4 - homework 19 FISHER, CHRISTIAN Due: Apr 6 2008, 11:00 pm...

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Unformatted text preview: homework 19 FISHER, CHRISTIAN Due: Apr 6 2008, 11:00 pm 1 Question 1, chap 13, sect 4. part 1 of 1 10 points A solid steel sphere of density 7 . 87 g / cm 3 and mass 0 . 5 kg spins on an axis through its center with a period of 3 s. Given V sphere = 4 3 R 3 , what is its angular momentum? Correct answer: 0 . 000256661 kg m 2 / s (toler- ance 1 %). Explanation: The definition of density is M V = M 4 3 R 3 , Therefore R = bracketleftbigg 3 M 4 bracketrightbigg 1 3 = bracketleftbigg 3 (0 . 5 kg) 4 (7870 kg / m 3 ) bracketrightbigg 1 3 = 0 . 0247534 m . Using = 2 T = 2 (3 s) = 2 . 0944 s 1 and I = 2 5 M R 2 = 2 5 (0 . 5 kg)(0 . 0247534 m) 2 = 0 . 000122547 kg m 2 , we have L I = 4 M R 2 5 T = 4 (0 . 5 kg)(0 . 0247534 m) 2 5 (3 s) = . 000256661 kg m 2 / s . Question 2, chap 13, sect 4. part 1 of 1 10 points A force F x = (2 . 7 N) + (2 . 8 N) is applied to an object that is pivoted about a fixed axis aligned along the z coordinate axis. The force is applied at the point x = (3 . 8 m) +(5 . 1 m) . Find the z-component of the net torque. Correct answer: 3 . 13 N m (tolerance 1 %). Explanation: Basic Concept: vector = vectorr vector F Solution: From the definition of torque vector = vectorr vector F = [ x + y ] [ F x + F y ] = [(3 . 8 m) + (5 . 1 m) ] [(2 . 7 N) + (2 . 8 N) ] = [(3 . 8 m) (2 . 8 N) (5 . 1 m) (2 . 7 N)] k = ( 3 . 13 N m) k In this case, the net torque only has a z- component. Question 3, chap 13, sect 4. part 1 of 2 10 points A particle is located at the vector position vectorr = (1 . 4 m) + (4 . 4 m) and the force acting on it is vector F = (5 . 4 N) + (3 . 3 N) . What is the magnitude of the torque about the origin? Correct answer: 19 . 14 N m (tolerance 1 %). Explanation: Basic Concept: vector = vectorr vector F homework 19 FISHER, CHRISTIAN Due: Apr 6 2008, 11:00 pm 2 Solution: Since neither position of the par- ticle, nor the force acting on the particle have the z-components, the torque acting on the particle has only z-component: vector = [ x F y y F x ] k = [(1 . 4 m) (3 . 3 N) (4 . 4 m) (5 . 4 N)] k = [ 19 . 14 N m] k . Question 4, chap 13, sect 4. part 2 of 2 10 points What is the magnitude of the torque about the point having coordinates [ a, b ] = [(4 m) , (7 m)]?...
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4 - homework 19 FISHER, CHRISTIAN Due: Apr 6 2008, 11:00 pm...

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