To find the resultant force when two forces act at right angles to each other, you can use the Pythagorean theorem.
Let \( F_1 = 6 , \text{N} \) and \( F_2 = 8 , \text{N} \).
The resultant force \( R \) can be calculated as follows:
\[ R = \sqrt{F_1^2 + F_2^2} \]
Substituting the values:
\[ R = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 , \text{N} \]
Now, to determine the direction of the resultant force, you can use the tangent function to find the angle \( \theta \) relative to the 6N force:
\[ \tan(\theta) = \frac{F_2}{F_1} = \frac{8}{6} = \frac{4}{3} \]
Calculating \( \theta \):
\[ \theta = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.13^\circ \]
So, the resultant force is:
- Magnitude: \( 10 , \text{N} \)
- Direction: approximately \( 53.13^\circ \) from the 6N force towards the 8N force.
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