- #1
steven09
- 2
- 0
1. Homework Statement
A particle moves under the influence of a central force, F_r(r) = − α r^−3. At time t = 0, the radius = r0 and the velocity = v0 as shown in the figure.
(A) Determine the potential energy function U(r).
(B) Determine the velocity vc such that the particle will move on the circle.
(C) Now suppose v0 = vc /2. The particle will spiral into the origin. Calculate the time it will take the particle to reach r = 0.
2. Homework Equations
U(r) = - integral F(r) dr
3. The Attempt at a Solution
I got U(r).
For my Part B) I don't know how to get velocity and Part C) how to get time. I think I might have to set ma=− α r^−3 but that doesn't seem right
A particle moves under the influence of a central force, F_r(r) = − α r^−3. At time t = 0, the radius = r0 and the velocity = v0 as shown in the figure.
(A) Determine the potential energy function U(r).
(B) Determine the velocity vc such that the particle will move on the circle.
(C) Now suppose v0 = vc /2. The particle will spiral into the origin. Calculate the time it will take the particle to reach r = 0.
2. Homework Equations
U(r) = - integral F(r) dr
3. The Attempt at a Solution
I got U(r).
For my Part B) I don't know how to get velocity and Part C) how to get time. I think I might have to set ma=− α r^−3 but that doesn't seem right