Engineering Statics

A-15


Three cables support a crate as shown. Determine the weight of the crate knowing that the tension in cable AC is 423 pounds.

We draw a free body diagram through point A because all of the forces pass through that point.
Calculate the length of each cable.
Set up knowns and unknowns for cable AB.
We ignore the term for ABz because we can determine by observation that ABz=0.
Set up knowns and unknowns for cable AC.
Set up knowns and unknowns for cable AD.
Sum the forces in the x-direction.
Substitute ABx, ACx, and ADx in terms of AB, AC and AD.
Sum the forces in the x-direction.
Substitute ABy, ACy, and ADy in terms of AB, AC and AD,
but note that we already know AC and therefore ACy.
Note that W is the weight of the crate in the negative y-direction.
Sum the forces in the x-direction.
Substitute ADz in terms of AD, and sum because we already know AC.
Note that ABz=0, so that term is dropped.
Use your calculator to solve for 3 equations with 3 unknowns.
Note that the weight, W, is negative or downward.