Question

Name (Last) Total Points: Name (First) Last) Problem 2: A car is pushing a barrel to the right. The pushing force P is applied by the front bumper which is level with the center G of the barrel (see figure). The barrel has mass m, radius R, and radius of gyration ko. The coefficients of static and kinetic friction between the The coefficients of static and kinetic friction imper and the barrel are Hs and between the barrel and the road are also us and uk 1) If the barrel doesn't slip on the road, find the acceleration of the barrel and the minimum value of us required to ensure no slipping. If the barrel slips on the road, find the acceleration of G and the angular acceleration of the barrel. 2) n1

Answer 1

The barrel doesn't slip: - (pure rolling). = > a = R.alpha -(1) and p - f = ma -(2) and equation of torque about 'G': - f_s. R = (m k^2_G) alpha -(3) from (1) and (3) a = f_s R^2/m k^2_G -(4) from (2) and (4) = > p - f_s = m.(f_sR^2/mk^2_G) = > f_2 = pk^2_g/R^2 + k^2_G now f_s lessthanorequalto mu_s mg = > mu_s mg greaterthanorequalto pk^2_G/R^2 + k^2_G \r\n mu_s greaterthanorequalto pk^2_G/mg(R^2 + k^2_G) mu_s minimum = pk^2_G/mg(R^2 + K^2_G) (2) when the barrels slips: - = > a notequalto R alpha (gt is not b valid) = > p - f_k = ma p - mu_k mg - ma -(1) and f_k R = (mk^2_G)alpha -(2) and alpha = f_K R/mk^2_g = mu_k mg R/m k^2_g alpha = mu_k gR/k^2_G