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 200 mm D

Please show all work and steps. Any help will be appreciated and thank you for your time!

Answer 1

page, povestiom solution briven that Two years are of different diameter in mesting with each other and carrying a weight with supe. Gear A ! mA= 15kg Radius of Gygation (KG) = 1o mom = 0.1 m A → (Gear B + Drum c) :-(om otme) = 25 kg Radius of gyration about centre of mass=k.com (Kurlete 165 mom on 165 m → system start from rest weight of D= womo = sskg

page- we have to determine each gear il speed of the weight 5s-kg after it has beem Lowered Bom. (ii) Angular velocity of ie WA = ? WB = ? (iii) Linear velocity and of the meshifong deeth between hear A and Gear B. NA= (samom trear B breast Doum C 8c = lumm 982200 mm Kg/D 715579

page. Free body diagram of bear B douma'c' and weight o Carbine QB B > със IT at starting IT assg 55 Kg D 99 Apply Togare. conservation (559) & Twet Btc B χ α about COM = (ssg) rc FX AB imb tmc [Kalaula & mox la8²

page- → (5589.911* 2 X pins (o Fx200 ino les 29% 0.115 2B 558 volt (53.955) -(0.2)F (1.23 dB (1 = > Free body diagram of hear. A LA A raa (sammom - 0r15m Apply Torare conservation ETnet = FFA Jabout. XCA Cam >> FX 0.15 E [mA (A x LA [(5x (0-1) 2.] LA V FXonis

Page - F = List okol ofis (1) A and / from equation 6 and ② put the value of F = xal in eavation 2 153.955-(0.27 LA & (1023) 2B (0-2) 2A +(1-23 ) dB = 53.955 L o Since, from the Law of hearing NA NE WANA =WBOB dWA MA dWB dt. dt dB. No LA V NA

page- IA TB VA = 2067 X5 XA z 4. 3 dA=.4 dB 3 So from equation ③ - 55.955 (0:2)x d8 +(1.239 dB V. LB 255.gsS [ 3. 0.8.+ 1:23] dB [ 0.267 267 + 7023] LB 55.gss "55.955 rad/S² 1.497 dB 6. (37.37 rad 15² angular acceleration of Gear B aswell as drum C.

page-① so, LA 1 2 3 4 X 37:37 7 = (49.82] sad 15? Amgular acceleration of hear A. Now, li) for Velocity of D (55kg) do = dB (3 7637 g radis ac V = 37:37 V ac 37:37370 37.37 x 0, ) mis? ac (3.7377 mis . lapa ac. (3.737) mis aca 9= 3 m = ?

Pagento Apply Linear tho tiom equatran ffbarch* velo = (UE) @ + 2001 s = > (4) + 2X 3073723 Velo- 6 x 3.737 i Velo (4.735 m is (ii) for Angular velocity when D seach at s= 3m them VA), = e) = (4.735) omis (We) xre = 4.735 We a 4.735 = 4.735 re o 1 We = (47.359 gadis

page-@ We WB Because Aniq of Jo Aation in same WB= (17.35) sadis Rowy Ve= fronte >> WA NB = 4 20 1877 =413 WB NA 3 → WA x Wis = AM X 42.35 3 → WA = 63.13 189.4 3 WA = (63.13) radis liji ) for Linear velocity of the esting teeth m

Pagino IVA VO at point of contact (WA) VA = VB NA (WB) OB ". NA= (WA) NA = 163-138 0.15 [NA = VB = (3. 469) mis velocity of mething of death when (wat = 55 kg) fall G S = 3m