Lesson 1, Topic 5
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# Two or More Vectors Acting at a Point

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When there are two or more vectors acting at a point, each of the vectors is resolved into the vertical and horizontal components.

After you have calculated the vertical component and the horizontal component of each vector, you then proceed to add all the vertical components to get a single vertical component.

In a similar fashion, you are also to add all the horizontal components to get a single horizontal component.

The directions of the vectors must not be ignored. If the calculated vertical component is on the negative side of the y-axis, your calculated vertical component must be negative ( -ve / minus ). Also, if your calculated horizontal component is on the negative side of the x-axis, then your calculated horizontal component must be negative ( – ve / minus ).

This is shown below. Consider forces F1, F2, F3 and F4 acting at a point.

R2 = $$\scriptsize F_y^2 + F_x^2$$

R = $$\scriptsize \sqrt{F_y^2 + F_x^2}$$

tan Î¸ = $$\frac{F_y}{F_x}$$

Example:

Find the Magnitude and the Direction of the Resultant Forces.

R = $$\scriptsize F_y^2 + F_x^2$$

R = $$\scriptsize 1.68^2 + (-1.23)^2$$

R2 = 1.5129 + 2.8224

R = $$\scriptsize \sqrt {4.3353}$$

R = 2.082N

The direction of the force

tan Î¸ = $$\frac{F_y}{F_x}$$

tan Î¸ = $$\frac{-1.23}{1.68}$$

Î¸ = $$\scriptsize tan^{-1} (-0.732) \\ = \scriptsize\: – 36.2^o$$

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