physics problem?

Question

Consider a block on an incline plane. The co-
fficients of static and kinetic friction between
the block and the incline are us = 0.433 and
uk = 0.31. The block is 1 kg
Calculate the critical angle theta c, where the
block just begins to slide. Answer in units of
degrees.

part2
Determine the magnitude of the frictional
force f when theta < theta critical.
1. abs(f) = mg sin theta
2. jfj = uk mg cos theta
3. jfj = usmg sin theta
4. jfj = usmg cos theta
5. jfj = uk mg sin theta
6. jfj = mg cot theta
7. jfj = mg cos theta

part3
Determine the magnitude of the frictional
force f when theta > theta critical.
1. jfj = mg cos theta
2. jfj = uk mg sin theta
3. jfj = uk mg cos theta
4. jfj = usmg sin theta
5. jfj = mg cot theta
6. jfj = usmg cos theta
7.jfj = mgtan theta

Answer 1

Part 1.
θ = arccos(μs) = arccos(0.433) = 64.342°
Part 2.
For θ < 64.342° the block has not begun to move, so
Ff = μs*m*g*cosθ
Part 3.
For θ < 64.342° the block is moving, so
Ff = μk*m*g*cosθ

Answer 2

theta 2