Question

The following problem is not multiple choice. Final numerical answer is not sufficient to get full credits on the problem. You need to explain what you did and what you used to get your answers. One end of a uniform beam of weight 225 N is hinged to a wall; the other end is supported by a wire that makes angles 0=30.0° with both wall and beam. Find (a) the tension in the wire and the (b) horizontal and (c) vertical components of the force of the hinge on the beam. Hinge C Paragraph BI U ---

Answer 1

-T. B 0=30° a 20 O A = length of beam. As beam is uniform, so is at the middle. point. OB = 1 2. weight 20 W = 225N at 'o'=0 T= tension in the we're 'At eauilibrium torane about hinge se =0 (OB) (W) Sin 20 = 0 d. (OA) (t) sino by groom l I sin 30° T Sin30° - l w Sin 600 2 W sin 60° 2. W X3 2 => TXtz [w= 225 T= 2258 V3 2 - 194.86 N. An Tension in the wire = 194.86 N.

B Ny Isih60° ok с LC AB = 180-(ABC ALBCA) = 180° - ( + 90') = 180° - (30+90) 20 + TCODIGO" А w ISO - 120 = 60° B. Tsin60° Nv 0 NH - Horizontal component of force at →NH 66 20 A Tongo C hinge ' Ny = rertical force at hinge o H At ean'librium I Fy=0 I Fx = =o I fx = NH - Efy Ton60° NV +Tsin 60-W. NH - T longo =) NH = T Con 600 T=194. 86N NH (194.86) Congoo 97.43 N: W=225 N. Nv + Tsin60°_w=0 => Nr = W- Tsin 600. = 225 - (194.86)(3) 56.25 N Amb horizontal component = o vertical component 97.43 W 56.25N.