Question

6. A mill in a textile plant uses the belt-and-pulley arrangement shown below to transmit power. Pulley A rotates with an angular acceleration of aA = (10t + 5) rad/s, where t is in seconds. The hub at D is rigidly connected to pulley C and turn with it. Pulley A has an angular velocity of 15 rad/s when t=0s. i) Determine the angular velocity and angular displacement of Pulley A when t=2s ii) Determine the angular velocity and angular displacement of Pulley C when t=2s iii) Determine the angular velocity and angular displacement of Pulley D when t=2s iv) Determine the angular velocity and angular displacement of Pulley B when t=2s (35 points) B 4 cm 3cm с 5 cm 4 cm 001

Answer 1

Given : RB = 4cm, Ro=3cm RC=5cm and RA= 4cm 1 = (10r75) rad/s² WA = 15 rods when to Sol d = do at dangolar accelarahon W - angular velocih o angular displacement Sadar WACH) = = 5 clor+5) dr WA (t) = lot 10+2 +5rta at +=o 15 = otot Ci15 WA (t) = 5+² +51+ 15 Swat Of(t) = s(s+2+5++15)dt OACE) + 5+2 +15+ + C2 = 5t at t=0 5) OA (0) = 0 =) 03 (2 LOA (t) = 563 3 543 + 5+² +15t

from given arrangement of Pulley 'À and Ć" Wc = RA Oc OA Oc OA wo OA Pulley 'cand 'D' Shaft same are WoW and Op = Od For Pulley arrangement 'B' and D' B - Ro RB OB WB LD Ako Polley A WA (2) = 5x2² + 5x2 + 15 WA (2) = 45 rad's OA (2) = 5x23 + 5x2² + 15X2 = 53.33 rad 2 OA (2) = 53.33 rad

(ii) Pulley Gi Wc (2) = 4/8 X WA and Oc (2) = 4/2 TOA c 5 x 45 = 5*53:33 oc= 36 rad)s and Oc = 42.67 rad (iii) pulley Di WD = wo and Op = OC WD = 36 rad's and 0o = 42.6) rad (iv) Polley B: WB = 3 wo and Osa 20 and 3 WR = = 3 x 36 4 X 42.60 Wg= 27 rad/s and OB = 32 rad