Final answer:
To find the radius of a spherical protein with a known terminal velocity, density, and suspension medium's viscosity, we use Stokes' law which equates the drag force to gravitational force and buoyant force, and solve for the radius.
Step-by-step explanation:
To calculate the radius of a spherical protein that is falling at a terminal speed in a liquid, we use the balance of forces as described by Stokes' Law. Since the drag force (Fs) is given by 6πηRv, where η is the coefficient of viscosity, R is the sphere's radius, and v is the terminal velocity, we can solve for R once we have the viscosity (taken to be 3.5 times that of water) and the given terminal velocity (1.60 x 10-6 m/s).
Here's the equation from Stokes' law that fits our scenario:
V = 2R2g(Ps - P1) / 9η,
where V is the terminal velocity, Ps is the density of the sphere, P1 is the density of the fluid, g is the acceleration due to gravity (9.80 m/s2), and R is the radius.
Assuming that η (viscosity of blood) is 3.5 times that of water (about 0.001 kg/m·s), we can rearrange the equation to solve for R:
R = √((9ηV) / (2g(Ps - P1)))
Substituting the known values, including the given density of the spherical protein (Ps = 5.90 x 103 kg/m3) and assuming the density of blood (about 1060 kg/m3), we can compute the radius.