Homework 10 - homework 10 GADHIA TEJAS Due Apr 4 2007 4:00...

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homework 10 – GADHIA, TEJAS – Due: Apr 4 2007, 4:00 am 1 Question 1 part 1 of 1 10 points A uniform rod of mass 4 . 4 kg is 17 m long. The rod is pivoted about a horizontal, fric- tionless pin at the end of a thin extension (of negligible mass) a distance 17 m from the cen- ter of mass of the rod. Initially the rod makes an angle of 64 with the horizontal. The rod is released from rest at an angle of 64 with the horizontal, as shown in the figure below The acceleration of gravity is 9 . 8 m / s 2 . Hint: The moment of inertia of the rod about its center-of-mass is I cm = 1 12 m ℓ 2 . 17 m 17 m 4 . 4 kg O 64 What is the magnitude of the horizontal acceleration of the center of mass of the rod at the instant the rod is in a horizontal position? Answer in units of rad / s 2 . Question 2 part 1 of 3 10 points A 5 . 5 kg mass is connected by a light cord to a 3 . 3 kg mass on a smooth surface as shown. The pulley rotates about a frictionless axle and has a moment of inertia of 0 . 19 kg · m 2 and a radius of 0 . 85 m. The acceleration of gravity is 9 . 81m / s 2 . 5 . 5kg 3 . 3kg F 1 F 2 R Note: Figure is not drawn to scale Assume that the cord does not slip on the pulley. a) What is the acceleration of the two masses? Answer in units of m / s 2 . Question 3 part 2 of 3 10 points b) What is the magnitude of the force F 1 ? Answer in units of N. Question 4 part 3 of 3 10 points c) What is the magnitude of the force F 2 ? Answer in units of N. Question 5 part 1 of 2 10 points Assume: When the disk lands on the sur- face it does not bounce. The disk has mass 8 kg and outer radius 70 cm with a radial mass distribution (which may not be uniform) so that its moment of inertia is 3 7 m R 2 . The disk is rotating at angular speed 4 rad / s around its axis when it touches the surface, as shown in the figure below. The disk is carefully lowered onto a horizontal sur- face and released at time t 0 with zero initial linear velocity along the surface. The coef- ficient of friction between the disk and the surface is 0 . 02 . The kinetic friction force between the sur- face and the disk slows down the rotation of the disk and at the same time gives it a hor- izontal acceleration. Eventually, the disk’s
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