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p201f04-homework07-sol

p201f04-homework07-sol - Version One Homework 7 Heinz 81204...

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Version One – Homework 7 – Heinz – 81204 – Oct 07, 2004 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Serway CP 05 76 08:05, trigonometry, numeric, > 1 min, wording-variable. 001 (part 1 of 1) 10 points A 2 kg block situated on a rough incline with 37 angle is connected to a spring of negligible mass having a spring constant of 100 N / m. The block is released from rest when the spring is unstretched, and the pulley is fric- tionless. The block moves 20 cm down the incline before coming to rest. The acceleration of gravity is 9 . 8 m / s 2 . 100 N / m 2 kg μ 20 cm 37 Find the coefficient of kinetic friction be- tween block and incline. Correct answer: 0 . 114709 . Explanation: Given : m = 2 kg , θ = 37 , k = 100 N / m , and Δ x = 20 cm . The work done by the friction force is W f = ( f x cos 180 ) Δ x = - μ k n Δ x = - μ k ( m g cos θ ) Δ x Applying the work-kinetic energy theorem, W nc = W f = Δ K + Δ U s + Δ U g . Since the block stars from rest and comes to a stop, - μ m g Δ x cos θ = 0 + 1 2 k x ) 2 - m g Δ x sin θ . Thus μ = - k Δ x 2 m g cos θ + tan θ = - (100 N / m) (0 . 2 m) 2 (2 kg) (9 . 8 m / s 2 ) cos 37 + tan 37 = - (0 . 638845) + (0 . 753554) = 0 . 114709 . Return to the Shuttle 09:01, trigonometry, numeric, > 1 min, nor- mal. 002 (part 1 of 1) 10 points A(n) 65 kg astronaut becomes separated from the shuttle, while on a space walk. She finds herself 50 m away from the shuttle and mov- ing with zero speed relative to the shuttle. She has a(n) 0 . 65 kg camera in her hand and decides to get back to the shuttle by throw- ing the camera at a speed of 12 m / s in the direction away from the shuttle. How long will it take for her to reach the shuttle? Answer in minutes. Correct answer: 6 . 94446 min. Explanation: Let : M = 65 kg , m = 0 . 65 kg , d = 50 m , and v = 12 m / s . Because of conservation of linear momentum, we have 0 = M V + m ( - v ) m v = M V
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Version One – Homework 7 – Heinz – 81204 – Oct 07, 2004 2 where V is the velocity of the astronaut and it has a direction toward the shuttle. V = m v M = (0 . 65 kg) (12 m / s) 65 kg = 0 . 12 m / s . And the time it takes for her to reach the shuttle t = d V = 50 m 0 . 12 m / s · 1 min 60 s = 6 . 94446 min . Serway CP 06 59 09:01, trigonometry, numeric, > 1 min, nor- mal. 003 (part 1 of 2) 5 points A small block of mass 55 g is released from rest at the top of a curved frictionless wedge of mass 333 g which sits on a frictionless hori- zontal surface as shown.
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