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# Answer to Question #104790 in Mechanics | Relativity for havefun7741

Question #104790

where d8 is 4
1
2020-03-11T14:18:58-0400

(ii) Consider block A only and write Newton's second law for it:

"Ox:-T\\text{ cos}30^\\circ+\\mu_kN_{A}=0,\\\\\nOy: T\\text{ sin}30^\\circ+N_{A}-m_Ag=0."

Express the normal force from the second equation:

"N_{A}=m_Ag-T\\text{ sin}30^\\circ,\\\\\n-T\\text{ cos}30^\\circ+\\mu_km_Ag-\\mu_kT\\text{ sin}30^\\circ=0,\\\\\n\\space\\\\\nT=\\frac{\\mu_km_Ag}{\\text{cos}30^\\circ+\\mu_k\\text{ sin}30^\\circ}=14.5\\text{ N}."

Consider only block B and find its acceleration from Newton's second law:

"Oy: N_B-m_Bg-N_A=0,\\\\\nOx: m_Ba=-\\mu_kN_B-\\mu_kN_A+N.\\\\\n\\space\\\\\na=\\frac{N-\\mu_k(N_B+N_A)}{m_B}=\\\\\n\\space\\\\\n=\\frac{N-\\mu_k[m_Bg+2(m_Ag-T\\text{ sin}30^\\circ)]}{m_B}=0.36\\text{ m\/s}^2."

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