How to Find the Magnitude When Force & Angle Is Given?

Push a door at an angle, and less force will turn it.
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When a force works in the same direction as a body moves, the entire force acts on the body. In many cases, however, the force points in a different direction. When an object slides down a slope, for instance, gravity acts straight downward, but the object moves at an angle. The effective force on the object is a vector quantity related to but separate from the original force. The two vectors are related through trigonometry.

    Subtract the angle between the force and the resultant vector you want to calculate from 90. If, for instance, the force acts at a 30-degree angle from the object's direction of motion then 90 - 30 = 60.

    Find the sine of this angle. With the example for Step 1, sin (60) = 0.866.

    Multiply this answer by the original force. If the force equals, for instance, 100 Newtons then 0.866 × 100 = 86.6 Newtons. This is the magnitude of the resultant force vector on the object.

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