Question

Description Evaluate the position, velocity and the time at which the 0.5 kg block leaves the surface of a cylindrical surface on which it slides. The block is assumed to have an initial velocity Vo at the top of the cylinder and is subject to a constraint friction force of kinetic coefficient of friction, Hk (See the below Figure). Consider the coefficient of kinetic friction between the block and surface to be zero in one case and Hk in the other, Compare your results. The radius of cylinder, r l'

Answer 1

m = 0.5 kg let, friction is zero F_c = Centripetal force for, block not leave, N > 0 F_c + N = mg cos theta N = mg cos theta - F_c > 0 - (1) F_c = mv^2/r = m(v_0^2 - 2g(r - r cos theta)/r from eq^n(1), mg cos theta - mv_0^2/r + 2gr(1 - cos theta) m/r > 0 g cos theta - v_0^2/r + 2g - 2g cos theta > 0 g cos theta - v_0^2/r + 2g > 0 g cos theta < -v_0^2 + 2g cos theta < 2 - v_0^2/rg Now, friction b/w block & path notequalto 0, mu alpha = co - efficient of friction N = mg cos theta - mv^2/R - (1) from, work energy theorem 1/2 mv^2 - 1/2 mv_0^2 = mg r(1 - cos theta) + w - (11) w = friction work done w = integral F_f dr =