Engineering Statics

B-10


A foot valve for a pneumatic system is hinged at point B. Knowing the the angle a is 32 degrees, determine the moment of the 18 N force about point B.

The force and the radius can be separated into x and y components.

"Notice that in the x-direction the distance is to the left, hence negative." >

"The x and y components of the force are negative since the force is pointed to the left and down." >
The determinant form of the cross porduce yields the answer.  Note 
that since the force and the distance are in the x-y plane, the 
moment is perpendicular to that plane, hence in the k direction.
The magnitude of the radius is given.
The component of the force perpendicular to the radius is given 
as the magnitude of the force times the sine (opposite side) of 
the angle.
The magnitude of the moment is the radius times the component 
of the force perpendicular to the radius.  The component 
parallel to the radius cannot cause a moment.
The moment may also be calculated by multiplying perpendicular 
components of the distance and the force.
Values are substituted.
Arithmetic yields the same value for M as was found before.