In the figure, a uniform beam with a weight of 44.3 N and a length of 3.52 m is
ID: 1865416 • Letter: I
Question
In the figure, a uniform beam with a weight of 44.3 N and a length of 3.52 m is hinged at its lower end, and a horizontal force Upper F Overscript right-arrow EndScripts of magnitude 54.7 N acts at its upper end. The beam is held vertical by a cable that makes angle ? = 23.8° with the ground and is attached to the beam at height h = 1.79 m. What are (a) the tension in the cable, (b) the x-component of the force on the beam from the hinge, and (c) the y-component of the force on the beam from the hinge.
Explanation / Answer
given
W = weight of 44.3 N
L = length of 3.52 m
F = 54.7 N acts at its upper end
angle ? = 23.8°
height h = 1.79 m
a )
the tension in the cable is " T "
we have equation for T = F L / h cos?
T = 54.7 X 3.52 / 1.79 X cos23.8
T = 117.5641 N
b )
the x-component of the force on the beam from the hinge is Fhinge
Fhinge, x = - F + T cos?
= - F + F L / h
= F ( L/h - 1 )
= 54.7 X ( 3.52 / 1.79 - 1 )
Fhinge, x = 52.8664 N
c )
the y-component of the force on the beam from the hinge is
Fhinge, y = W + T sin23.8
= W + ( F L tan23.8 / h )
= 44.3 + ( 54.7 X 3.52 X tan23.8 / 1.79 )
= 44.3 + 47.44
Fhinge, y = 91.74 N