HW #6-solutions - wolz (cmw2833) HW #6 Antoniewicz (57420)...

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Unformatted text preview: wolz (cmw2833) HW #6 Antoniewicz (57420) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 3) 4.0 points Starting from rest, a(n)8 kg block slides 11 m down a frictionless ramp (inclined at 30 from the floor) to the bottom. The block then slides an additional 19 m along the floor before coming to stop. The acceleration of gravity is 9 . 8 m / s 2 . 1 1 m 8 kg 8 k g 30 19 m Find the speed of the block at the bottom of the ramp. Correct answer: 10 . 3827 m / s. Explanation: L m m d Given : m = 8 kg , = 30 , L = 11 m , and d = 19 m . Let P = 0 at the bottom of the ramp. Using conservation of energy along the ramp, we have U i + K i = U f + K f mgL sin + 0 = 0 + 1 2 mv 2 bottom where L is the length moved along the ramp. v bottom = radicalbig 2 gL sin = radicalBig 2(9 . 8 m / s 2 )(11 m) sin 30 = 10 . 3827 m / s . 002 (part 2 of 3) 3.0 points Find the coefficient of kinetic friction between block and floor. Correct answer: 0 . 289474. Explanation: Let d be the distance moved along the floor. The frictional force is given by f = k N = k mg . Applying the work-kinetic energy theorem, we have W f = ( K U g ) f ( K + U g ) i , where K i is the kinetic energy at the bottom of the ramp and K f = 0. k mg d = (0 + 0) parenleftbigg 0 + 1 2 mv 2 i parenrightbigg k = v 2 i 2 g d = (10 . 3827 m / s) 2 2(9 . 8 m / s 2 )(19 m) = . 289474 . 003 (part 3 of 3) 3.0 points Find the magnitude of the mechanical energy lost due to friction. Correct answer: 431 . 2 J. Explanation: All of the initial potential energy is lost due to friction along the floor, so is mg y i = mg L sin = (8 kg) (9 . 8 m / s 2 ) (11 m) sin30 = 431 . 2 J . wolz (cmw2833) HW #6 Antoniewicz (57420) 2 004 10.0 points The spring has a constant of 14 N / m and the frictional surface is 0 . 2 m long with a coefficient of friction = 2 . 25 . The 6 kg block depresses the spring by 34 cm, then is released. The first drop is 2 . 4 m and the second is 2 m. The acceleration of gravity is 9 . 8 m / s 2 . h h L m k x 1 2 s How far from the bottom of the cliff does it land? Correct answer: 3 . 9636 m. Explanation: Basic concepts The potential energy of a spring is U s = 1 2 k x 2 = 1 2 (14 N / m) (34 cm) 2 = 0 . 8092 J . Gravitational potential energy is U g = mg h = (6 kg) (9 . 8 m / s 2 ) (2 . 4 m) = 141 . 12 J . Work done against friction on a flat surface is W fr = mg L = (2 . 25) (6 kg) (9 . 8 m / s 2 ) (0 . 2 m) = 26 . 46 J . Kinetic energy is K = 1 2 mv 2 . The height of the cliff determines how long it takes for the mass to reach the bottom....
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HW #6-solutions - wolz (cmw2833) HW #6 Antoniewicz (57420)...

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