Engineering Statics

C-14


Neglecting friction, determine the tension in cable ADB and the reaction at C.

The two diagrams of right triangles allow us to find the hypotenuse of each triangle.
The moment equation about point C eliminates the two unknows 
at C and allows us to solve for the tension, T.
T is factored out of two terms.
Combination of terms simplifies the equation.
Notice that tension must always be positive!
The sum of forces in the x direction equals zero.  Notice 
how the tension (152) appears in two terms.  This is 
because the cable is connected at A and B.
The horizontal component of the force at C is to the left.
The equilibrium equation in the y-direction also has only 
one unknown.
The force in the y direction is down.  This makes sense 
since the tension at A and B is upward.
The force at C is expressed as a vector by adding the 
two components.