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h16 - hernandez(ejh742 homework 16 Turner(58120 This...

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hernandez (ejh742) – homework 16 – Turner – (58120) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points A block of mass 0 . 5 kg is pushed against a hor- izontal spring of negligible mass, compressing the spring a distance of Δ x as shown in the fig- ure. The spring constant is 319 N / m. When released, the block travels along a frictionless, horizontal surface to point B , the bottom of a vertical circular track of radius 0 . 4 m, and continues to move up the track. The speed of the block at the bottom of the track is 16 m / s, and the block experiences an aver- age frictional force of 5 N while sliding up the track. The acceleration of gravity is 9 . 8 m / s 2 . m k R v B v T T B x What is Δ x ? Correct answer: 0 . 633446 m. Explanation: From conservation of energy, the initial po- tential energy of the spring is equal to the kinetic energy of the block at B . Therefore, we write 1 2 k x ) 2 = 1 2 m v 2 B Δ x = radicalBigg m v 2 B k = radicalBigg (0 . 5 kg) (16 m / s) 2 (319 N / m) = 0 . 633446 m . 002 (part 2 of 3) 10.0 points What is the speed of the block at the top of the track? Correct answer: 14 . 6693 m / s. Explanation: The change in the total energy of the block as it moves from B to T is equal to the work done by the frictional force Δ E = W f E T - E B = W f . The total energy at B is E B = 1 2 m v 2 B = 1 2 (0 . 5 kg) (16 m / s) 2 = 64 J . The work done by the frictional force is W f = - f π R = - (5 N) ( π ) (0 . 4 m) = - 6 . 28319 J . Therefore, the total energy at T is E T = E B + W f = 64 J + ( - 6 . 28319 J) = 57 . 7168 J . We can find now the speed of the block at T from 1 2 m v T 2 = E T - m g h T . Since v T 2 = 2 E T m - 2 g h T , = 2 (57 . 7168 J) 0 . 5 kg - 2(9 . 8 m / s 2 ) (0 . 8 m) = 215 . 187 m 2 / s 2 , then v T = radicalBig 215 . 187 m 2 / s 2 = 14 . 6693 m / s .
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hernandez (ejh742) – homework 16 – Turner – (58120) 2 003 (part 3 of 3) 10.0 points What is the centripetal acceleration of the block at the top of the track? Correct answer: 537 . 968 m / s 2 . Explanation: The centripetal acceleration at T is a c = v 2 T R = (14 . 6693 m / s) 2 0 . 4 m = 537 . 968 m / s 2 . 004 10.0 points A compact car “consumes” 37 . 5 mi / gal when traveling at 41 . 3 mi / h. Its fuel efficiency is 16 . 4%. (That is, 16 . 4% of the available fuel energy is delivered to the wheels.) How much power is delivered to the wheels at a speed of 41 . 3 mi / h? The mechanical
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