- #1
Cake
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Homework Statement
This Problem involves solving a simple Diff. Eq.
A block of mass m slides on a frictionless table. It is constrained to move inside a ring of radius L that is fixed to the table. At t=0 the block is moving along the inside of the ring (In the tangential direction) with velocity [itex]v_0[/itex]. The coefficient of friction between the block and the ring is [itex]\mu[/itex]
a) Find the velocity of the block at later times
b)Find the position at later times
The Attempt at a Solution
I don't have the ability to post a picture, but I'm using the radius inward from the block for the positive x direction, and direction of motion perpendicular to the radius as the positive y direction.
Sum of the forces:
SUM-X=[itex]\frac{m(v_0)^2} {L}[/itex]
SUM-Y=[itex]m\frac{dv} {dt}-m\mu\frac{dv} {dt}[/itex]
I'd like to know if I'm right so far. My problem is I'm not sure where to go from here. I think my sum of the forces in the x direction are faulty because dividing through, solving for dv/dt, and then working the diff. eq. doesn't give the right answer.
Thanks for any help :D