# Heres a tough one i had on my final im dying to find out how to do it

1. Jun 13, 2007

### xxacefirexx

I dont remember the question verbatim, but here is all the info

1. The problem statement, all variables and given/known data

There is a mass attached to a rope which is attached to a pole. It is set to rotate on a horizontal surface (basic circular motion scenario). There is no kinetic friction along the table, but there is air friction.

The magnitude of air friction is related to velocity with the equation .2v.
m=3 kg
r=2 m
v(initial)=10 m/s

What is the centripetal acceleration after 5 s.

2. Relevant equations

F=ma=m(v^2/r)

3. The attempt at a solution

i know you gotta integrate the air friction function over the 5 s interval, but i cant express it in terms of t.

I am completely lost, please help. I know I got it wrong, but i really wanna know how to do it.

Thanks!

2. Jun 13, 2007

### PhanthomJay

F=mv^2/r is the correct centripetal force formula for the tension in the rope, but the problem is asking for the centripetal acceleration only. You need first, however, to use newton's 2nd law in the tangential direction, where the tangential acceleration is not constant. Thus,
use F=m(dv/dt), where F is the given air resistance force (presumably in force units of Newtons). You get a first order differential equation you must solve of the form -kv = mdv/dt. Solve for v and don't forget the boundary condition. Is this where you are stuck?

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