Question

A 10.0 kg beam is attached to a wall by means of a hinge. A cable...

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