Question

You drop a steel ball bearing, with a radius of 3.40 mm, into a beaker of honey. Note that honey has a viscosity of 6.00 Pa/s and a density of 1360 kg/m3, and steel has a density of 7800 kg/m3. Assume that g = 9.8 m/s2. (a) What is the terminal speed of the ball bearing? m/s (b) Aluminum has a density of 2700 kg/m3. What radius should an aluminum ball have to have the same terminal speed in honey that the steel ball has?. mm

Answer 1

here,

radius of steel ball , r1 = 3.4 mm = 0.0034 m

viscocity , n = 6 Pa/s

density of honey , p1 = 1360 kg/m^3

a)

density of steel , p2 = 7800 kg/m^2

let the terminal speed be v1

when teriminal speed is achived

weight = buoyant force + viscous force

m * g = p1 * V * g + 6 * pi * n * r * v1

p2 * (4/3 * pi * r1^2 ) * g = p1 * (4/3 * pi * * r1^3) * g + 6 * pi * n * r * v1

7800 * (4/3 * pi * 0.0034^2 ) * 9.81 = 1360 * (4/3 * pi * * 0.0034^3) * 9.81 + 6 * pi * 6 * 0.0034 * v1

solving for v1

v1 = 9.62 m/s

the terminal speed is 9.62 m/s

b)

density of alumunium , p3 = 2700 kg/m^3

let the radius of alumunium ball be r2

when teriminal speed is achived

weight = buoyant force + viscous force

m * g = p1 * V * g + 6 * pi * n * r2 * v1

p3 * (4/3 * pi * r2^2 ) * g = p1 * (4/3 * pi * r2^3) * g + 6 * pi * n * r2 * v1

2700 * (4/3 * pi * r2^2 ) * 9.81 = 1360 * (4/3 * pi * r2^3) * 9.81 + 6 * pi * 6 * r2 * 9.62

solving fore r2

r2 = 9.86 * 10^-3 m

the radius of aluminium ball is 9.86 mm