Question

A roller coaster heads into a circular loop with radius 5m. At what minimum speed must the coaster go at the top of the loop to be sure it stays on the track?

I don't really understand what I am supposed to be solving for.

Answer 1

gravity and the curved track are supplying the centripetal force

if the required force is less than gravity (too slow in the loop), the coaster will not stay on the track

Answer 2

I am not certain about that at all.
Gravity is pushing the coaster down. to keep in on the loop, gravity must be greater than a force needed to keep the coaster in a circular path, if the force of gravity is not greater, the coaster will fly off the track.
The speed of "decision" is when gravity equals the force needed to keep the coaster on the track.
mg=mv^2/r
v=sqrt(rg)=sqrt(5*9.8) about 7m/s. This is the minimum speed to keep in on the track. Above this, the coaster flys off.
Gravity keeps the train on. If the coaster is faster, something else (magnets, or clamps, or ???) has to be attached to keep it on the track, to supply the inward (downward) force on the coaster to accelerate it downward.

Answer 3

Depends on if the train is under the loop looking up or over the loop looking down.

Since it says "minimum" speed I suspect we are under the track and need big speed to keep from dropping
mv^2/R > mg
or centripetal acceleration greater than g

Answer 4

Thank you!