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Analytical Mech Homework Solutions 40

Analytical Mech Homework Solutions 40 - 2sin 2 = 2 gh = 1 2...

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2 2 2 2 0 0 2 0 1 2 2sin 1 1 csc 1 gh gh gh v v v α α = = + = + Finally … 2 2 0 2 1 gh v α = + csc (b) Solving for R max max 2 2 sin 1 2sin 1 2 csc h h h R ϕ α α = = = Substituting for 2 csc α and solving … 2 0 max 2 0 1 v gh R g v = + 4.10 We can again use the results of problem 4.8. The maximum slope range from problem 4.8 is given by … ( ) 2 0 max 1 sin sin v h R g ϕ ϕ = = + Solving for sin ϕ 2 2 0 0 sin 1 gh gh v v ϕ = Thus … max max cos cos sin x R h ϕ ϕ ϕ = = We can calculate cos ϕ from the above relation for sin ϕ ( ) 1 1 2 2 2 2 2 0 0 cos 1 sin 1 2 1 gh gh v v ϕ ϕ = =
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