Engineering Statics


An underground holding tank is to be positioned in an excavation. Determine the magnitude and direction of the smallest force, P, for which the resultant, R, is vertical. Determine the magnitude of the resultant, R.

The first thing we do is identify the x and y axes, 
creating a diagram of the forces with a frame of reference.
The resultant of the two forces can be divided into components in the i and j directions.
The x components are added together to get the resultant's x component in the i direction.
Similarly, the y components are added together to get the resultant's y component in the j direction.
But remember that the resultant is vertical, so the sum of the x forces is zero.
Summing the forces in the x-direction, and knowing that they are equal to zero, we can solve for tension P.
The magnitude of force P can be determined to be 480 lb.
We know that the resultant, R is the sum of the two force vectors...
... or 928 lb.