- #1

hobbes1235

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- Homework Statement
- Question 1. A student on a distant planet performs a "loop-the-loop" 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 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 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 "loop-the-loop", 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 loop-the-loop)}
- 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 loop-the-loop).

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 "loop-the-loop", 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.