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Unformatted text preview: Create assignment, 00224, Homework 1, Jan 10 at 4:03 pm 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. Gravity on a New Planet 13:05, trigonometry, numeric, > 1 min, nor- mal. 001 Having landed on a newly discovered planet, an astronaut sets up a simple pendulum of length 0 . 7 m and finds that it makes 120 com- plete oscillations in 446 s. The amplitude of the oscillations is very small compared to the pendulums length. What is the gravitational acceleration on the surface of this planet? Correct answer: 2 . 00056 m / s 2 . Explanation: Basic Concept A simple pendulum oscil- lating with small amplitude has period T = 2 s g where is the pendulums length and g is the gravitational acceleration at the pendulums location. The pendulum in question made n = 120 complete oscillations in time t = 446 s, which implies the period of T = t n . Thus t n = 2 s g t 2 n = s g t 2 4 n 2 2 = g g = 4 n 2 2 t 2 Thus the planets surface gravity is g = 4 n 2 2 t 2 = 2 . 00056 m / s 2 ....
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