Answers for Two Forces Act At Angle Of 120 Degrees The Bigger Force Is 60 Degree M And Resultant Is Perpendicular To The Smaller One Find The Smaller Force

Question

Answers for Two Forces Act At Angle Of 120 Degrees The Bigger Force Is 60 Degree M And Resultant Is Perpendicular To The Smaller One Find The Smaller Force

Answer 1

To determine the smaller force, we can break down the problem into components and use trigonometry to solve it.

Let's assume that the magnitude of the smaller force is "F" and the magnitude of the larger force is "L".

First, we can find the component of the larger force that is perpendicular to the smaller one. The angle between the larger force and the resultant force is given as 60 degrees, so the component of the larger force perpendicular to the smaller force can be found using the formula:

Perpendicular component of larger force = L * sin(60°)

Next, since the resultant force is perpendicular to the smaller force, we know that the component of the larger force parallel to the smaller force is equal in magnitude to the smaller force. So:

Parallel component of larger force = F

Now, let's find the resultant force. The resultant force is the vector sum of the two forces. Since the angle between the two forces is 120 degrees and the resultant force is perpendicular to the smaller force, we can use the formula:

Resultant force = sqrt((perpendicular component of larger force + F)^2 + (parallel component of larger force)^2)

Given that the resultant force is perpendicular to the smaller force, we can write:

Resultant force = sqrt(F^2 + F^2)

Simplifying this equation, we get:

Resultant force = sqrt(2F^2)

Since we know that the resultant force is sqrt(3) times larger than the smaller force, we can write:

sqrt(2F^2) = sqrt(3) * F

Squaring both sides of the equation to eliminate the square root, we have:

2F^2 = 3F^2

Subtracting 2F^2 from both sides, we get:

F^2 = 0

This implies that the magnitude of the smaller force is zero. However, physically, this doesn't make sense. Therefore, the smaller force cannot be determined with the given information.

Please note that in order to find the smaller force accurately, we would need additional information or clarification on the problem statement.