An object of mass m moves in a circular path at constant speed v. The centripetal force on the object is F. If the object had double the mass and 1/4 the speed

Question

then the magnitude of the centripetal force on the object would be ____. answer in terms of F. (the answer is 1/8 F I just don't know how to get there)

Answer 1

Think of it as solving a proportion. In the first case you were given the initial parameters for an object moving in a circle, namely F=ma, or more specifically F=m(v^2/r). In the second part (we can call this force F') you're changing the parameters so that F'=2m(1/4v)^2/r or F'=2m(v^2/16)/r and simply F'=(1/8)m(v^2/r). Now look at those side by side:

F=m(v^2/r) and F'=(1/8)m(v^2/r)

The proportion then is F'=(1/8)F