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Unformatted text preview: lim (kl9356) – Homework 10 – Weathers – (17104) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A spring with a springconstant 3 . 5 N / cm is compressed 31 cm and released. The 4 kg mass skids down the frictional incline of height 27 cm and inclined at a 18 ◦ 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 . 5 . 4 kg 18 ◦ μ = . 5 . 7 m 27 cm 31 cm k = 3 . 5 N / cm v f Figure: Not drawn to scale. What is the final velocity v f of the mass? Correct answer: 2 . 6789 m / s. Explanation: Let : g = 9 . 8 m / s 2 = , k = 3 . 5 N / cm = 350 N / m , x = 31 cm = 0 . 31 m , μ = 0 . 5 , ℓ = 0 . 7 m , h = 0 . 27 m , m = 4 kg , and θ = 18 ◦ , 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 (350 N / m) (0 . 31 m) 2 = 16 . 8175 J . It gains kinetic energy because of the potential energy lost in moving down the incline K gained = U lost = mg h (2) = (4 kg) (9 . 8 m / s 2 ) (0 . 27 m) = 10 . 584 J . and loses kinetic energy by doing work on the frictional surface K lost = W fr = μmg ℓ cos θ (3) = (0 . 5) (4 kg) (9 . 8 m / s 2 ) × (0 . 7 m) cos(18 ◦ ) = 13 . 0485 J . Since energy is concerved, the final kinetic energy is K f = U s + U l − W fr = (16 . 8175 J) + (10 . 584 J) − (13 . 0485 J) = 14 . 353 J . However, the final kinetic energy is K f = 1 2 mv 2 . (3) Multiplying by 2 and dividing by m gives us 2 K f m = v 2 , so v = radicalbigg 2 K f m = radicalBigg 2 (14 . 353 J) (4 kg) = 2 . 6789 m / s . Alternate Explanation: The potential energy at the top of the hill will be converted into kinetic energy at the bottom of the hill minus energy lost due to the nonconservative friction force....
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 Fall '08
 Weathers
 Magnetism, Energy, Kinetic Energy, Potential Energy, Work, lim

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