# Calculating the Resultant

Force(N) Direction (deg) x Component y Component

F3 110 30 95.3 55

F4 100 125 122.6 81.9

F5 85 200 100.1 150.9

Resultant ? ? ? ?

Can somebody help me check on my data because I think I did the whole thing wrong and also when I got the resultant of x component it was 318 and 287.8

then I calculated the force which was like 428.

When I was solving for x component and y for F3 i got a few negatives and somewhere in the book said i had to add 180 degrees.

PhanthomJay
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You should draw a rough sketch first on a typical x-y 4 quadrant graph. . For the F3 force of 110 N, your components are correct . For the F4 force of 100 N at 125 degrees ccw from positive x axis, your sketch should show for example that the x component of that force is -100cos55. (it lies in the 2nd quadrant, and points up and to the left..it's x componnet is the magnitude of the x leg of the right triangle formed using F4 as the hypotenuse...and the x component points left, so throw a negative sign on it. Continue..

Oh so when i add up all the x components it would be 95.3 + (-) 57.4 + (-) 79.87 = -42.27?

and how about calculating the resultant for force and direction you use pythagoream therom and the tan-1(opp/adj)?

PhanthomJay
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Oh so when i add up all the x components it would be 95.3 + (-) 57.4 + (-) 79.87 = -42.27?
yes, good.
and how about calculating the resultant for force and direction you use pythagoream therom and the tan-1(opp/adj)?
Yes, first find the sum of the y components, add 'em up, and then calculate the resultant force and direction. Be sure to draw a sketch that will help deternine what is opposite, what is adjacent, and what the angle is.

It would seem weird to have a negative angle wouldn't it?

final components -42.27 and 107.8

PhanthomJay
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What angle are you getting for a result? Are you drawing a sketch of the x (pointing left) and and y (pointing up) components of the resultant? In what quadrant does the resultant lie?

Well the triangle would like on quadrant 2 where x is negative and y is positive.

PhanthomJay
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Well the triangle would like on quadrant 2 where x is negative and y is positive.
Yes, and what is the angle measured ccw from the positive x axis?

tan-1(-42.27/107.8) = -21.4

PhanthomJay
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Calculators don't know too much about quadrants . That's why it is important to draw a sketch. Using tan theta = opp/adj, that value of 21.4 degrees is measured in which direction from which axis?

from top to bottom

PhanthomJay
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from top to bottom
I am unsure what you mean by 'from top to bottom'.

from the y axis to the x axis the angle above the x axis

PhanthomJay
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If the x comp is -42 and the y comp is + 108, and you are using tan theta = x/y, then then it's 21.2 degrees ccw from the pos y axis, right?

yeah thats what i was trying to say

PhanthomJay
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OK, that's correct. Which is how many degrees counterclockwise from the positive x axis (conventionally, the way angles are measured).?

90+21.2 = 111.2

PhanthomJay