(a) Take into account that the centrifugal force experienced by each car is given by:
where v1 and v2 are the speed of both cars and R1 and R2 are the radius of the curve traveled by each car, m is the mass of the cars.
If you solve for m, you obtain:
due to the masses of the cars are identical, you have:
(b) Now, consider that:
R1 = 2R
v1 = v
R2 = 6R
v2 = 3v
Now, divide the equation for F1 over the equation for F2, replace the previous expressions for the parameters and simplify for F1: