Resultant Force of Two Forces Acting at Right Angles

When two forces act on an object at right angles to each other, the resulting force can be determined using the Pythagorean theorem.

Calculating the Resultant Force

To calculate the resultant force of two forces acting at right angles to each other, follow these steps:

1. Draw a diagram of the forces acting on the object, with arrows showing the direction and magnitude of each force.
2. Using the Pythagorean theorem, find the magnitude of the resulting force by squaring each force, adding the squares together, and taking the square root of the sum.
Fresultant = √(F1^2 + F2^2)
3. Determine the direction of the resulting force by finding the angle between the two forces using the tangent function.
θ = tan^-1(F2/F1)
4. Draw the resulting force as an arrow with the magnitude and direction determined in steps 2 and 3.

Example Calculation

In the case of a 6N force and an 8N force acting at right angles to each other, the resulting force can be calculated as follows:

1. Draw a diagram of the forces, with the 6N force acting to the right and the 8N force acting upward.
2. Using the Pythagorean theorem, find the magnitude of the resulting force:
Fresultant = √(6^2 + 8^2) = 10N
3. Determine the direction of the resulting force using the tangent function:
θ = tan^-1(8/6) = 53.1 degrees
4. Draw the resulting force as an arrow with a magnitude of 10N and a direction of 53.1 degrees above the horizontal.

Conclusion

When two forces act on an object at right angles to each other, the resulting force can be determined using the Pythagorean theorem and the tangent function. By following these steps, we can calculate the magnitude and direction of the resulting force and draw it as an arrow on a diagram.