PHYSICS. What is the speed of a roller coaster car as it hits the top on a 50.0m loop-the-loop. w=w(app)?

Question

As a roller coaster car crosses the top of a 50.0 -diameter loop-the-loop, its apparent weight is the same as its true weight. What is the car's speed at the top?

Detail/questions: I've gotten that far but still haven't figured out how to use F(net) and R to figure out the speed of the car, does anyone know that? I don't even request numbers, just a formula or clue, anything! thanks!

Answer 1

Very interesting.

The formula for centripetal force is

F = mv^2/r

Using Arbiter's idea, below, we have

2mg = mv^2/r

m cancels, as you would expect. The speed should be the same regardless of the mass of the car, and indeed the mass of the car is not given in the problem.

Then we have

2g = v^2/r

and r is given as 50 meters.

Answer 2

At that instant then, gravity pulls downward with 1 g of force, while centripetal force pulls upward with 2 g, to counteract the downward force of gravity.