A physics problem in my textbook reads:
A 0.40kg ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 60N, what is the maximum speed the ball can have? How would your answer be affected if there were friction?
Obviously the first question is easy to calculate. But the second one gave me some trouble. The book answer states that friction would not affect the problem, however I believe it would. In order for a limp cord to accelerate the ball in uniform circular motion, the force moving the cord would have to go in a circle of its own if there were friction. Below I drew a picture of my idea of the problem. (The text in the middle says center of rotation). 
You can see that the net force has to be greater than it would otherwise have been because of friction. Assuming that the book answer is wrong though, I have another question about the diagram I drew. Would the force of friction act tangent to the circle as I have indicated below? Or would it behave differently?
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