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Unformatted text preview: homework 16 YOO, HEE Due: Feb 26 2008, 4:00 am 1 Question 1, chap 8, sect 1. part 1 of 1 10 points A 7 . 1 kg mass is attached to a light cord that passes over a massless, frictionless pulley. The other end of the cord is attached to a 2 . 6 kg mass. The acceleration of gravity is 9 . 8 m / s 2 . 7 . 1 m 7 . 1 kg 2 . 6 kg Use conservation of energy to determine the final speed of the first mass after it has fallen (starting from rest) 7 . 1 m. Correct answer: 8 . 03485 m / s (tolerance 1 %). Explanation: Let : m 1 = 7 . 1 kg , m 2 = 2 . 6 kg , and = 7 . 1 m . Consider the free body diagrams 7 . 1 kg 2 . 6 kg T T m 1 g m 2 g a a Let the figure represent the initial config uration of the pulley system (before m 1 falls down). From the conservation of energy K i + U i = K f + U f 0 + m 1 g = m 2 g + 1 2 m 1 v 2 + 1 2 m 2 v 2 ( m 1 m 2 ) g = 1 2 ( m 1 + m 2 ) v 2 Therefore v = radicalBigg ( m 1 m 2 ) ( m 1 + m 2 ) 2 g = bracketleftbigg 7 . 1 kg 2 . 6 kg 7 . 1 kg + 2 . 6 kg 2 (9 . 8 m / s 2 )(7 . 1 m) bracketrightbigg 1 / 2 = 8 . 03485 m / s . Question 2, chap 8, sect 1. part 1 of 3 10 points A block starts at rest and slides down a fric tionless 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 . b b b b b b b b b b b b 516 g 3 . 5m 1 . 8m x 9 . 81m / s 2 v What is the speed v of the ball when it leaves the track? Correct answer: 5 . 77529 m / s (tolerance 1 %). Explanation: Let : x = 3 . 49857 m , g = 9 . 81 m / s 2 , m = 516 g , h 1 = 1 . 7 m , h 2 = 1 . 8 m , h = h 1 + h 2 , and v x = v . homework 16 YOO, HEE Due: Feb 26 2008, 4:00 am 2 b b b b b b b b b b b b m h h 1 h 2 3 . 5 m g v Basic Concepts: Conservation of Me chanical Energy U i = U f + K f + W . (1) since v i = 0 m/s. K = 1 2 mv 2 (2) U g = mg h (3) W = mg . (4) Choosing the point where the block leaves the track as the origin of the coordinate system, x = v x t (5) h 2 = 1 2 g t 2 (6) since a x i = 0 m/s 2 and v y i = 0 m/s....
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This note was uploaded on 05/04/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner
 Friction, Mass, Work, Light

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