The picture is a table with a box on top (m_A) with a rope going to a pully (45
ID: 2133990 • Letter: T
Question
The picture is a table with a box on top (m_A) with a rope going to a pully (45 degrees out of the corner) and then the rope goes down to the second box (m_B) which is free hanging. m_A----------0 | | m_b Determine a formula for the acceleration of the system shown in the figure(Figure 1) in terms of m_A, m_B, and the mass of the cord, m_C. Assume f f to be the fraction of the cord that is hanging down between m_B and the pulley, and u_k to be the coefficient of kinetic friction between mass m_A and the table. Express your answer in terms of the variables m_A, m_B, m_C mc , u_kmu k , f, and appropriate constants. The picture is a table with a box on top (m_A) with a rope going to a pully (45 degrees out of the corner) and then the rope goes down to the second box (m_B) which is free hanging. m_A-Explanation / Answer
mBg -T = mBa-----------------------(1)
T-T' = dm(a- g) = mC*g*f------------------(2)
T'-T1 = mc(mu_k*(1-f)*g+a)------------------------(3)
T1-ukmAg = mA a -------------(4)
solving these 4 we get th answer
a = mBg+f*mc*g-mu_k*(ma + (1-f)mC)g/(mA+mB+mC)
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