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(7) - Create assignment 00223 Homework 5 Oct 02 at 10:06 am...

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Create assignment, 00223, Homework 5, Oct 02 at 10:06 am 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. Conceptual 08 03 07:01, highSchool, numeric, < 1 min, normal. 001 A car is moving at 60 miles per hour. The kinetic energy of that car is 500000 J. How much energy does the same car have when it moves at 120 miles per hour? Correct answer: 2 × 10 6 J. Explanation: Let : v 1 = 60 mi / h , v 2 = 120 mi / h , and K 1 = 500000 J . K = 1 2 m v 2 v 2 , so K 2 K 1 = v 2 2 v 2 1 K 2 = v 2 2 v 2 1 K 1 = (120 mi / h) 2 (60 mi / h) 2 (500000 J) = 2 × 10 6 J . keywords: Cart Full of Bricks 07:03, trigonometry, numeric, > 1 min, nor- mal. 002 A cart loaded with bricks has a total mass of 18 . 2 kg and is pulled at constant speed by a rope. The rope is inclined at 20 above the horizontal and the cart moves 20 m on a hori- zontal floor. The coefficient of kinetic friction between ground and cart is 0 . 5 . The acceleration of gravity is 9 . 8 m / s 2 . What is the normal force exerted on the cart by the floor. Correct answer: 75 . 4493 N. Explanation: F 20 18 . 2 kg μ = 0 . 5 Summing the components of the forces along the vertical direction provides X F y = F sin θ + N - m g = 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 - m g = 0 F μ k sin θ + F cos θ = μ k m g F = μ k m g μ k sin θ + cos θ . Since μ k sin θ + cos θ = (0 . 5) sin 20 + cos 20 = 1 . 1107 , the force on the cart by the floor is N = F cos θ = μ k m g cos θ μ k sin θ + cos θ = (0 . 5) (18 . 2 kg) (9 . 8 m / s 2 ) cos 20 (1 . 1107) = 75 . 4493 N . 003 How much work is done on the cart by the rope? Correct answer: 1 . 41798 kJ. Explanation:

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Create assignment, 00223, Homework 5, Oct 02 at 10:06 am 2 The work done on the cart is given by W F = F d cos θ = μ k m g μ k sin θ + cos θ d cos θ = (0 . 5) (18 . 2 kg) (9 . 8 m / s 2 ) (1 . 1107) × (20 m) cos 20 = 1 . 41798 kJ . 004 Note: The energy change due to friction is a loss of energy. What is the energy change W f due to fric- tion? Correct answer: - 1 . 41798 kJ. Explanation: Since the cart does not accelerate, the force due to friction is found from our horizontal equilibrium. f k = F cos θ The energy lost due to friction is just the work done by friction on the cart: W f = f k d cos 180 Substituting the frictional force and simplify- ing, cos (180 ) = - 1, we obtain the result, W f = - F d cos θ = - (75 . 4493 N)(20 m) cos 20 = - 1 . 41798 kJ .
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