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Unformatted text preview: Hood, Charles Homework 10 Due: Nov 16 2006, 11:00 pm Inst: Jan Opyrchal 1 This printout should have 6 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A spring with a springconstant 2 . 6 N / cm is compressed 24 cm and released. The 4 kg massskidsdownthefrictionalinclineofheight 15 cm and inclined at a 19 angle. The acceleration of gravity is 9 . 8 m / s 2 . The path is frictionless except for a dis tance of 0 . 7 m along the incline which has a coefficient of friction of 0 . 3 . 4 kg 19 = . 3 . 7 m 15 cm 24 cm k = 2 . 6 N / cm v f Figure: Not drawn to scale. What is the final velocity v f of the mass? Correct answer: 1 . 671 m / s. Explanation: Let : g = 9 . 8 m / s 2 = , k = 2 . 6 N / cm = 260 N / m , x = 24 cm = 0 . 24 m , = 0 . 3 , = 0 . 7 m , h = 0 . 15 m , m = 4 kg , and = 19 , Consider the kinetic energy of the mass. The mass receives its initial kinetic energy from the potential energy of the spring K i = U spring = 1 2 k x 2 (1) = 1 2 (260 N / m)(0 . 24 m) 2 = 7 . 488 J . Itgainskineticenergybecauseofthepotential energy lost in moving down the incline K gained = U lost = mg h (2) = (4 kg)(9 . 8 m / s 2 )(0 . 15 m) = 5 . 88 J ....
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