Minimum speed on roller coaster loop and normal force on rounded hill

[DLxX]

Help with these questions please

At what minimum speed must a roller coaster be traveling when upside down at the top of a circle if the passengers are not to fall out? Assume a radius of curvature of 8.6.

2. A 1000kg sports car moving at 20m/s crosses the rounded top of a hill(radius = 100m). Determine (a) the normal force on the car, (b) the normal force on the 70kg driver, and (c) the car speed at which the normal force equals zero.

Thanks

 

[Zlex]

Well, I would solve the question for you, but looking around the forums that seems to be the thing not to do.

I'm not awesome at physics so perhaps I wll be corrected. But, consider the following for the first question:

1] F = m*a
2] For centripetal motion a = v^2 / r
3] Centripetal force will have to conteract that Force of gravity. ie Fg = Fc

2 would also seem to be pretty simple. Again, F = m*a, a =mv^2 / R

Mostly looks like plug and chug to me

Someone correct me if I'm wrong.

 

[Sirus]

Centripetal force is not counteracting the force of gravity; they both point in the same direction.

 

[rhia]

Centripetal force is not counteracting the force of gravity; they both point in the same direction.

Thats right...if you solve the problem in the frame of the roller-coaster then centrifugal force will counteract gravity.

From the Earth's frame the gravity and reaction force of the seat will provide the centripetal force.
So R+mg=mv^2 /r
For min v, R=0 i.e. the passengers are not in contact with their seats.
So vmin = sqroot(gr)

 

[Sirus]

if you solve the problem in the frame of the roller-coaster then centrifugal force will counteract gravity.

Actually centrifugal force does not exist.