homework 34-solutions

# homework 34-solutions - klare(alk736 homework 34...

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klare (alk736) – homework 34 – Turner – (58220) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A flowerpot is knocked o ff a balcony 18 . 8 m above the sidewalk and falls toward an un- suspecting 1 . 71 m tall man who is standing below. How close to the side walk can the flower pot fall before it is too late for a warning shouted from the balcony to reach the man in time? Assume that the man below requires 0 . 203 s to respond to the warning, and the velocity of sound in air to be 344 m / s. The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 6 . 02171 m. Explanation: Let : v s = 344 m / s , H = 18 . 8 m , h m = 1 . 71 m , and t r = 0 . 203 s . h 2 = gt 2 2 /2 t 2 = t - t 1 h = H - h m t = (2 h / g ) 1/2 h 1 = h - h 2 t 1 = t r + t s h m h m H H 1 The distance from the balcony to the man’s head is h = H - h m and the time for a warning to travel this dis- tance is t s = h v s = H - h m v s . The total time needed to receive the warn- ing and react is t 1 = t s + t r = H - h m v s + t r , and the time for the pot to fall this distance (starting from rest) is t = 2 h g = 2 ( H - h m ) g . Thus the latest the warning can be sent is at t 2 = t - t 1 = 2 ( H - h m ) g - H - h m v s - t r = 2 (18 . 8 m - 1 . 71 m) 9 . 8 m / s 2 - 18 . 8 m - 1 . 71 m 344 m / s - 0 . 203 s = 1 . 61487 s into the fall. In this time the pot has fallen a distance of h 2 = 1 2 g t 2 2 and the corresponding height above the side- walk is H 1 = H - h 2 = H - 1 2 g t 2 2 = 18 . 8 m - 1 2 ( 9 . 8 m / s 2 ) (1 . 61487 s) 2 = 6 . 02171 m . 002 10.0 points Sound waves travel through a liquid of density 783 kg / m 3 at a speed of 4450 m / s. What is the bulk modulus of this liquid? Correct answer: 1 . 55054 × 10 10 Pa. Explanation:

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klare (alk736) – homework 34 – Turner – (58220) 2 Let : ρ = 783 kg / m 3 and v sound = 4450 m / s . In fluids, sound waves are pressure waves, and their speed depends on the fluid’s density and bulk modulus: v sound = B ρ B = ρ v 2 sound = (783 kg / m 3 ) (4450 m / s) 2 = 1 . 55054 × 10 10 Pa . 003 10.0 points A harmonic wave y = A sin[ k x - ω t - φ ] , where A = 1 m, k has units of m - 1 , ω has units of s - 1 , and φ has units of radians, is plotted in the diagram below.
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