Ch08-p122 - 122 The connection between angle(measured from vertical and height h(measured from the lowest point which is our choice of reference

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(a) We use energy conservation in the form of Eq. 8-17. KU KU mgL mv mgL 11 2 2 12 2 2 01 1 2 1 +=+ +−=+− cos cos θθ bg With L = 1.4 m, θ 1 = 30°, and 2 = 20°, we have vg L 22 1 21 4 =− = cos cos . b g ms . (b) The maximum speed v 3 is at the lowest point. Our formula for h gives h 3 = 0 when 3 = 0°, as expected. From mgL mv 33 13 2 1 2 0 +−=+ cos we obtain v 3 19 = .m s . (c) We look for an angle 4 such that the speed there is vv 43 3 = . To be as accurate as possible, we proceed algebraically (substituting L 3 2 1 cos at the appropriate place) and plug numbers in at the end. Energy conservation leads to mgL mv mgL mgL m v mgL gL gL gL 4 4 14 2 4 1 3 2 4 1 1 4 1 2 1 1 1 29 1 1 2 9 +− =+− −=+ −= cos cos cos cos cos cos cos where in the last step we have subtracted out
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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