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Question
35
tion of the particle when t= 0.500 s. from the origin to x = 5.00 cm and released from rest at / = 0. ity and the maximum acceleration of the particle? (f) Deter- the amplitude of the motion? (e) What are the maximum veloc- motion? (c) What is the total energy of the system? (d) What is mine the displacement x of the particle from the equilibrium Unless otherwise noted, all content on this page is © Cengage Learning. 33. Given that x = A cos (wi) is a sinusoidal function of time, show angular frequency w, the frequency, and the period of the (a) What is the force constant of the spring? (b) What are the attached to the free end of the spring. The particle is displaced and is partic 41. The si positiv (a) ar the wa 0.500 s. (g) Determine the velocity and accelera- position chat v (velocity) and a (acceleration) are also sinusoidal func- tions of time. Hint: Use Equations 13.6 and 13.2. 42. An 13.5 Motion of a Pendulum mo (a) (d) (f) 84. VA man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 15.5 s. (a) How tall is the tower? (b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s², what is the period there? 35. A simple pendulum has a length of 52.0 cm and makes 82.0 com- plete oscillations in 2.00 min. Find (a) the period of the pendu- lum and (b) the value of gat the location of the pendulum. 36. A “seconds" pendulum is one that moves through its equilib- boo rium position once each second. (The period of the pendulum leo is 2.000 s.) The length of a seconds pendulum is 0.992 7 m at Tokyo and 0.994 2 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations?
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Transcribed Image Text:tion of the particle when t= 0.500 s. from the origin to x = 5.00 cm and released from rest at / = 0. ity and the maximum acceleration of the particle? (f) Deter- the amplitude of the motion? (e) What are the maximum veloc- motion? (c) What is the total energy of the system? (d) What is mine the displacement x of the particle from the equilibrium Unless otherwise noted, all content on this page is © Cengage Learning. 33. Given that x = A cos (wi) is a sinusoidal function of time, show angular frequency w, the frequency, and the period of the (a) What is the force constant of the spring? (b) What are the attached to the free end of the spring. The particle is displaced and is partic 41. The si positiv (a) ar the wa 0.500 s. (g) Determine the velocity and accelera- position chat v (velocity) and a (acceleration) are also sinusoidal func- tions of time. Hint: Use Equations 13.6 and 13.2. 42. An 13.5 Motion of a Pendulum mo (a) (d) (f) 84. VA man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 15.5 s. (a) How tall is the tower? (b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s², what is the period there? 35. A simple pendulum has a length of 52.0 cm and makes 82.0 com- plete oscillations in 2.00 min. Find (a) the period of the pendu- lum and (b) the value of gat the location of the pendulum. 36. A “seconds" pendulum is one that moves through its equilib- boo rium position once each second. (The period of the pendulum leo is 2.000 s.) The length of a seconds pendulum is 0.992 7 m at Tokyo and 0.994 2 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations?
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