Question

The weight is used to turn the gear system shown below. Gear A has a mass of 15 kg and a radius of gyration of 100 mm about its center of mass. Gear B and Drum C have a combined mass of 25 kg and a radius of gyration about their mass center of 165 mm. If the system starts from rest, determine the speed of the 55-kg weight after it has been lowered 3 m, the angular velocity of each gear, and the linear velocity of the meshing teeth between Gear A and Gear B. 100 mm 150 mm 0.0 B 200 mm D

Answer 1

mg = by si KA = 0.1 m Downward desplacement of ka @ 3910 ? mg = 25 E7 mo= 55 kg Лот D. - 3 m и ( о г шw aoj = 24 шza - 9А raa NA = 0.15 m TR TR agad B A VT AT А ТА — 0 82 = a ad a da a 2 Lg= Үg TR = IALA сі , Tre- TR = IB LB сь) (ін) ть? — T - та (f) + (ii) + (iii) x x mo8 хvс - Ід ад + IgM + траха maka ada + mo kpl a Тр + тос а 22. & dщ € PA & щ 2 MAK та так Те + ФоYe

SS X 9.81 x 0.1 > 11 15x 0.12 25 X 0.1652 + + 55 Xool D.IS 0.22 a = 2.2944 m/s2 VaRd v = 13 stray 0? + 2 x 2.2944 X3 V = 2x 2.29443 > % = 3.7103 m/s I w speed of 55 kg mass WA VA = WBTB = V WA * 0.15 = WB x 0.2 = 3.7103 WA = W { 24.7353 rad/see = 18.5515 Radsee ( clockwise) Canti-clockwise) w WB Lineas relacity of messing teeth would be same relocity of mass D. Hence, lineas relacity of messing feeth 3.7103 m/s