The magnitude of the resultant of two mutually perpendicular forces, F1 and F2 is 13N, if the magnitude of F1 is 5N, what is the magnitude of F2?

The magnitude of the resultant of two mutually perpendicular forces, F1 and F2 is 13N, if the magnitude of F1 is 5N, what is the magnitude of F2?

Answer Details

When two forces act on an object at the same time, their combined effect is given by their resultant. The magnitude of the resultant force can be found by using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we know that the magnitude of the resultant force is 13N, and one of the forces, F1, has a magnitude of 5N. Since F1 and F2 are perpendicular, they form the two sides of a right-angled triangle, with the resultant force as the hypotenuse. Therefore, we can use the Pythagorean theorem to find the magnitude of F2: Resultant force^2 = F1^2 + F2^2 13^2 = 5^2 + F2^2 F2^2 = 13^2 - 5^2 F2^2 = 144 F2 = √144 F2 = 12N Therefore, the magnitude of F2 is 12N.