What would friction be in this pulley system

[spectravoid]

1. You have a mass hanging off of a frictionless pulley (massless string). The other mass is on a table. The weight of the mass causes the block on the table to slide at an acceleration. There is friction between the block and the table. What would the coefficient of kinetic friction be for this set up?



2. F = ma
w = mg



3. Well Since the system is accelerating, I thought it was

T(rope) - fk = ma
Acceleration and the masses are known. T isn't.

But you can set this up for both masses

T(rope) - ukm1g = m1a
T(rope) - m2g = m2a
T(rope) = m2g + m2a
m2g + m2a - ukm1g = m1a
-ukm1g = m1a -m2a - m2g
-uk(0.483)(10) = 0.483(1.66) - 0.25(1.66) - 0.25(10)
uk = 0.438

Does this make sense?

 

[rl.bhat]

In the second equation g and a are in the same direction. Hence they must have the same sign.