Final answer:
To calculate the liquid's viscosity, Stokes' law is used. By inserting the known values like the sphere's mass and radius, the liquid's density, and the terminal velocity into the viscosity formula derived from Stokes' law, the viscosity is determined. This assumes spherical shape and laminar flow have been reached.
Step-by-step explanation:
Calculating the Viscosity of a Liquid
To calculate the viscosity (η) of a viscous liquid through which a sphere falls, we use Stokes' law. Stokes' law describes the drag force (Fs) acting on a sphere moving through a viscous fluid, which is given by the equation Fs = 6πηrv, where r is the sphere's radius, v is the terminal velocity, and η is the viscosity of the liquid.
At terminal velocity, the forces acting on the sphere are balanced, meaning the gravitational force (weight) of the sphere, minus the buoyant force (the weight of the displaced liquid), equals the drag force. The gravitational force can be calculated using the sphere's mass (m) and the acceleration due to gravity (g), while the buoyant force is the volume (V) of the sphere times the density of the liquid (ρ1) times g.
The formula to find viscosity is then given from rearranging Stokes' law as follows:
η = πs9r2g(v/π1 - πs)
Where:
- πs is the density of the sphere
- π1 is the density of the viscous liquid
- r is the radius of the sphere
- v is the terminal velocity
- g is the acceleration due to gravity
By substituting the given values (sphere's mass of 2.80 g, radius of 0.50 cm, liquid's density of 1.20 x 103 kg/m3, terminal velocity of 5.0 cm/s) into the rearranged equation, we can calculate the viscosity of the liquid.
Please note: This calculation assumes spherical particles, laminar flow, and that terminal velocity has been reached. Additionally, the radius should be converted to meters, and mass needs to be converted to kilograms to keep the units consistent.