Angle between two forces

To find the angle between two forces, both acting away from a point and having a magnitude of their resultant as 10 kN, we can use the method of vector addition. Let's break down the problem into steps.

Step 1: Understanding the problem

We are given two forces, each with a magnitude of 10 kN, and both forces are acting away from a point. The magnitude of their resultant is also given as 10 kN. We need to find the angle between these two forces.

Step 2: Vector addition

Since the two forces are acting away from the point, we can represent them as vectors pointing in the same direction. Let's call these forces F1 and F2.

To find the resultant force, we can use the formula:

Resultant = √(F1^2 + F2^2 + 2F1F2cosθ)

Where θ is the angle between the two forces.

Since the magnitude of the resultant force is given as 10 kN, we can rewrite the formula as:

10 = √(10^2 + 10^2 + 2(10)(10)cosθ)

Simplifying this equation, we get:

100 = 200 + 200cosθ

Step 3: Solving for θ

Let's solve the equation for θ:

100 - 200 = 200cosθ

-100 = 200cosθ

cosθ = -100/200

cosθ = -0.5

To find the value of θ, we can take the inverse cosine (cos^-1) of -0.5:

θ = cos^-1(-0.5)

Using a calculator, we find that θ is approximately 120 degrees.

Step 4: Conclusion

The angle between the two forces, each with a magnitude of 10 kN and both acting away from a point, is approximately 120 degrees.

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