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 Homework Statement:

Question 1. A student on a distant planet performs a "looptheloop" experiment. She releases a frictionless 1.3kg cart from a height of 4.50m. It is observed that the track exerts a downward, normal reaction force of 21 N on the cart at the top of the circle. Calculate the gravitational field strength of the distant planet.
Question 2.
A certain asteroid has a radius of 7.0x10^3 m and a mass of 5.0x10^15 kg. How fast would a cyclist have to travel on the surface of this asteroid in order for her apparent weight to be onefifth of her weight when stationary.
 Relevant Equations:

Fcentripetal = ma
a = v^2 / r
Fg = GMm / r^2
Potential Energy = GMm / r
Kinetic Energy = 0.5(mV^2)
Total Energy (Ek + Ep) = 0.5(GMm) / r
g = Fg / m
Diagram for question 1:
I know the mass, I need Fg.
My work:
Main equation: g = Fg/m I need to find Fg.
Epi = Ekf > GMm/r = 1/2(mV^2) < PROBLEM. When I solve this I can't square root it since it's a negative.
Let's say I solved this and found the velocity. For the "looptheloop", would the equation for the conservation of energy be Eki = Epf + Ekf?
Diagram for question 2:
So I started out by trying to find the strength of the gravitational field as I wanted to use Fc = Fg  Fn to find the velocity but I didn't have the mass of the cyclist. I tried to cross out all the masses on the equation but Fn prevented me from doing that. I don't know what I can do here.
I know the mass, I need Fg.
My work:
Main equation: g = Fg/m I need to find Fg.
 Fg= Fc  Fn [Fn = 21 N Fc = ?] {I need to find Fc.}
 Fc = ma > Fc = (mV^2)/ r [Mass = 1.3kg V = ? r = 0.70] {Now I need the velocity at that point where Fn = 21 N (the top of the looptheloop)}
 I break up the course into parts. I use the conservation of energy to try and solve the first part (4.50m) and use that velocity to solve the second parts velocity at the top (the looptheloop).
Epi = Ekf > GMm/r = 1/2(mV^2) < PROBLEM. When I solve this I can't square root it since it's a negative.
Let's say I solved this and found the velocity. For the "looptheloop", would the equation for the conservation of energy be Eki = Epf + Ekf?
Diagram for question 2:
So I started out by trying to find the strength of the gravitational field as I wanted to use Fc = Fg  Fn to find the velocity but I didn't have the mass of the cyclist. I tried to cross out all the masses on the equation but Fn prevented me from doing that. I don't know what I can do here.