Enter. the answer in m/s

Question

You are on a roller coaster with a vertical loop of radius 12.6 m. At the top of the loop you are inverted and you momentarily feel weightless. Find your speed at this moment.

Enter your answer, in m/s, in the box below.

    

Answer 1

Free-body at the top of the loop:

So the net force is F_N + F_g and that equals mass times acceleration. The acceleration is the centripetal acceleration pointing inward just like the forces so:

F_N + F_g = ma

(Note that a typical orientation would be to use negative signs on each of these terms but I have chosen to consider positive as downwards - it works out the same mathematically.)

A key to this is that to fell "weightless", the normal force would need to be zero so:

F_N = 0

F_g = mg

The centripetal acceleration is calculated from:

a = v²/r so putting those together:

F_N + F_g = ma

0 + mg = m(v²/r)

g = v²/r

gr = v²

v = √(gr)

So the velocity to feel weightless is √(gr) = √(9.81•12.6) = 11.1 m/s