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# hw16_s - homework 16 YOO HEE Due 4:00 am Question 1 chap 8...

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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 ω 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 ℓ = m 2 g ℓ + 1 2 m 1 v 2 + 1 2 m 2 v 2 ( m 1 - m 2 ) g ℓ = 1 2 ( m 1 + m 2 ) v 2 Therefore v = radicalBigg ( m 1 - m 2 ) ( m 1 + m 2 ) 2 g ℓ = 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 . 516 g 3 . 5 m 1 . 8 m x 9 . 81 m / 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 .

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homework 16 – YOO, HEE – Due: Feb 26 2008, 4:00 am 2 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 m v 2 (2) U g = m g h (3) W = μ m g ℓ . (4) Choosing the point where the block leaves the track as the origin of the coordinate system, Δ x = v x Δ t (5) h 2 = - 1 2 g Δ t 2 (6) since a x i = 0 m/s 2 and v y i = 0 m/s. Solution: 1 2 m v 2 x = - m g h 1 v 2 x = - 2 g ( h - h 2 ) = - 2 g h 1 v x = radicalbig - 2 g h 1 (4) = radicalBig - 2 (9 . 81 m / s 2 ) ( - 1 . 7 m) = 5 . 77529 m / s . Question 3, chap 8, sect 1.
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hw16_s - homework 16 YOO HEE Due 4:00 am Question 1 chap 8...

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