Question

PROBLEM: The rod OA in Fig. 12–33a rotates in the horizontal plane such that 0 = (rº) rad. At the same time, the collar B is sliding outward along OA so that r = (1001) mm. If in both cases t is in seconds, determine the velocity and acceleration of the collar when 1 = 1 s. SOLUTION Coordinate System. Since time-parametric equations of the path are given, it is not necessary to relate r to 0. Velocity and Acceleration. Determining the time derivatives and evaluating them when t = 1 s, we have r = 100+| = 100 mm A = 7 = 1 rad = 57.3° (a)

Answer 1

at toisec r=100t 3 = (13= 1 rad=57.3 100 (1) 2 = 16 mm = 200t o = 3t - 200(1) = 200 mm/s 3 (1) – 3 rad's 8= 66 = 6(1) = 6 radhe r 2.00 mmfi velouty varur troño 200 urt too (100) (3) no = (200 u + 300 M) Magnitude: * = (u) = post + 300 361 mm/s. direction, so tan (300 = 56.30 Total = St 5.57.3 56.3+57.3 200 11636 2114 Acceleration: (r-r8²) un + (röterso) ou (200 - 100(3)), +(10016) + 2(200X3)) ūg (-700 700 urt 1800 to) mm/s magnitude, a -700 + 1800* 1930 mm/s Direction, &- tam (150 (150-1) + 57,3 & 150 - 68.2") 157,3° . 682