1. Two forces F = (8i + 3j )N and F, = (4i + 6j )N are acting on an object. What is the

magnitude and direction of the resultant force?

1 answer

To find the magnitude and direction of the resultant force, we need to find the sum of the two forces.

To find the sum of the forces, we add the corresponding components together:

F + F' = (8i + 3j)N + (4i + 6j)N = (8+4)i + (3+6)j = 12i + 9j

Therefore, the resultant force is F_r = 12i + 9j.

To find the magnitude of the resultant force, we use the Pythagorean theorem:

|F_r| = sqrt((12^2) + (9^2)) = sqrt(144 + 81) = sqrt(225) = 15

So, the magnitude of the resultant force is 15 N.

To find the direction of the resultant force, we use trigonometry:

θ = arctan(9/12) = 0.6435 radians

Therefore, the direction of the resultant force is approximately 0.6435 radians (or about 36.87 degrees) with respect to the positive x-axis.