Problem 1.13

# Problem 1.13 - Problem 1.13[Difficulty 5 Given Data on...

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Problem 1.13 [Difficulty: 5] mg kV t Given: Data on sphere and terminal speed from Problem 1.12. Find: Distance traveled to reach 99% of terminal speed; plot of distance versus time. Solution: Use given data; integrate equation of motion by separating variables. The data provided are: M11 0 13 × slug = V t 0.2 ft s = Newton's 2nd law for the general motion is (ignoring buoyancy effects) M dV dt Mg kV = (1) Newton's 2nd law for the steady state motion becomes (ignoring buoyancy effects) t = so k V t = k11 0 13 × slug 32.2 × ft s 2 s 0.2 ft × lbf s 2 slug ft × = k 1.61 10 11 × lbf s ft = To find the distance to reach 99% of V t , we need V ( y ). From 1: M dV dt M dy dt dV dy = MV dV dy = = VdV g k M V dy = Separating variables Integrating and using limits y M 2 g k 2 ln 1 k V M k V = We must evaluate this when V 0.99 V t = V 0.198 ft s = y1 1 0 13 slug () 2 32.2 ft s 2 ft 1.61 10 11

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Problem 1.13 - Problem 1.13[Difficulty 5 Given Data on...

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