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posted by  parker4788 on 7/20/2008 5:52:52 PM  |  status: Live  

Mulitplication of sines and cosines

Course Textbook Chapter Problem
Classical Mechanics Vector Mechanics for Engineers: Statics (8th) by Johnston, Eisenberg, Beer 2 73P
Question Details:
I understand that to find Fy you have to multiply the Force F by the sin(40) because of the diagram:
however, what I do not understand is why Fx has to be found by Fcos(40) x cos(40).  I would think that looking at the diagram it would be Fx=F*cos(40).  Why do you have to multiply by cos(40).  Also the same question for Fz.  Why do you have to muliply by sin(40) to get the answer?
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posted by mousey on 7/20/2008 7:51:11 PM  |  status: Live
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40° (its complement, actually) is a direction angle (θy) to the y-axis for TAB (you get TABy by a single "projection" - a single sine (or cosine) operation).  To get the x-component TABx, you can't do it with a single "projection" because Fig. P2.73 does not provide this direction angle θx (angle that sweeps from TAB directly onto the x-axis), so the direct "projection" of TAB onto the x-axis is not possible.  Instead the figure provides two angles (elevation and azimuth) allowing a double "projection" to be made. The first one onto the x-z-plane (cos 40°) and the second onto the x-axis (cos 40°) or TABx = TAB cos 40° cos 40°.  I recommend that first you read the top of section 2.12 paying attention to Figures 2.30 and 2.31, and second you give it a try with P2.75 a) and b) for which you have the answers at the back of your textbook.

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