HW5sol - ME 363 Homework#5 1(a h0 h f = 2R First roll = 2...

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ME 363 Homework #5 1. (a) 2 0 h h R 2 1.5 First roll: = 0.183 15 1.5 1.5 0.75 Second roll: = 0.158 15 1.125 1.125 0.75 Third roll: = 0.137 15 minimum 0.183 f μ μ μ μ μ = = × = × = = (b) ( ) ( ) ( ) 0 0 0 1 1 1 2 2 2 3 3 0 0 0 3 3 3 3 0 3 3 0 0 0 3 0 3 3 3 0 3 3 0.75 0.75 0.75 1.03 12 26.1 0.75 1.03 40 86.8 ft min 0.46 0.75 1.03 V w t V w t V w t V w t w t l w t l t t w w w t l l in w t v v × × = × × = × × = × × × × = × × = × × = × = × = = × × = = = × 3 1
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(c) ( ) 0 1 0 0 0 1 0 0.08 - 15 0.5 2.74 0.75 1.03 1.147 45.9 / min 2 2 1 45.9 12 / 60 1 ln ln 0.964 0.75 2.74 0.75 24,000(0.964) 23,929 2 ' 23,929 27,631 3 ' 1 2 2.74 10 2 r r m avg avg ev L R h h in V V V V V V V L C p Y L F L W Y h ε σ ε μ = = × = + + × = = = = × = = = = × = = = = = × × + = × × ± ± ft si 3 0.183 2.74 7,631 1 865 10 2 1.75 lbs + × + = × × 2
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2. (a) ( ) ( ) ( ) ( ) 2 2 0 0 2 0 0 2 2 1 0 0.2 1 1 2 2 6 - 1 180 a n=0.2 π 4 4 1 2 0.5 . 2 0.5 ln ln -1.386 2 180 1.386 192 0.3 2 1 192 1 3 3 0.5 269 269 10 2 25.4 10 4 4 545 f f f f n f f d h d h d h h in d h h a d a h a F a d π ε σ ε μ σ π π Κ = ΜΡ = = × = = = = = = Κ = = ΜΡ × Ρ = + = + × = ΜΡ = Ρ × = × × × × = ΚΝ 6 (b) ( ) ( ) 0.07 2 6 - 500 39.37 0.5 25.4 80 39.37 103.4 0.3 2 103.4 1 144.8 3 0.5 144.8 10 2 25.4 10 4 293 m f a h C M P M F KN 6 Pa Pa υ ε σ ε π + = = = × = × = = × = + = × = × × × × × = ± ± 3
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3. ( ) 0 0 0 2 0 3 3 0 1 2 0 3 3 100 20 100 ln 2ln 2ln 3.22 20 6 tan - 6 200 (100) tan30 3.22 100 - 20 22.49 f f f d mm d mm d d d d d ε υ α ε ε = = Α = = = = Α = × × × = × = ± ( ) 0 0.1 0 0 0 2 6 -6 @900 0.1 150 150 (22.49) 204 2 1.7ln 2 100 204 1.7 3.22 100 1,524 1,524 10 100 10 4 12 Neither is sufficient. One must reduced the speed by
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