Question

Dynamics

Question 1: The 50-kg, uniform crate slides down the inclined surface with an initial speed of 10 m/s. If the coefficient of kinetic friction between the crate and the inclined surface is My = 0.15, determine the distances the crate has moved when it momentarily stops. (Assume tipping over does not happen.) (a) 4.88 m (b) 7.26 m (C) 9.81 m (d) 13.8 m S 30°

Answer 1

50 kg Given :- m u = initial speed = 10 mis elk = .0.15 ve Final Speed o (crate stops at last) S = ? soln :- FBD of crate y ma a N Direction of motion L Fe = UK.N 130 A wsin 30 30 WCOS 30 w EFy = 0 N = WCOS 30 WCOS 30 = mg cos 30 = mg cos 30 - 50x9.81 x Cos 30 :- IN 424.785 N = m a De-alembert principle E Fn =ma wsin3o elk N mg sin 30 - Mk N (50X9.81 x0.5) - (0:15 x 424.785) = 50 a m a - 181.533 = 50 a a = 3.63 mis²

= Using kinematic equations v2=u²+2 as 0 = (10)? + 2 (3.63) S -100 S Negative sign as 2 x 3.63 crate slides down and in the end stops. SE 13.774 m It is required distance 's crate has moved Hence, correct answer is option (d)