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hw6 - zhou(cz3574 HW6 mackie(10611 This print-out should...

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zhou (cz3574) – HW6 – mackie – (10611) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A 2 . 58 kg block initially at rest is pulled to the right along a horizontal surface by a constant, horizontal force of 18 N. The coefficient of kinetic friction is 0 . 0972. The acceleration of gravity is 9 . 8 m / s 2 . Find the speed of the block after it has moved 3 . 09 m. Correct answer: 6 . 10159 m / s. Explanation: We have to use the equation Δ K = - f s (1) , to calculate the change in the kinetic energy, Δ K . The net force exerted on the block is the sum of the applied 18 N force and the frictional force. Since the frictional force is in the direction opposite the displacement, it must be subtracted. The magnitude of the frictional force is f = μ N = μ m g . Therefore the net force acting on the block is F net = F - μ m g = 18 N - (0 . 0972) (2 . 58 kg) (9 . 8 m / s 2 ) = 15 . 5424 N . Multiplying this constant force by the dis- placement, and using equation (1), we obtain Δ K = F net s = (15 . 5424 N) (3 . 09 m) = 48 . 026 J = 1 2 m v 2 , since the initial velocity is zero. Therefore, v f = radicalbigg 2 Δ K m = radicalBigg 2 (48 . 026 J) 2 . 58 kg = 6 . 10159 m / s . 002 10.0 points You leave your 125 W portable color TV on for 3 hours each day and you do not pay attention to the cost of electricity. If the dorm (or your parents) charged you for your electricity use and the cost was $0 . 3 / kW · h, what would be your monthly (30 day) bill? Correct answer: 3 . 375 dollars. Explanation: Let : P = 125 W and t = 3 h / day , The energy consumed in each day is W = P t = (125 W) (3 h / day) · kW 1000 W = 0 . 375 kW · h / day . In 30 days, you would use (30 day) (0 . 375 kW · h / day) = 11 . 25 kW · h , which would cost you (11 . 25 kW · h) ($0 . 3 / kW · h) = $3 . 375 . 003 10.0 points A car of weight 3150 N operating at a rate of 154 kW develops a maximum speed of 39 m / s on a level, horizontal road. Assuming that the resistive force (due to friction and air resistance) remains constant, what is the car’s maximum speed on an incline of 1 in 20; i.e. , if θ is the angle of the incline with the horizontal, sin θ = 1 / 20 ? Correct answer: 37 . 5041 m / s. Explanation:
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zhou (cz3574) – HW6 – mackie – (10611) 2 If f is the resisting force on a horizontal road, then the power P is P = f v horizontal , so that f = P v h = (1 . 54 × 10 5 W) (39 m / s) = 3948 . 72 N . On the incline, the resisting force is F = f + m g sin θ = f + W 20 = P v h + W 20 . And, F v = P , so v = P F = P P v h + W 20 = (1 . 54 × 10 5 W) (1 . 54 × 10 5 W) (39 m / s) + (3150 N) 20 = 37 . 5041 m / s . 004 (part 1 of 2) 10.0 points A frictionless roller coaster is given an ini- tial velocity of v 0 at height h = 13 m . The radius of curvature of the track at point A is R = 25 m. The acceleration of gravity is 9 . 8 m / s 2 . R 2 3 h h h v 0 A B Find the maximum value of v 0 so that the roller coaster stays on the track at A solely because of gravity. Correct answer: 12 . 6517 m / s. Explanation: let : h = 13 m and R = 25 m .
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