HW 14 - Morby Grant Homework 14 Due noon Inst Drummond This...

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Morby, Grant – Homework 14 – Due: Feb 24 2006, noon – Inst: Drummond 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points A 78 . 3 g bullet is fired from a rifle having a barrel 0 . 783 m long. Assuming the origin is placed where the bullet begins to move, the force exerted on the bullet by the expanding gas is F = a + b x - c x 2 , where a = 15400 N, b = 5720 N / m, c = 36300 N / m 2 , with x in meters. Determine the work done by the gas on the bullet as the bullet travels the length of the barrel. Correct answer: 8003 . 05 J. Explanation: The work is found by integrating the force over the distance. W = Z x f x i F · ds For the force in this problem we have, W = Z 0 ( a + b x - c x 2 ) dx = a x + 1 2 b x 2 - 1 3 c x 3 fl fl fl 0 = (15400 N)(0 . 783 m) + 1 2 (5720 N / m) (0 . 783 m) 2 - 1 3 (36300 N / m 2 ) (0 . 783 m) 3 = 8003 . 05 J . 002 (part 2 of 2) 10 points If the barrel is 0 . 953 m long, how much work is done? Correct answer: 6800 . 85 J. Explanation: For the barrel of length n = 0 . 953 m m, we need only change the limits of integration, W = Z n 0 ( a + b x - c x 2 ) dx = a x + 1 2 b x 2 - 1 3 c x 3 fl fl fl n 0 = (15400 N)(0 . 953 m) + 1 2 (5720 N / m) (0 . 953 m) 2 - 1 3 (36300 N / m 2 ) (0 . 953 m) 3 = 6800 . 85 J . 003 (part 1 of 1) 10 points A block starts at rest and slides down a fric- tionless track except for a small rough area on a horizontal section of the track (as shown in the figure below). It leaves the track horizontally, flies through the air, and subsequently strikes the ground. The acceleration of gravity is 9 . 81 m / s 2 . μ =0 . 3 1 . 4 m 451 g h 2 . 1 m 3 . 53 m 9 . 81 m / s 2 v At what height h above the ground is the block released? Correct answer: 4 . 00344 m. Explanation: Let : x = 3 . 53 m , g = 9 . 81 m / s 2 , m = 451 g , μ = 0 . 3 , = 1 . 4 m , h 2 = - 2 . 1 m , h = h 1 - h 2 , and v x = v .
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Morby, Grant – Homework 14 – Due: Feb 24 2006, noon – Inst: Drummond 2 μ m h h 1 h 2 x g v Basic Concepts: Conservation of Me- chanical Energy U i = U f + K f + W . (1) since v i = 0 m/s.
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