Question

An object is acted upon by a 3n force and by a 4n force. Each diagram also shows the two forces. Which diagram also shows the resultant X of these two forces

Answer 1

Given:

An object is acted upon by a 3N force and by a 4N force.

To Find:

The resultant of the two forces.

Solution:

• We know Forces are vectors.

• It has a magnitude and direction.
• Here F1 = 4N and F2 = 3N are the two forces.
• Let Ф be the angle between these two vectors.
• |F1 + F2| = |√ (|F1| ²+ |F2|² + 2|F1||F2| cosФ)|

If the forces are perpendicular to each other,

say 4N in positive y direction and 3N in positive x direction,

• F1+F2 = √3² + 4² + 0 = √25 = 5N
• Angle will be $cos^{-1} \frac{F1cos\phi +F2}{F}$
• Angle will be $cos^{-1} \frac{4}{5}$

The magnitude of resultant force is 5N and it is  $cos^{-1} \frac{4}{5}$ angle from 3N force.