Finding Viscosity Using a Sphere-Drop Method

[cody11]

Homework Statement

A sphere of radius 1.06 cm is dropped into a glass cylinder filled with a viscous liquid. The mass of the sphere is 13.0 g and the density of the liquid is 1146 kg/m3. The sphere reaches a terminal speed of 0.166 m/s. What is the viscosity of the liquid?

Variables (in standard units):
Radius of sphere: 0.0106 m
Mass of sphere: 13.0 g
Density of liquid: 1.146*10⁶ g/m³
Terminal speed: 0.166 m/s

Variables I calculated:
Volume of sphere 4/3*pi*0.0106 m=0.0444
Density of sphere 13.0/0.0444=292.793

Homework Equations

(density_object-density_fluid)Vg=6*pi*viscosity*r*v

The Attempt at a Solution

(292.793-1.146*10⁶)(0.0444)(9.8)/6*pi*0.0106*0.166

This gives me a value of -1.50*10⁷ Pa * s. Obviously I don't think viscosity can be negative and that negative value is coming from my computation of drag
(density_object-density_fluid. So I'm thinking something is wrong there. Thanks for the help.

 

[lippyka]

The problem is in the equation. The equation you used is for the drag force, not the viscosity. The equation you want is Stokes' law:F = 6πηrv