HW 8 solution_pdf

HW 8 solution_pdf - ghei (mg42382) HW 8 opyrchal (11130)...

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ghei (mg42382) – HW 8 – opyrchal – (11130) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points The angular position oF an object that rotates about a fxed axis is given by θ ( t ) = θ 0 e βt , where β = 3 s - 1 , θ 0 = 0 . 7 rad, and t is in seconds. What is the magnitude oF the total linear acceleration at t = 0 oF a point on the object that is 8 . 4 cm From the axis? Correct answer: 64 . 5971 cm / s 2 . Explanation: Let : r = 8 . 4 cm . We can fnd the angular velocity and accel- eration: θ ( t ) = θ 0 e βt ω ( t ) = d θ ( t ) dt = β θ 0 e βt and α ( t ) = d ω ( t ) dt = β 2 θ 0 e βt . At t = 0, since e 0 = 1, ω = β θ 0 and α = β 2 θ 0 , so the tangential and radial accelerations are a t = αr = β 2 θ 0 r and a r = ω 2 r = β 2 θ 2 0 r , and the magnitude oF the total linear acceler- ation is a = r a 2 t + a 2 r = r β 4 θ 2 0 r 2 + β 4 θ 4 0 r 2 = β 2 θ 0 r r 1 + θ 2 0 = (3 s - 1 ) 2 (0 . 7 rad) (8 . 4 cm) r 1 + (0 . 7 rad) 2 = 64 . 5971 cm / s 2 . 002 (part 1 of 2) 10.0 points A ±ywheel with a very low Friction bearing takes 1 . 4 h to stop aFter the motor power is turned o². The ±ywheel was originally rotating at 47 rpm. What was the initial rotation rate in radi- ans per second? Correct answer: 4 . 92183 rad / s. Explanation: Let : f = 47 rpm . ω 0 = (47 rpm) 2 π rev 1 min 60 sec = 4 . 92183 rad / s . 003 (part 2 of 2) 10.0 points How many revolutions does the ±ywheel make beFore it stops? Correct answer: 1974 rev. Explanation: Let : t = 1 . 4 h . The angular acceleration oF the ±ywheel is α = - ω 0 t , so the angle is θ = ω 0 t + 1 2 α t 2 = ω 0 t + 1 2 p - ω 0 t P t 2 = 1 2 ω 0 t = 1 2 (4 . 92183 rad / s) (1 . 4 h) 3600 s 1 h 1 rev 2 π = 1974 rev . 004 (part 1 of 2) 10.0 points A small turtle, appropriately named “Dizzy”, is placed on a horizontal, rotating turntable at a distance oF 21 . 6 cm From its center. Dizzy’s mass is 54 . 8 g, and the coe³cient oF static
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ghei (mg42382) – HW 8 – opyrchal – (11130) 2 friction between his feet and the turntable is 0 . 32. Find the maximum angular velocity the turntable can have if Dizzy is to remain sta- tionary relative to the turntable. The accel- eration of gravity is 9 . 8 m / s 2 . Correct answer: 0 . 606431 rev / s. Explanation: Let : r = 21 . 6 cm = 0 . 216 m , m = 54 . 8 g , μ = 0 . 32 , and g = 9 . 8 m / s 2 .
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HW 8 solution_pdf - ghei (mg42382) HW 8 opyrchal (11130)...

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