Question

Two Boxes (with masses 2kg and 7kg) are stacked on top of each other and connected through a pulley system as shown. The coefficients of friction between the boxes ar $\mu _{s}$ =0.5 and $\mu _{k}$ =0.3. Assume the floor is frictionless

A. apply newton's second law to free body diagrams, write out the equation.

B. find an equation for the magnitude of $\underset{F}{\rightarrow}$ where the boxes are just on the verge of sliding over each other. Call that magnitude $^{F_{slide}}$

Answer 1

Block B from vertical force balance N_1 = m_B g from horizontal force balance T.f_1 = m_B a where f_1 = mu N or mu_k N - (2) Block A Applying force balance in vertical N_2: N_1 + m_a g horizontal F - T - f_1 = m_A a - (2) b) Boxes are on the range of sliding therefore acceleration of both the blocks will be zero at the instant also static friction will be applied since will be a real Therefore from 1 and 2 T - mu_s m_B g = 0 = > T = mu_1 m_B g - (3) F = 2 mu_1 m_N g Force to be applied = 2 times 0.5 times 9.8 = 19.6 N