9_ch 03 Mechanical Design budynas_SM_ch03

# 9_ch 03 Mechanical - β An equation for an upward bend can be found by changing the sign of W The moment will no longer be correcting A curved

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22 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design So W = l 1 + 1 = l 2 x = l 2 + 1 = l 3 y = l 3 + 1 = l 4 z = l 4 + 1 = l 5 (b) With straight rigid wires, the mobile is not stable. Any perturbation can lead to all wires becoming collinear. Consider a wire of length l bent at its string support: ± M a = 0 ± M a = iWl i + 1 cos α ilW i + 1 cos β = 0 iWl i + 1 (cos α cos β ) = 0 Moment vanishes when α = β for any wire. Consider a ccw rotation angle β , which makes α α + β and β α β M a = iWl i + 1 [cos( α + β ) cos( α β )] = 2 iWl i + 1 sin α sin β . = 2 iWl β i + 1 sin α There exists a correcting moment of opposite sense to arbitrary rotation
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Unformatted text preview: β . An equation for an upward bend can be found by changing the sign of W . The moment will no longer be correcting. A curved, convex-upward bend of wire will produce stable equilibrium too, but the equation would change somewhat. 3-8 (a) C = 12 + 6 2 = 9 CD = 12 − 6 2 = 3 R = ² 3 2 + 4 2 = 5 σ 1 = 5 + 9 = 14 σ 2 = 9 − 5 = 4 2 ± s (12, 4 cw ) C R D ² 2 ² 1 ³ 1 ³ ³ 2 2 ± p (6, 4 ccw ) y x ² cw ² ccw W iW il i ± 1 T i ´ µ l i ± 1...
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## This note was uploaded on 12/13/2011 for the course EML 3013 taught by Professor Shingley during the Fall '11 term at UNF.

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