I need someone to clarify a conceptual problem I can't seem to surpass. Image there is a rollercoaster loop and a rollerbcoaster car enters the loop at high speed.
Once the car completes the full loop and is then at the last point at the bottom of the loop, I am trying to understanding the forces at play.
I can see that there is gravitational force: $F_g$ = $mg$ and centripetal force: $F_c = \frac{mv^2}{r}$, and then there is the normal force $F_N$.
Let's say $F_g = 10$ ,and $F_c = 25$, wouldn't $F_N = 35$?
And if so, I am very confused about the force diagram. We have $F_N$ pointing up and $F_g$ pointing down, but what about $F_c$? My calculation has it pointing down, but in reality I thought centripetal force always points to the center of a circle?
Thanks for the help!
Best Answer
The centripetal force isn't a separate force. It is the vector sum of the forces that are present. In the case of a roller coaster, the normal force and the force of gravity will add vectorically to produce a net force, and that net force must apply the centripetal force to keep you moving in a circle. Because the force of gravity is constant, the normal force will change (both in magnitude and direction) to provide the remainder of the centripetal force.
When you are at the top of the loop, both the normal force and gravity point in the same direction. When you are at the bottom of the loop, the normal force points up, the opposite direction as gravity (down). So the normal force will have to be larger in magnitude when you are at the bottom of the loop than it is when you are at the top of the loop.