Question

Suppose the coefficient of kinetic friction between m_A and the plane in the figure(Figure 1) is mu_k = 0.12, and that m_A = m_B = 2.7kg. As tub moves down, determine the magnitude of the acceleration of m_A and m_B, given theta = 32 degree. Express your answer using two significant figures. What smallest value of mu_k will keep the system from accelerating? Express your answer using two significant figures.

Answer 1

a) T −mAgsinθ−μk*FN =mAaA ............. (1)

T=mBg−mBa ...........(2)

From (1) and (2),
mBg−mBa−mAgsinθ−μk*mAgcosθ=mAaA

g−a−gsinθ−μk*gcosθ= a

10 - a - 5.3 - 1.018 = a
a = 1.84 m/s2

b) To keep it stationary,
mg = mg(sinθ + μk*cosθ)
0.53 + μk*0.848 = 1
μk = 0.554