Question

No vector method pls

3. The step pulleys shown are connected by a crossed belt. If the angular acceleration of B is 2 ofa 3rad/sec, what time is required for D to travel 12m from rest? Through what distance will A move while D moves 18m? 250mm 100mm 400mm 500mm

Answer 1

Angular acceleration of B, alpha_B = 3rad/s^2 is given From that we will find alpha_c as below alpha infinity 1/r Hence, alpha_B/ alpha_C = r_C/r_B Therefore alpha_C = alpha_B times r_B/r_C = 3 times 0.25/0.1 = 7.5 rad/sec rightwardsdoublearrow Now, linear acceleration of outer pulley of D, a_2 = alpha_c . r_D = 7.5 times 0.4 = 3 m/s^2 rightarrow From equation of motion, S = ut + 1/2 alpha t^2, we will find time required for D to travel 12 m. \r\n Therefore R = 0 + 1/2 times (3) t^2 (as initial velocity = 0) Therefore t^2 = 8 Therefore t = 2.828 sec rightwardsdoublearrow Now, we have to find distance S_A while D moves 18m Therefore Linear acceleration of outer pulley of A a_1 = alpha_B times r_A = 3 times 0.5 = 1.5 m/s^2 Therefore S_A = 0 + 1/2 times a_1 times t_2^2 rightarrow where t_2 is final from equation of motion applied to pulley B for S = 18m