Box Friction Problem help ASAP!

Question

A box (m = 10.00 kg) is on a ramp with an incline of 30.0°. The ramp has a coefficient of static friction of 0.6 and a coefficient of kinetic friction of 0.2. Does the box slide down the ramp? If yes, what is the acceleration of the box? If no, what is the force of friction on the box?

(a) Draw a Free Body Diagram (FBD) of the box . Include coordinate axes.

(b) Split the forces on the box into x and y components.

(c) Use Newton’s Laws to determine the acceleration or force of friction. Be sure to include all steps (equation, substitution, algebra, result).

Answer 1

If the box were static then the friction and weight force components along the ramp would balance as

kmg cosθ ≥ mg sinθ i.e., 0.6 = k ≥ tanθ = tan30º = 0.577 (to 3 digits).