Answer to Question #267810 in Classical Mechanics for zaw

Question

A 400 kg mass on 30∘ inclined plane is acted upon by a force equal to 4800 N at an angle 30∘ with the incline as shown in the figure below.

a) Find the acceleration of the mass if the incline is frictionless

b) Find the acceleration of the mass if the coefficient of fiction between the mass and inclined plane is μk=0.2 

Answer 1

a)

$m\vec a=\vec F+m\vec g,$

$a=\frac Fm\cos 30°-g\sin 30°=5.5~\frac m{s^2},$

b)

$m\vec a=\vec F+m\vec g+\vec F_{fr},$

$a=\frac Fm\cos 30°-g\sin 30°-\mu g\cos 30°=3.8~\frac m{s^2}.$