Why no static friction in an inclined plane tension problem

[rzn972]

Homework Statement

PART A only

Homework Equations

The Attempt at a Solution

The answer suppose to be mg sin theta- t cos alpha = 0 ( Newton's law).
15g sin36.9 = t cos 30
However, why don't we need a force of static friction?

 

[TSny]

I agree with your concern. Part (a) is poorly worded. There would actually be a range of possible values for T depending on the amount and direction of the static friction.

Certainly T = 0 would be one of the possible values since you are given that the block stays in place when the cable is cut!

The supposed answer that you gave apparently assumes that the tension in the cable in part (a) has been adjusted to a particular value that makes the static friction force zero. But the wording of the problem doesn't imply that condition.

I suggest that you contact your instructor and ask about it.

 

[goraemon]

The problem notes at the bottom that the solutions to the 3 parts are "independent" of each other. So the most reasonable assumption to make, given what you say is supposed to be the answer for (a), would be that there is no static friction for a), while for parts b) and c), there is friction. But yes, the problem should have made these conditions much more explicit, and is confusing as written.