Question

Problem k - 2.5 m - Body A, a 50 kg train signal, is attached to beam B of mass 250 kg. Bis suspended from a rigid support by a hinge and a cable. The geometry of the system is shown at right. – hinge a) What is the tension in the cable? Be sure to include a detailed free body diagram to accompany your analysis. -- 2.0 m B b) What is the magnitude of the force provided by the hinge? c) What is the moment of inertia of A + B as a rigid system, if rotating about the hinge? 0.5 m If the cable were to break, what would the angular acceleration of A+B be at the moment of breakage? What tangential acceleration would A experience? What tangential acceleration would the end of B (where it was previously attached to the cable) experience?

Answer 1

220m FBD VL LX 2.5m e A 2011 H 0.5m 9509 N Weisha Song of rod weight of A Calculation of so and coso sind = 32.5²-22 cow 2 - 5 = 0.8 2.5 Sino = 0.6 (a) now taking net torque at hinge is zero. Canticlockwise is positive) =) TX2 - 50x (2.0-0.5) coso - 250gx (20) coso = 0 -) 27 - 509x1.5 70.8-2500x1X0-8=0 =) 2T = 60g 200g = 260g - T = 130g =) T=1300N take g=10m/s² (6) Now taking Efa 20 and Efyzo -H+ Tsino =0 = H = 1300x0.6 =) H =780N and V+ T coso - 250g - 50g=0 =) V=300g - 1300x0.8 = 1960N magnitude of force by linge = 5H2+U2 = 1780) (19607 = 2109.5N

(s moment of inestia of A+B about linge = MAX (2.0-0.5)2 + max (2-0)? - 5015² + 250x2.02 3 = 445.8 Kg m² (d) of the cable will break T=0 = net torque at bringe = 50g x 15 cose + 250g x 20 cosa (clockwise) = 500X1.5X0.8 +2500x1.o X0-8 = 2600 N-m clockwise angular acceleration & = I 2 = 2600 25.83 rad/s² - 445.8 - 225-83 rad/3² tangential acceleration of end of B a = axra radius [AB = 5.8362.0 = 11. 66 m/s2 tangential acceleration of end of A ata = 5:83 x/2.0-0.5) [aA = 8.75 m/s2