 #1
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 Homework Statement:
 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 2:
Please check if my work is correct.
Main equation: Fc = Fg  Fn
Fn = Fg  Fc
I assume that: Fn = Fg when stationary
Fg = mg
I divide by 5 because the apparent weight must be one fifth of her weight when stationary
Fg = mg / 5
Fn = Fg
Fn = mg / 5
Now to substitute back into the equation Fn = Fg  Fc
Fn / m = g  V^2 / r
Fn(r) / m = g(r)  V^2
mgr / 5m = gr  V^2
(gr / 5) + gr = V^2
V = 6.17 m/s^2
Please check if my work is correct.
Main equation: Fc = Fg  Fn
Fn = Fg  Fc
I assume that: Fn = Fg when stationary
Fg = mg
I divide by 5 because the apparent weight must be one fifth of her weight when stationary
Fg = mg / 5
Fn = Fg
Fn = mg / 5
Now to substitute back into the equation Fn = Fg  Fc
Fn / m = g  V^2 / r
Fn(r) / m = g(r)  V^2
mgr / 5m = gr  V^2
(gr / 5) + gr = V^2
V = 6.17 m/s^2