Two forces P&Q of magnitude 25N and 10N are acting at a point. The forces P & Q make angle 15 & 45, measured counter clockwise with the horizontal. What is the resultant in magnitude and direction?
Solution
Hint:
ie. adopting notation convention so that force P has magnitude and direction … makes an angle to the “horizontal”
The problem is —
Given:
, (always do angles in radians!)
,
Find and
Strategy: (I am not going to do it for you!)
You can do this by expressing and in horizontal and vertical components, adding components, and the recombining to get .
You can also do this using triangle geometry… adding the vectors head-to-tail makes a triangle with one unknown side.
ie the exterior angle going from to is
These are coming out to really nice numbers if you know about triangles.
The solution is in the cosine rule:
If we define (the angle between and ) then you can find :
(cosine rule again!) … and thus .
You are all done!
If that is all gibberish to you — go the “components” rout.
If x is the horizontal axis:
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