hw 18 sol - Patel(pnp223 – homework 18 – Turner...

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Unformatted text preview: Patel (pnp223) – homework 18 – Turner – (92160) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Consider a frictionless roller coaster such as depicted below. The acceleration of gravity is 9 . 8 m / s 2 . 27 m A B C h A Passenger cars start at point A with zero initial speed, accelerate as they go down to point B, swing around the circular vertical loop B → C → B of radius 27 m, then go on towards further adventures (not shown). When a car goes through the top of the loop (point C), the passengers feel weightless (for just a moment). What is the height h A of the starting point A above the loop’s bottom B? Correct answer: 67 . 5 m. Explanation: Let : R = 27 m and g = 9 . 8 m / s 2 . A passenger feels weightless when his ac- celeration vectora is precisely equal to the free- fall acceleration vectorg . At the top of the loop (point C), passengers have no tangential ac- celeration while their normal acceleration is directed straight down and has magnitude a N = v 2 R . Weightlessness happens when this accelera- tion equals g , therefore the cars should go through point C at speed v C = radicalbig Rg . In the absence of friction, the mechanical energy of a car is conserved as it follows the coaster’s route, thus K A + U A = K C + U C = ⇒ m 2 v 2 A + mg h A = m 2 v 2 C + mg 2 R. Therefore, in light of the initial condition v A = 0, we have mg h A = mg 2 R + m 2 v 2 C = mg 2 R + m 2 Rg = 5 2 mg R h A = 5 2 R = 5 2 (27 m) = 67 . 5 m . 002 (part 1 of 3) 10.0 points The figure is a graph of the gravitational po- tential energy and kinetic energy of a 72 g yo-yo as it moves up and down on its string....
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hw 18 sol - Patel(pnp223 – homework 18 – Turner...

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