the force f1 and f2 are acting on a body one force is double that of the other force and the resultant is equal to the greater force.then the angle between two forceis what. How?
Use the law of cosines, and solve for the cosine.
what is force
To find the angle between two forces, given that one force is double the other and their resultant is equal to the greater force, we can utilize vector addition and trigonometry. Here's how to do it step by step:
1. Assume that the smaller force is denoted as F1, and the larger force is denoted as F2.
2. We are given that F2 is double the magnitude of F1. Let's represent this relationship mathematically: F2 = 2 * F1.
3. We also know that the resultant force is equal to the greater force, which means the magnitude of the resultant force (R) is equal to F2. So, R = F2.
4. Since we have the magnitudes, we need to consider their directions. Let's assume F1 acts at an angle α with respect to some reference direction, and F2 acts at an angle β with respect to the same reference direction.
5. The resultant force R can be found using vector addition: R = sqrt(F1^2 + F2^2 + 2 * F1 * F2 * cos(θ)), where θ is the angle between F1 and F2.
6. Since R = F2 and F2 = 2 * F1, we can rewrite the equation as: 2 * F1 = sqrt(F1^2 + (2 * F1)^2 + 2 * F1 * (2 * F1) * cos(θ)).
7. Simplify and solve the equation for cos(θ): 4 * F1^2 = 5 * F1^2 * cos(θ).
8. Cancel out F1^2: 4 = 5 * cos(θ).
9. Rearrange the equation to isolate cos(θ): cos(θ) = 4/5.
10. Finally, take the inverse cosine (cos^(-1)) of both sides to find the angle θ: θ = cos^(-1)(4/5).
Therefore, the angle between the two forces is equal to the inverse cosine of 4/5 (approximately 36.87 degrees).
F1 = F2*Cos A.
Replace F2 with 2F1:
F1 = 2F1*Cos A
Divide both sides by 2F1:
Cos A = 0.50.
A = 60o.