In: Mechanical Engineering
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.
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°