Question

In the figure below, a force F1 of magnitude 6.30 units acts on a crate at the origin in a direction = 27.0° above the positive x-axis. A second force F2 of magnitude 5.00 units acts on the crate in the direction of the positive y-axis. Find graphically the magnitude and direction (in degrees counterclockwise from the +x-axis) of the resultant force F1 + F2.

Answer 1

The resultant force has of magnitude 9.66N and at an angle of 54.4° above the x axis.

What is the resultant force?

The resultant force and is obtained by using the cosine.

Let the resultant force is be F

$F = \sqrt{F_{1}^{2} + {F_{2}^{2} - 2*{F_{1} + {F_{2} *cos (90 +27)}$

$F = \sqrt{6.3^{2} + 5^{2} - 2*6.3 + 5 *cos (117)}$

F = 9.66 unit

Using the sine rule to determine the direction:

9.66/sin 117 = 5/sin x

x = Sin⁻¹(5 * sin 117/9.66)

x = 27.4°

Therefore the direction is 27.4 + 27 = 54.4°

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