Answer to Question #130934 in Electrical Engineering for Mustafa

Question #130934
The rod OA in Fig . 12-33a rotates in the horizontal plane such that A = ( trad . At the same time , the collar B is sliding outward along OA so that r = ( 100+ ) mm . If in both cases / is in seconds , determine the velocity and acceleration of the collar when I = I s .
1
Expert's answer
2020-09-01T07:11:07-0400

Solution

coordinate system-Since time-parametric equation of the are given,it is not necessary to relate r to theta.

Velocity and acceleration- determining the time derivatives and evaluating them when t = 1s, we have

r = 100t2 |t=1s = 100 mm theta = t3 |t=1s = 1 rad = 57.30

r' = 200t |t=1s = 200 mm/s theta = 3 t3 |t=1s = 3 rad/s

r'' = 200 |t=1s = 200 mm/s2 theta = 6 t |t=1s = 6 rad/s2

v = rur + r thetha u theta = { 200 ur + 300utheta } mm/s

the magnitude of v is

v = sqrt 2002 + 3002 = 361 mm/s

sigma = tan-1 (300/200) = 56.30 sigma + 57.30 = 1140

also

a = [200-100(3)2]ur + [100(6) + 2(200) 3]utheta

the magnitude of a is

a = sqrt 7002 + 18002 = 1930 mm/s2

delta = tan-1 (1800/700)=68.70 (1800-delta) +57.30 = 1690



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