# Tricky Forces Problem

1. Homework Statement

Two masses, m1 = m2 = 2.7 kg, are connected by a light cord over a frictionless pulley. The coefficient of kinetic friction is 0.15 and the angle of the inclined plane is 25°. Find the acceleration of the system and the tension in the cord. What minimum value of μk will keep the system from accelerating?

2. Homework Equations

Fnet = summation of all forces
Fnet = ma

3. The Attempt at a Solution

My problem begins when I am trying to find the new coefficient of kinetic friction that will prevent the masses from accelerating.

I found the acceleration to be 2.2 m/s^2 and the tension in the cord to be 21 N. When solving for the coefficient that will prevent the system from accelerating, I made the net force in the horizontal direction (parallel to the motion of mass 1) equal 0 N since it would mean that the object would no longer accelerate. I found the new force of friction to be 9.4 N and found the coefficient of kinetic friction to be 0.39.

However, a thought just came to me now .... if the force of friction changed ... wouldn't that also change the force of tension in the string thus making my answer incorrect? If so, how would I solve it?