N/m. The effect of air resistance is represented by the damping coefficient b = 3.00 N·s/m. (a) Calculate the frequency of the damped oscillation. (b) By what percentage does the amplitude of the oscillation decrease in each cycle? (c) Find the time interval that elapses while the energy of the system drops to 5.00% of its initial value.
P 51A small ball of mass M is attached to the end of a uniform rod of equal mass M and length L that is pivoted at the top (Fig. P15.51). (a) Determine the tensions in the rod at the pivot and at the point P when the system is stationary. (b) Calculate the period of oscillation for small displacements from equilibrium, and determine this period for L = 2.00 m. (Suggestions: Model the object at the end of the rod as a particle and use Eq. 15.28.) Let F represent the tension in the rod. pivot (a) At the pivot, F M g M g 2M g (b) L y A fraction of the rod’s weight Mg L as well as y the weight of the ball pulls down on point P. Thus, the tension in the rod at point P is M y y F M g M g M g 1 L L . FIG. P15.51 1 2 2 4 2 Relative to the pivot, I Irod Iball M L M L M L 3 3 I For the physical pendulum, T 2 where m 2M and d is the distance from the pivot m gd to the center of mass of the rod and ball combination. Therefore, For L 2.00 m , L 2 3 M M L 4 L 3 ML 4 2L d and T 2 . M M 4 3L 2M g 3 g 4 2 2.00 m T 2.68 s . 2 3 9.80 m s 2 4 P
Page 2 and 3: P 5 The position of a particle is g
Page 4 and 5: P31 A simple pendulum has a mass of
Page 9 and 10: Discussion Problems: 32, 57, 59, 67
Page 11 and 12: 59.Review problem. A particle of ma
Page 13: 74. Review problem. Imagine that a

Physics 41 HW Set 1 Chapter 15

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