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Unformatted text preview: valdez (vv689) Homework 14 florin (58140) 1 This printout should have 21 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points A solid sphere of radius 40 cm is positioned at the top of an incline that makes 24 angle with the horizontal. This initial position of the sphere is a vertical distance 2 m above its position when at the bottom of the incline. The sphere is released and moves down the incline. 40 cm M 24 2m Calculate the speed of the sphere when it reaches the bottom of the incline if it rolls without slipping. The acceleration of gravity is 9 . 8 m / s 2 . The moment of inertia of a sphere with respect to an axis through its center is 2 5 M R 2 . Correct answer: 5 . 2915 m / s. Explanation: From conservation of energy we have M g h = 1 2 M v 2 + 1 2 I 2 = 1 2 M v 2 + 1 2 parenleftbigg 2 5 M R 2 parenrightbigg parenleftbigg v 2 R 2 parenrightbigg = 7 10 M v 2 v 1 = radicalbigg 10 7 g h = radicalbigg 10 7 (9 . 8 m / s 2 ) (2 m) = 5 . 2915 m / s . keywords: 002 10.0 points The top in the figure has moment of inertia . 000304 kg m 2 and is initially at rest. It is free to rotate about the stationary axis AA . A string wrapped around a peg along the axis of the top is pulled in such a manner as to maintain a constant tension of 3 . 9 N. F A A' If the string does not slip while being un wound, what is the angular speed of the top after 81 . 6 cm of string has been pulled off of the peg? Correct answer: 144 . 696 rad / s. Explanation: Let : I = 0 . 000304 kg m 2 , F = 3 . 9 N , and L = 81 . 6 cm . The top starts from rest, so by conservation of energy, W = K = I 2 f 2 I 2 2 F L = I 2 f 2 f = radicalbigg 2 W I = radicalbigg 2 F L I = radicalBigg 2(3 . 9 N)(81 . 6 cm) . 000304 kg m 2 = 144 . 696 rad / s . 003 10.0 points A system of two wheels fixed to each other is valdez (vv689) Homework 14 florin (58140) 2 free to rotate about a frictionless axis through the common center of the wheels and per pendicular to the page. Four forces are ex erted tangentially to the rims of the wheels, as shown below. F 2 F F F 2 R 3 R What is the magnitude of the net torque on the system about the axis? 1. = F R 2. = 5 F R 3. = 14 F R 4. = 2 F R correct 5. = 0 Explanation: The three forces F apply counterclockwise torques while the other force 2 F applies a clockwise torque, so = summationdisplay F i R i = ( 2 F ) (3 R ) + F (3 R ) + F (3 R ) + F (2 R ) = 2 F R . 004 10.0 points A rod can pivot at one end and is free to rotate without friction about a vertical axis, as shown. A force vector F is applied at the other end, at an angle to the rod....
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