Question

3m- -2m- 4501 450N Kim 20° 500N Main 200N 20. On a busy intersection a 3.00 m beam of 150 N is connected to a post at an angle upwards of 20.0 degrees to the horizontal. From the beam straight down hang a 200 N sign 1.00 m from the post and a 500 N signal light at the end of the beam. The beam is supported by a cable which connects to the beam 2.00 m from the post at an angle of 45.0 degrees measured from the beam; also by the hinge to the post which has horizontal and vertical components of unknown direction. a. Find the tension in the cable b. Find the magnitude and direction of the horizontal and vertical forces on the hinge. c. Find the total moment of inertia around the hinge as the axis. d. Find the instantaneous angular acceleration of the beam if the cable were to break.

Answer 1

a Using The Second equilibrum cond tion 3m M2 T-1809 Nm Fy 45 S00N T.Sinl45) 2- 1501.5 SinGo) Soo 3 Sintol-200 1x Sinao)0 L5ON ఇం 200N Pivot TSin(25) point First egu ibrum condition Fxo 5 ΣΗ F Tcas (25) = 12 casles) 2 Tx= {159N T5inles) =200+ 150 S00 y 2011N Homent of inetia Mer2 m, = 200 - 2o.4K 9.8 me Soo 9.8 H150 5.3 kg 9.8 then (15.3)3)2(20. 4)(22+ 51.af3- s86.5 m2 Apply ing S86.50 a30x rad See pat YO9536. 5a S2