# Hw 5 - Bell Evan Homework 5 Due 11:00 pm Inst Furlan This...

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Bell, Evan – Homework 5 – Due: Feb 18 2005, 11:00 pm – Inst: Furlan 1 This print-out should have 32 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. The due time is Central time. 001 (part 1 o± 1) 10 points A cart loaded with bricks has a total mass o± 21 kg and is pulled at constant speed by a rope. The rope is inclined at 27 . 2 de- grees above the horizontal and the cart moves 17 . 3 m on a horizontal sur±ace. The coe²- cient o± kinetic ±riction between ground and cart is 0 . 587. The acceleration o± gravity is 9 . 8 m / s 2 . How much work is done on the cart by the rope? Correct answer: 1605 . 56 J. Explanation: T 27 . 2 Summing the components o± the ±orces along the vertical direction provides X F y = F sin θ + N - mg = 0 For the horizontal direction we have X F x = F cos θ + μ k N = 0 N = F cos θ μ k , so that F sin θ + F cos θ μ k - mg = 0 F μ k sin θ + F cos θ = μ k mg F = μ k mg μ k sin θ + cos θ . Since μ k sin θ + cos θ = 0 . 587sin27 . 2 + cos27 . 2 = 1 . 15773 , the work done on the cart is given by W F = F d cos θ = μ k mg d cos θ μ k sin θ + cos θ = 0 . 587(21 kg)(9 . 8 m / s 2 )(17 . 3 m)cos27 . 2 1 . 15773 = 1605 . 56 J , 002 (part 1 o± 5) 10 points A crate is pulled up a rough incline. The pulling ±orce is parallel to the incline. The crate is pulled a distance o± 5 . 79 m. The acceleration o± gravity is 9 . 8 m / s 2 . 8 91 kg μ = 0 292 142 N 1 48 m / s 23 . 4 What is the magnitude o± the work is done by the gravitational ±orce? Correct answer: 200 . 787 J. Explanation: Let : d = 5 . 79 m , θ = 23 . 4 , m = 8 . 91 kg , g = 9 . 8 m / s 2 , μ = 0 . 292 , and v = 1 . 48 m / s . F μ N N mg v θ The gravitational ±orce directed down the plane is F grav = - mg sin θ , and the motion

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Bell, Evan – Homework 5 – Due: Feb 18 2005, 11:00 pm – Inst: Furlan 2 is directed up the plane, so the work by the gravity is W grav = - mg d sin θ = - (8 . 91 kg) g (5 . 79 m)sin23 . 4 = - 200 . 787 J | W grav | = 200 . 787 J . 003 (part 2 of 5) 10 points The work done by the gravitational ±eld is 1. zero. 2. positive. 3. negative. correct Explanation: see Part 1. 004 (part 3 of 5) 10 points How much work is done by the 142 N force? Correct answer: 822 . 18 J. Explanation: W = F d = (142 N)(5 . 79 m) = 822 . 18 J , where d is the distance along the incline. 005 (part 4 of 5) 10 points What is the change in kinetic energy of the crate? Correct answer: 485 . 908 J. Explanation: W f = - f d = - 135 . 485 J . Δ K = W grav + W app + W f = 485 . 908 J . 006 (part 5 of 5) 10 points What is the speed of the crate after it is pulled 5 . 79 m? Correct answer: 10
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Hw 5 - Bell Evan Homework 5 Due 11:00 pm Inst Furlan This...

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