HW_10 - negligible mass so that their center-to-center...

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Physics 112 Homework #10 Fall 2006 Read: Chapter 10 (intro., sections 10.1, 10.5) Chapter 11 (intro., sections 11.1 thru 11.3) For discussion: Chapter 10: Qs #Q10.12, Q10.21, Q10.22 (not turned in) Chapter 10: Es & Ps: #10.1, 10.2, 10.3, 10.35 Chapter 11: Qs #Q11.2, Q11.4 Chapter 11: Es & Ps #11.7, 11.17, 11.45, 11.51 Due Friday, Nov. 3 at lecture: #10.4 [Bike wheel] #10.21 [Spheres] #9-22 [CD] 1. [Lab Disks] Two identical uniform solid disks are stuck together at their rims, as shown, and rotate about an axis perpendicular to the plane of the disks ( page) that passes through their point of contact. (a) Find an expression for the moment of inertia of the two disks about this rotation axis through their point of contact. Give your answer in terms of the mass m and radius R of each disk. [HINT: You'll need to use the Parallel Axis Theorem along the way.] (b) Now suppose the same disks are stuck together by a layer of Velcro of
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Unformatted text preview: negligible mass so that their center-to-center distance D is noticeably greater than twice the physical radius R of each disk, as shown. Again, find the moment of inertia of these two disks about their point of contact. Give your answer in terms of the mass m and radius R of each disk and the distance D. (c) Show that your expression from part (b) properly reduces to the expression from part (a) when D = 2R. 2. A cylindrical section of a tree trunk 50 cm in diameter and 75 cm long is seen rolling at a speed of 12 m/s down a sloping road below a sawmill. (Wood has a density of 750 kg/m 3 .) Assuming that the road has an incline of 5% (meaning that if you travel 100 m along the road, you go up or down by 5 m), at least how far up the road is the sawmill? Describe any assumptions or approximations that you make. Please include a carefully-labeled diagram to illustrate your solution. D R R m m...
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