Question

Chapter 2, Practice Problem 2/067 For an interval of motion the drum of radius b = 137 mm turns clockwise at a constant rate w = 2.7 rad/s and causes the carriage P to move to the right as the unwound length of the connecting cable is shortened. The distance h = 1.1 m. Use polar coordinates r and and find the magnitudes of the velocity v and acceleration a of P in the horizontal guide when the angle = 20°. Check your solution by a direct differentiation with time of the relation x2 + 2 = r. Answers: m/s m/s2

Answer 1

Soln As per problem h2+x2=720 : as the drom is moving Avs - or rotating with angolor Blve the speed w=27radis k o hina the String Spud is ve = wb = 0:137 *2.7 = 0.34 m/s Differentiate equatim o with respect to time. . (z ostaje = (20 dia] =) xdx = 1 - 0 dt Vaze From figure. Iva = Sacro vs | Vz = Sec20° X Vs = 0.393 mls Differentiatin equation again with respect to time. | (0) + 4 = 2 + 4 , Sing', A Gencle+ ve te ax = [Vs )? fer 0= 20, x=hton 20' = 'ix tem 20 dtz 0.3922 6 ) Acceleration ada = VS_V2 = 0.37 Az = 0.372-0.3932 -0.044 m/s2 Tiex tn 20 d2. 12 = ar