Question

Two forces of fƒ— 1=75.02√(iˆ-jˆ)n and fƒ— 2=150.02√(iˆ-jˆ)n act on an object. Find the third force fƒ— 3 that is needed to balance the first two forces?

Answer 1

The third force f­­­ 3 needed to balance f­­­ 1 and f­­­ 2 is -225.04√(iΗ-jΗ)n, having the same magnitude but opposite direction to the vector sum of f­­­ 1 and f­­­ 2.

Step-by-step explanation:

To find the third force f­­­ 3 that is needed to balance the first two forces f­­­ 1 and f­­­ 2, we use vector addition. Since both forces provided are of the form f­­­ 1=75.02√(iΗ-jΗ)n and f­­­ 2=150.02√(iΗ-jΗ)n, we can add them directly because they are parallel and have the same direction of action. The sum f (sum of f­­­ 1 and f­­­ 2) equals 225.04√(iΗ-jΗ)n. To balance these forces, the third force must have the same magnitude but opposite direction. Thus, f­­­ 3 will be -225.04√(iΗ-jΗ)n. This ensures that the net force on the object will be zero, thereby satisfying equilibrium conditions.