12. [013 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER A 600-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform. llO-N rod as indicated in the gure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0\" angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) G) (a) Find the (magnitude of the) tension Tin the cable. _x In order to nd the tension in the cable, impose the requirements that the net torque and net force must satisfy at equilibrium. N (b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.) horizontal component E N vertical component E N Need Help? Use the hinge as your pivot point. Make sure you remember to include the hinge force acting to push the rod away from the wall and upwards (so it has an x- and a y-component). You'll need all three equilibrium equations to get the answers. Submit Answer T = 525. 3887 N T= 525.4 NV 2) Horizontal, vertical component of force exerted on left and of rod by hinge ( Frett ) in = 0 For - TC0860 = 0 Fot = TO8 60' = 5 25 . 3887 X (08 60 - 969.694 For= 1 6 2. 69 N Ex= $62. 7 N Horizontal for a exerted by hinge on left and rod Q vertical component + ( Fret ty ? ' Fy + T Sin6."- Wp - Wj = 10 Ey = WRthis - IsinG . = 1/0 + 600 - 525 . 38 87 x Sin 60 Fy - 25 5 . 000 0 38 9 N IFy = 25 5 . ON Vertical force eater, exerted by hinge onF. B. D A " Tsinto phy (90 - 35 2 Ices 60 0 3 m Sign Board -2 m we WS Given Weight of Sign Board WS = 60ON weight of god We = llON angle blw grope and wall = 30' angle b) w sope and sedend = 60 from triangle property width of board - 4m height of board = 3 m Since the system is in Rotational & Translational equilibrium . past ( a ) Find tension in cable taking torque about hinge zero We x 3 X Si n go + W