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A spherical ball of density rho and radius 0.003 m is dropped into a vertical tube of viscous fluid (viscosity = 1.260 N*s/m², fluid density rho_L = rho/2 = 1260 kg/m³) filled up to the 0 cm mark. The ball is assumed to have reached terminal speed by the 10 cm mark. Find the time it takes to travel from the 10 cm mark to the 20 cm mark. (g = 10 m/s²)
- 0.5 s
- 1 s
- 2 s
- 3 s
Correct answer: 0.5 s
Solution
Between the 10 and 20 cm marks the ball already moves at constant terminal speed. Using Stokes' law vₜ = (2/9)*r²*g*(rho - rho_L)/eta with rho = 2520 kg/m³, rho_L = 1260 kg/m³, r = 0.003 m, eta = 1.260, the terminal velocity comes out to 0.2 m/s. The 0.10 m gap is then covered in time = 0.10/0.2 = 0.5 s.
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