Gravitational Potential Energy of an object

[mickellowery]

Homework Statement

Consider a large uniform ring having a mass of 2.36x10²⁰kg and a radius 1.00x10⁸m. An object with a mass of 1000kg is placed at a point 2.00x10⁸m from the center of the ring. When the object is released, the attraction of the ring makes the object move along a straight line toward the center of the ring. Calculate the gravitational potential energy of the object-ring system when the object is at the starting point, and then calculate the potential energy at the ending point. Calculate the object's speed as it passes through B.

Homework Equations

U= -Gm₁m₂/r

The Attempt at a Solution

I used this equation for the initial condition with G=6.673x10^-11 m₁=2.36x10²⁰ m₂=1000 and r=2.00x10⁸. The answer I got was -7.87x10⁴. The book says that the answer is -7.04x10⁴, I am assuming that I need to factor in the radius of the ring somehow but I don't know how I should work it into the equation.

 

[Doc Al]

You're using the wrong distance. You need the distance between the object and the ring (where the mass is), not between the object and the center of the ring.

 

[mickellowery]

Aaaahh I see, treat it like a right triangle and then use this equation. You've saved my sanity one more time Doc. Thanks so much.