As the angle between two concurrent forces decreases from 180 deg, their resultant

As the angle between two concurrent forces decreases from 180 deg, their resultant

• A. Decreases
• B. Increases
• C. Unchanged
• D. Cannot be determined

Answer: (B)

The magnitude of the resultant of two concurrent forces depends on how aligned the forces are. If the angle between them is theta, the resultant magnitude is R = sqrt(F1^2 + F2^2 + 2 F1 F2 cos theta). As theta decreases from 180° toward 0°, cos theta increases from -1 to +1, so R^2 increases from (F1 − F2)^2 to (F1 + F2)^2. This means the resultant grows, since it goes from the difference of the forces (when they are opposite) to their sum (when they point the same way). Hence the resultant increases as the angle between the forces decreases.

The magnitude of the resultant of two concurrent forces depends on how aligned the forces are. If the angle between them is theta, the resultant magnitude is R = sqrt(F1^2 + F2^2 + 2 F1 F2 cos theta). As theta decreases from 180° toward 0°, cos theta increases from -1 to +1, so R^2 increases from (F1 − F2)^2 to (F1 + F2)^2. This means the resultant grows, since it goes from the difference of the forces (when they are opposite) to their sum (when they point the same way). Hence the resultant increases as the angle between the forces decreases.