Answer to Question #130934 in Electrical Engineering for Mustafa

Question

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 .

Answer 1

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 = ru_r + r thetha u _theta = { 200 u_r + 300u_theta } 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]u_r + [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