Engineering Statics

C-4


A couple, M, of magnitude 18 N-m is applied to the handle of a screwdriver to tighten a screw into a block of wood. Determine the magnitude of the two smallest horizontal forces that are equivalent to M if they are applied at corners A and D and anywhere on the block.

The top view view of the diagram indicates the location of the moment 
and its point of application.
The further apart the forces are applied the less their magnitude has 
to be to achieve the same moment if the forces are applied perpendicular 
to the moment arm between them.
-18 = (-.24)FA        FA = N
FD = N
" "Applying the forces at A and D give two equal and opposite forces of magnitude 75 N. Note that the forces are perpendicular to line AD." 0.00 0>" 0.00 "" 0.00 "" 0.00 "" 1042 <="c-04" 4 "

-18 = (-.24)FA        FA = N
FD = N
The distance between A and C is the greatest distance that can be achieved 
while still staying on the block of wood.If the forces are applied at A and C 
perpendicular to the line AC, the moment can be achieved with minimum forces." 0.00 "" 0.00 "" 0.00 "" 1043 <="c-04" 5 "

-18 = (-.24)FA        FA = N
FD = N

The distance AC is found by using the Pythagorean theorem." 0.00 "" 0.00 "" 0.00 "" 1044 <="c-04" 6 "

-18 = (-.24)FA        FA = N
FD = N


18 = (.4)FA        FA = N
FD = N
" "Since the forces at A and C are perpendicular to line AC, the moment is simply calculated by multiplying the force times the distance. The direction of the forces has to be such that the moment is in the same direction as the original moment applied to the block." 0.00 0>" 0.00 "" 0.00 "" 0.00 ""