Question

CLASS ID: (2) GIVEN: (35 PTS) A completely filled barrel A and its contents have a combined mass of 90 kg. Cylinder B is connected to the barrel by an ideal pulley/rope system that is attached to A at a height h=550 mm as shown. The coefficients of friction between the barrel and floor are respectively. u.=0.40 and 14=0.35. Find: (A) (-9 Pts) Determine the maximum allowable mass of B such that the barrel A will NOT TIP OVER its corner at D (the comer radius is of negligible dimensions). (Hint: Assume the barrel slides under the load, then validate with the results) (B) (-9 Pts) The ACCELERATION of the barrel: (C) (-9 Pts) The REACTION between the floor and barrel as the barrel reaches its tipping limit. (D) (-8 Pts) The TENSION (T) in the cord connecting A & B. W.500 mm som D ME 3133: Dynamics Spring 2018 - Final Exam

Answer 1

Given data:- combined mais cm) = 90 kg height Ch) = 550 mm coefficient friction between the barrel and floor Hs - 0.40 Hk = 0.35 w=500mm A H=900 mm 450 mm 550 mm Line diagram from the above figure T los mm G moa mag MIN N Therefore, = 0.35 N hhere, Frictional force CFp] = Mike N FF N is the normal reaction blw the floor and barrel .: Equilibrium in vesticle condition Efy = 0 N-woo N: We N= mog

N = 90x9.81 - 882-9 N Normal reaction blw floor and barrel N= 882.9 N Therefore moment about a EHG=0 NCL) - 1001 - 450 (0:35XN) -O NCL) - (450) C0.35N) T 100 NCL-64500.35)) 500 100 1169= 882.9 (250 - C450*0.35)] 100 816-6825 N Tension CT) - 816.6825 N Therefore Tension CT) in the cord connecting Ao B Tension CT) - 816-6825 N :: Equillibrium Equation in x- direction { Fx - mga T-0.35N - moa 816•6825 - 0:35C882.9) = 90ca)

.; acceleration ca) = 5064075 m/s Therefore acceleration of the bayxel acceleration ca) = 5.64075 m/s from the above figure Cylinder T :B mog mga Equillibrium Equation in veyhcal direchon {fy = mga 58 - 1 = mga mog - T = mga .. mg T 9-а 8166825 3 9.81-5.64075 195-882 kg .: MB - 195.882 kg Therefore , maximum allowable mass of c8) such that bartel A hill not tip over it comer at D. mais cmp] = 195-882 kg