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Math Help - Need help with this forces question

  1. #1
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    Need help with this forces question

    A particle is acted upon by the following four forces: 25 N pulling east, 30 N pulling west, 54 N pulling north and 42 N pulling south.

    Calculate the resultant and equilibrant of these forces.

    I don't know how to solve it, please help me a little, thanks.
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  2. #2
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    Quote Originally Posted by Soul to soul View Post
    A particle is acted upon by the following four forces: 25 N pulling east, 30 N pulling west, 54 N pulling north and 42 N pulling south.

    Calculate the resultant and equilibrant of these forces.

    I don't know how to solve it, please help me a little, thanks.
    let east/west be the x-direction ...

    25N - 30N = -5N ... west component

    north/south be the y-direction ...

    54N - 42N = 12N ... north component

    resultant magnitude, |R| = \sqrt{(-5)^2 + (12)^2} = 13N

    resultant direction, \theta = \arctan\left(\frac{12}{-5}\right) + 180 = 112.6^{\circ} counter-clockwise from east (the +x-axis), or 67.4^{\circ} north of west.

    If R is the resultant vector, then -R is the equilibrant vector.
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