Physics using incline planes

Question

The carton  lies on a plane tilted at an angle θ = 24.5° to the horizontal, with µk = 0.07.

(a) Determine the acceleration of the carton as it slides down the plane.

(b) If the carton starts from rest 8.80 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?

Answer 1

(a). The acceleration of the carton is found by calculating the net force on the carton divided by its mass, ∑F/m.  There are four forces, two of which cancel each other out.

F_par = W sin θ = mg sin θ.  [force parallel to the incline.]

F_perp = W cos θ = mg cos θ.  [force perpendicular to the incline.]

F_nor = F_perp [normal force, opposite in direction to F_perp.]

F_fric = µk * F_nor [force due to friction, opposite in direction to F_par.]

a = ∑F/m = (F_par - F_fric)/m = (mg sin θ - µk * mg cos θ)/m = g sin θ - µk * g cos θ = g(sin θ - µk * cos θ).

a = (9.81)(sin 24.5 - 0.07*cos 24.5) = 3.443 m/s².

(b). Try this one considering the acceleration has been calculated in (a).