A 10.0 kg beam is attached to a wall by means of a hinge. A cable is attached to the beam at a point halfway across the beam's length and pulls back at an angle of theta=40 degrees. A 5.00 kg box of desserts is attached at the end of the beam. a) What tension T in the support cable is required to maintain equilibrium? b) What vertical force acts on the hinge?
Here we have given that,
Mass of beam Mb = 10.0 kg
angle of theta=40 degrees
A 5.00 kg box of desserts is attached at the end of the beam ( Md)
a) now for the tension T in the support cable is required to maintain equilibrium we have to take the condition of static equilibrium so that,
Here sum of T = 0 for equilibrium
So that,
TSin40° × L/2 - MbgL/2-MdgL= 0
T = 2× (Mbg/2+Mdg)/Sin40° = (304.92187006464)N
Hence the tension in the support cable will be,
T = (304.92187006464) N
b) for the vertical force acts on the hinge we have
Sum of Fy = 0
So that,
Fv + TSin40° - Mbg - Mdg =
Fv= - (304.92187006464) Sin40° +15×9.8
Fv = 49 N
Hence the vertical force acts on the hinge will be
Fv = 49 N
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