Question #178516

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°


1
Expert's answer
2021-04-06T18:25:12-0400

mAgsinθT+Ff=mAa,m_Agsin\theta-T+F_f=m_Aa,

NmAgcosθ=0,N-m_Agcos\theta=0,

TmBg=mBa,T-m_Bg=m_Ba,

Ff=μN,F_f=\mu N,

N=mAgcosθ,N=m_Agcos \theta,

T=mB(g+a),T=m_B(g+a),

a=g(mAsinθmB+μmAcosθmA+mB=0.85 ms2<0,a=\frac{g(m_Asin \theta-m_B+\mu m_Acos \theta }{m_A+m_B}=-0.85~\frac{m}{s^2}<0,

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


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