Force Applied Vector Analysis Equations and Calculator

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Force Applied Vector Analysis Equations and Calculator

A force of F is exerted on a bolt A as shown in the illustration below. The following equations and calculator determine the horizontal and vertical components of the force.

Denoting by F the magnitude of the force F and by θ the angle between F and the x axis, which is measured counterclockwise from the positive x axis (Fig. 2.17), we may express the scalar components of F as

F_x = -F cos α

F_y = -F sin α

These relations hold for any value of the angle θ from 0° to 360°, and they define the signs as well as the absolute values of the scalar components Fx and Fy.

(a) Force F exerted on a bolt;
(b) rectangular components of F.

Source:

Vector Mechanics for Engineers - Statics | Dynamics
Ferdinand P. Beer
Late of Lehigh University

E. Russell Johnston, Jr.
Late of University of Connecticut

David F. Mazurek
U.S. Coast Guard Academy

Phillip J. Cornwell
Rose-Hulman Institute of Technology

Brian P. Self
California Polytechnic State University—San Luis Obispo