Question

You decide to hang another plant from a 1.5-m-long 2.9-kg beam that is attached by a hinge to the wall on the left. You orient the beam at a 38 ∘ angle above the horizontal and orient the cable horizontally from the wall to the end of the beam. The beam holds the 2.9-kg pot and plant hanging 0.1 m from its end. Determine the force that the cable exerts on the beam. Determine the force that the wall hinge exerts on the beam (its x- and y-components). Determine the force that the wall hinge exerts on the beam (its magnitude). Determine the force that the wall hinge exerts on the beam (direction of that force, counted from positive x-axis).

Answer 1

Here, sum the moments about the hinge: they must be zero, or the beam rotates.
ΣM = 0 = beam moment + plant moment - cable moment
=> 0 = 2.9kg*9.8m/s²*1.5m/2*cos38º + 2.9kg*9.8m/s²*1.4m*cos38º - T*1.5m*sin38º
=> 0 = 16.80 + 31.35 - T*0.92
=> T = 52.34 N [This is the force that the cable exerts on the beam]

Again, horizontal force on hinge Fh = 52.34 N (opposite cable tension)
The vertical force on the hinge must equal the weights:
Fv = 2 * 2.9kg * 9.8m/s² = 56.84 N

total force on beam F = √(Fh² + Fv²) = √(52.34^2 + 56.84^2) = 77.27 N

Θ = arctan(56.84 / 52.34) = 47.4º