TWO FORCES F1 AND F2 ARE ACTING AT RIGHT ANGLE TO EACH OTHER FIND THE EXPRESSION FOR THE RESULTANT FORCE?
Resolve F1 and F2 into x- and y-components, and then just add them up.
Fr = Sqrt(F1^2 + F2^2) = Resultant force
R=SQUARE ROOT OF SUM OF THE SQUARES OF THE TWO FORCES F1 AND F2
To find the expression for the resultant force, you can use vector addition. In this case, as the two forces F1 and F2 are acting at a right angle to each other, you can use the Pythagorean theorem and trigonometric ratios to determine the magnitude and direction of the resultant force.
1. Start by labeling the magnitudes of the two forces as F1 and F2, and the angle between them as theta (θ).
2. Use the Pythagorean theorem to determine the magnitude of the resultant force (Fr) using the formula:
Fr = sqrt(F1^2 + F2^2)
Here, F1^2 represents F1 squared, and F2^2 represents F2 squared.
3. Next, calculate the angle of the resultant force (Φ) using trigonometric ratios. Since F1 and F2 are acting at a right angle, you can use the following relationship:
tan(Φ) = F2 / F1
Rearrange the equation to solve for Φ:
Φ = arctan(F2 / F1)
Note: The arctan function gives you the angle in radians. If you need the angle in degrees, you can convert it by multiplying the result by (180/π).
4. The expression for the resultant force combines the magnitude (Fr) and the direction (Φ) as follows:
Resultant Force = Fr * cos(Φ) * i + Fr * sin(Φ) * j
Here, i and j represent the unit vectors along the x-axis and y-axis, respectively.
By following these steps, you can calculate the expression for the resultant force when two forces are acting at a right angle to each other.