Engineering Statics

A-14


Three cables are used to tether a balloon as shown. Knowing that the balloon exerts a 700 pound lifting force, determine the tension in each cable.

Calculate the length of each cable.
Set up knowns and unknowns for cable AB.
Set up knowns and unknowns for cable AC.
Set up knowns and unknowns for cable AD.
Because the denominator of ADx is zero, we also know that the x-component of AD, ADx, is zero. That particular term is ignored.
Summing the forces in the x-direction.
Note that ADx=0.
Substitute ABx and ACx in terms of AB and AC.
Summing the forces in the y-direction.
Substitute ABy, ACy and ADy in terms of AB, AC and AD.
Summing the forces in the z-direction.
Substitute ABz, ACz and ADz in terms of AB, AC and AD.
Use your calculator to solve for 3 equations with 3 unknowns.