Problem 1.11

# Problem 1.11 - Problem 1.11 [Difficulty: 3] Given: Data on...

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Problem 1.11 [Difficulty: 3] Given: Data on sphere and formula for drag. Find: Maximum speed, time to reach 95% of this speed, and plot speed as a function of time. Solution: Use given data and data in Appendices, and integrate equation of motion by separating variables. The data provided, or available in the Appendices, are: ρ air 1.17 kg m 3 = μ 1.8 10 5 × Ns m 2 = ρ w 999 kg m 3 = SG Sty 0.016 = d 0.3 mm = Then the density of the sphere is ρ Sty SG Sty ρ w = ρ Sty 16 kg m 3 = The sphere mass is M ρ Sty π d 3 6 = 16 kg m 3 π × 0.0003 m () 3 6 × = M 2.26 10 10 × kg = Newton's 2nd law for the steady state motion becomes (ignoring buoyancy effects) Mg 3 π V d = so V max 3 π μ d = 1 3 π 2.26 10 10 × × kg 9.81 × m s 2 m 2 1.8 10 5 × N s × 1 0.0003 m × = V max 0.0435 m s = Newton's 2nd law for the general motion is (ignoring buoyancy effects) M dV dt

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## This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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Problem 1.11 - Problem 1.11 [Difficulty: 3] Given: Data on...

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