- #1

hobbes1235

- 13

- 0

- 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 one-fifth 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