Answer to Question #104790 in Mechanics | Relativity for havefun7741

Question

[img]https://upload.cc/i1/2020/03/06/CsXpzH.jpg[/img]


where d8 is 4

Answer 1

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

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

Express the normal force from the second equation:

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

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

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