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Math: Calculus - Vectors

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Two forces of 90 N act on an object. The forces make an angle of 48 degrees to each other. Calculate the resultant force and the force that must be applied to the object to create equilibrium.

My work, using geometric vectors:

| r |^2 = 90^2 + 90^2 - 2(90)(90)cos132
| r | = 164.4 N

sin132 / 164.4 = sinx / 90
x = 24 degrees

Therefore the resultant force is 164.4 N, 24 degrees from 90 N.

*************MY QUESTION*********
-------- How do I find the equilibrium to this problem? Can you please provide a step by step solution?


  • Math: Calculus - Vectors -

    I assume you did the law of cos and of sin right, not checking
    To hold this force in equilibrium, you need a force equal and magnitude and opposite in direction to the resultant.
    so 164.4 N at 180+24 = 204 degrees from one of the original 90 N forces.

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