Any object moving in a fluid experiences a retarding drag fo

Any object moving in a fluid experiences a retarding drag force of magnitude F proportional to some power n of the velocity of the object in the fluid, F=kappa nu n where k and n are constants depending on the shape of the object and the properties of the fluid. Using linear regression, find the values of k and n from the following experimental values.

Solution

Consider the table:

As

F = k v^n

Then

log F = log k + n log v

Using technology, we get              
              
slope =    0.526326116          
intercept =    -1.032345006          
              
Thus, the regression line is              
              
y^ =    0.526326116x - 1.032345006

As

Thus,

slope = n = 0.526326116 [ANSWER, n]
intercept = log k --> k = 10^intercept = 0.09282287 [ANSWER, k]

v	F	log v	log F
10.1	0.315	1.004321	-0.50169
20	0.445	1.30103	-0.35164
29.9	0.555	1.475671	-0.25571
40	0.65	1.60206	-0.18709