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## Physics using incline planes

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?

(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.

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

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

Fnor = Fperp [normal force, opposite in direction to Fperp.]

Ffric = µk * Fnor [force due to friction, opposite in direction to Fpar.]

a = ∑F/m = (Fpar - Ffric)/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).