I was trying to solve this problem, I got the right answer with the wrong interpretation:
At what minimum speed must a roller coaster be traveling when upside down at the top of a circle so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.
So I drew up my free body diagram and I assumed that the forces acting on this scenario were:
$netforce = weight$
So I assumed the only force acting on the passengers was weight because they did not mention any friction. However, when my teacher explained this, he drew up his diagram including the normal force as well. I understood, of course there must be a normal force, due to the contact of the passenger with the seat, but I did not understand when he said that normal force was going the in direction of weight. How could normal force go in the direction of weight when the passenger is touching the seat, allowing them to avoid falling down, and pushing them upwards. So he said that the summation of forces was:
$netforce = weight + F_{normal}$
However, now there are two unknowns, how would you solved for velocity if we have the unknown of normal as well?