Two objects are traveling around different circular orbits with constant speed. They both have the same acceleration but object A is traveling twice as fast as object B. The orbit radius for object A is _______ the orbit radius for object B.
a. one-fourth
b. one-half
c. the same as
d. twice
e. four times
2007-02-12 06:06:43 · 3 answers · asked by el tuani 1 in Science & Mathematics ➔ Physics
I would have said a half, but thinking it could be a quater..... If A is going twice as fast as B then it must be closer to the centre of the orbit , so the orbit radius has got to be smaller... I think....
2007-02-12 06:11:51 · answer #1 · answered by Turtle 2 · 0⤊ 2⤋
I won't give you the answer, but I'll help you out.
The equation for circular acceleration is a = - v^2 / r (negative v-squared over r).
That equation holds true for both objects. So you'd have an a-sub-A for Object A and an a-sub-B for object B.
You know the accelerations are equal, so set the righthand sides equal to each other:
-v^2/r [for A] = -v^2/r [for B]
You know that A is travelling twice as fast as B, so you can substitute the B velocity with that information.
Solve for the radius, and you will end up with an equation like
r [of A] = (factor) r [of B]
That factor is your answer.
Good luck.
2007-02-12 06:18:08 · answer #2 · answered by Michael 4 · 0⤊ 0⤋
The radius of A is twice that of B.
2007-02-12 06:19:45 · answer #3 · answered by Swamy 7 · 0⤊ 0⤋