Question

Part C The rod is confined to move along the path due to the pins at its ends. At the instant shown, point A has the motion shown. Suppose that vA 7.5 ft/s and aA 2 t/s2.(Figure 1) Detenmine the magnitude of the acceleration of point B at this instant. Express your answer using three significant figures. Figure 1 of 1 Submit Request Answer Part D Determine the direction of the acceleration of point B at this instant. 5 t Express your answer using three significant figures 3 ft o, measured counterclockwise from the positive a-axis Submit Request Answer

Answer 1

Given data V_A = 7.5 ft/s a_n = 2 ft/s V_B = V_A + W r_B_n V_B_j = 7.5 + i (-wk) -4i -2j) [kxi = j kxj = -i] V_B_j = 7.5i + -4wj-2wi Equating 'I' coefficients 7.5-2w = 0 w = 3.75 w = 3.75 rad/s V_B = 4w = 4 times 3.75 = 15 V_B = 15 ft/s V_b 0i + 15j tan(theta_v) = (15/0) theta_v = tan^-1 (alpha) theta_v = 90 degree \r\n a_b = q_A + alpha r_BA-w^2 r_BA a_B = a_B_n I + a_B j a_B_n = V_B^2/r_B = = (15)^2/2 = 225/2 = 112.5 112.5 I + a_B j = -2i + alpha k (-4 i-2j)-(3-75)^2 (-4i-2j) 112.5 I + a_B_i = -2i-4 alpha j + 2 alpha I + 14.0625 (4i + 2j) Equating coefficients 112.5 I = -2 + 2 alpha + 14.0625 times 4 alpha = 112.5 + 56.25/2 alpha = 59.25/2 alpha 29.625 rad/s^2 Coefficient J implies a_Bt = -4 alpha + 14.0625 times 2