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PHYS310_homework_11_solutions

PHYS310_homework_11_solutions - Homework set 11 due...

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Homework set 11, due Wednesday, November 16, 11:30 am Following problems from Analytical Mechanics by Fowles & Cassiday 1. 8.12 cm mx mg T = - && cm I aT ϖ = & cm x a ϖ = && & 2 2 5 cm I ma = 2 1 2 2 5 5 cm cm cm cm I x mx mg mg ma mg mx a a a ϖ = - = - = - & && && && 5 7 cm x g = && 2. 8.20 (20 points) mx mg μ = && x g μ = && x gt μ = & , and 2 1 2 x gt μ = 2 2 5 I ma mga ϖ ϖ μ = = - & & 5 2 g a μ ϖ = - & 5 2 g t a μ ϖ ϖ = - o Slipping ceases to occur when v a ϖ = 5 2 gt a gt μ ϖ μ = - o 2 7 a t g ϖ = o 2 1 2 2 7 a x g g ϖ μ μ = o 2 2 2 49 a x g ϖ μ = o 3. 8.22 (20 points) From section 8.7 (see Figure 8.7.1), the instantaneous center of rotation is the point O . If x is the distance from the center of mass to O and 2 l is the distance from the center of mass to the center of percussion O , then from eqn. 8.7.10 … a x T r mg r
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2 2 1 2 12 12 cm I l Ml l x M M = = = 6 l x = 4. 9.1 (20 points) 9.1 (a) ( 29 2 2 xx I y z dm = + dm dxdy ρ = and 2 2 m a ρ = ( 29 2 2 0 0 0 y a x a xx y x I y dxdy ρ = = = = = + 2 0 2 a a y dy ρ = 2 4 2 3
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