In the figure, one end of a uniform beam of weight 420 N is hinged to a wall; the other end is supported by a wire that makes angles θ = 29° with both wall and beam. ?

How to find (a) the tension in the wire and the (b) horizontal and (c) vertical components of the force of the hinge on the beam.
enter image source here

1 Answer
Feb 5, 2016

Answer:

#a)T=420 . cos 29=367.34 N#
#b)#
#"horizontal component of net force :"98,716 . sin 2 theta=83,716 N#
#c)#
#"vertical component of net force :"98,716 .cos 2 theta=52,312N#

Explanation:

enter image source here
#P=420 .sin 2 theta#
#R=420 .cos 2 theta#
#L=T .cos theta#
#K=T . sin theta#
#M=T .sin theta#
#N=T .cos theta#
#K .2.l=P. l(" torque for point A)"#
#" R and L have no torque for point A"#
#K.2=P#
#2.T.sin theta=420 . sin 2.theta#
#T=210 .(sin 2 theta)/sin theta#
#sin 2. theta=2. sin theta .cos theta#
#T=210. (2.sin theta .cos theta)/sin theta#
#T=420 .cos theta#
#a)T=420 . cos 29=367.34 N#
#L=367.34 . cos 29=321.282 N#
#R=420 . cos 58=222,566 N#
#"net force on point hinge :" 321,282-222,566=98,716 N#
#"horizontal component of net force :"98,716 . sin 2 theta=83,716 N#
#"vertical component of net force :"98,716 .cos 2 theta=52,312N#