Answer to Question #178516 in Classical Mechanics for Zeke Miller

Question

Box A, resting on a ramp, is connected box B through a pulley system. The coefficient of kinetic friction for box A, the height of box B above the ground, and the angle of inclination for the ramp are provided in the information section below. After the boxes are released, how far up the ramp will Box A travel?

m A = 7.0 kg

m B = 4.0 kg

µ kA = 0.10

h = 1.5 m

θ = 20°

Answer 1

$m_Agsin\theta-T+F_f=m_Aa,$

$N-m_Agcos\theta=0,$

$T-m_Bg=m_Ba,$

$F_f=\mu N,$

$N=m_Agcos \theta,$

$T=m_B(g+a),$

$a=\frac{g(m_Asin \theta-m_B+\mu m_Acos \theta }{m_A+m_B}=-0.85~\frac{m}{s^2}<0,$

$l=\frac{h}{sin\theta}=4.39~m$ down.