Answer
(a) The normal force on the crate is directed at an angle of $80.0^{\circ}$ above the horizontal.
The force of static friction exerted on the crate is directed up the ramp at an angle of $10.0^{\circ}$ above the horizontal.
(b) The normal force on the crate is directed at an angle of $80.0^{\circ}$ above the horizontal.
The force of kinetic friction exerted on the crate is directed down the ramp at an angle of $10.0^{\circ}$ below the horizontal.
(c) The normal force on the crate is directed at an angle of $80.0^{\circ}$ above the horizontal.
The force of kinetic friction exerted on the crate is directed up the ramp at an angle of $10.0^{\circ}$ above the horizontal.
Work Step by Step
(a) The normal force on the crate is perpendicular to the surface of the ramp. Thus the normal force on the crate is directed at an angle of $80.0^{\circ}$ above the horizontal.
Since the crate is at rest, the force of static friction exerted on the crate is directed up the ramp at an angle of $10.0^{\circ}$ above the horizontal.
(b) The normal force on the crate is perpendicular to the surface of the ramp. Thus the normal force on the crate is directed at an angle of $80.0^{\circ}$ above the horizontal.
Since the crate is sliding up the ramp, the force of kinetic friction exerted on the crate is directed down the ramp at an angle of $10.0^{\circ}$ below the horizontal.
(c) The normal force on the crate is perpendicular to the surface of the ramp. Thus the normal force on the crate is directed at an angle of $80.0^{\circ}$ above the horizontal.
Since the crate is sliding down the ramp, the force of kinetic friction exerted on the crate is directed up the ramp at an angle of $10.0^{\circ}$ above the horizontal.
