Question

Consider a (macroscopic) mass of 10 kg sitting on a flat surface with μ.-0.3. Determine this mass's effective mass if we pretend there is no friction. Repeat part a if the mass now sits on an incline of 40°, and you want to push it down the incline. a) b)

Answer 1

Given that mass = 10 kg mu_k = 0.3 Normal force f = 10 times g N = 100 N 10 = g F_k = 100 times 0.3 F_k = 30 N Apply a force F & then get acceleration 'a' equation is F - 30 = 10 a - (0) F = M_eff a a = F/M_eff F - 30 = 10 (F/M_eff) M_eff = 10 F/F - 30 kg M_eff depends on force on are giving \r\n The free body diagram is Frictional force is F_k = mu_k mg cos theta = 0.3 times 100 times cos (40) = 30 times cos (40) = 30 times 0.766044 F_k = 22.981 N If we want to push the block down, the equation will F + mg sin theta - mu_k mg cos theta = ma F + 100 sin theta - 30 cos theta = 10 a - (2) effective mass F + M_eff g sin theta = m_eff a a = F + M_eff g sin theta/M_eff