Question

Find the resultant force and direction of forces 6N and 8N acting perpendicular to each other

Answer 1

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.