Question

in the walter lewin exam http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/exams/exam_2.pdf
question 1(b) why is the static friction facing the spring

Answer 1

As said in the question, "In absence of any forces on the spring." So along the plane, friction and a component of weight are the forces acting on the block. The component of weight goes down, so friction has to go up and face the spring. Please point out my mistakes if there is any because i am just a foreign high school student :)

Answer 2

in 1(b) the spring is stretched when the say ignoring the forces on spring they mean when its relaxed

Answer 3

i just checked the solution, the static friction goes down the plane.\[F{fr}=\mu _{s}mg \cos \theta\] so you are correct all along :\

Answer 4

The spring is stretched in the direction going down the inclined plane and so it's restoring force will act to pull the mass back up the inclined plane. Friction will oppose the motion of the mass and will act in the direction down the inclined plane and away from the spring. Not sure why you thought the friction was acting toward the spring in this one? But yeah, it isn't as you expect.