Question

The rigid structural member is subjected to a couple consisting of the two 100-N forces. Replace this couple by an equivalent couple consisting of the two forces P and -P, each of which has a magnitude of 400 N. Determine the proper angle θ.  

Answer 1

Solution

The original couple is counterclockwise when the plane of the forces is viewed from above, and its magnitude is

M= F*d=100(0.1)=10 N.m counterclockwise

The forces P and -P produce a counterclockwise couple

M=400(0.040) cosθ

Equating the two expressions gives

10=(400)(0.040) cosθ θ=cos^-1 10/16=51.3°