# 16 - roofner(bar784 – Homework 16 – Weathers –(17104...

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Unformatted text preview: roofner (bar784) – Homework 16 – Weathers – (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A woman with mass of 62 kg stands at the rim of a horizontal table having a moment of inertia of 560 kg m 2 and a radius of 2 . 7 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axis through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1 . 7 m / s relative to the Earth. With what angular speed does the turntable rotate? Correct answer: 0 . 508179 rad / s. Explanation: Basic Concepts: summationdisplay vector τ ext = d vector L d t The total momentum of a system is constant in our case, because there’s no external torque acting on the system. Therefore, the sum of the angular momenta of the woman and the turntable remains zero when the woman begins to walk. Hence L t = L w , and L t = m w v w r = (62 kg)(1 . 7 m / s)(2 . 7 m) = 284 . 58 kg m 2 / s where L t , L w are absolute values of the corre- sponding vector quantities. Since L t = Iω t , we have ω t = L t I = (284 . 58 kg m 2 / s) (560 kg m 2 ) = 0 . 508179 rad / s 002 (part 2 of 2) 10.0 points How much work does the woman do ON THE TABLE to set it into motion? Correct answer: 72 . 3087 J. Explanation: The work which the woman needs to perform to set the turntable into motion equals the change in kinetic energy of the turntable, i.e. W = I ω 2 t 2 = (560 kg m 2 ) (0 . 508179 rad / s) 2 2 = 72 . 3087 J 003 (part 1 of 2) 10.0 points A small puck of mass 38 g and radius 28 cm slides along an air table with a speed of 1 . 7 m / s. It makes a glazing collision with a larger puck of radius 65 cm and mass 89 g (ini- tially at rest) such that their rims just touch. The pucks stick together and spin around af- ter the collision....
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16 - roofner(bar784 – Homework 16 – Weathers –(17104...

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