the greatest and the least resultants of two forces acting on a body are 35kN and 5kN respectively,determine the magnitude of the forces,what would be the angle between these forces if the magnitude of the resultant is stated to be 5kN
Answer
I can't see how two forces of 35 and 5 can add up to 5.
35-5 <= |u+v| <= 35+5
I suspect a typo
To find the magnitudes of the forces, we need to consider the concept of vector addition. The resultant of two forces occurs when the forces are added together. The resultant can be calculated using the Pythagorean theorem.
Let's denote the magnitudes of the two forces as F1 and F2, and the magnitude of the resultant as R.
Given:
The greatest resultant (R) = 35 kN
The least resultant (R) = 5 kN
To find the magnitudes of the forces, we have two equations:
1. F1 + F2 = 35 kN - Equation 1
2. F1 - F2 = 5 kN - Equation 2
We can solve these equations simultaneously to find the magnitudes of the forces.
Adding Equation 1 and Equation 2, we get:
2F1 = 40 kN
Dividing by 2, we find:
F1 = 20 kN
Substituting the value of F1 in Equation 1, we get:
20 kN + F2 = 35 kN
Subtracting 20 kN from both sides, we find:
F2 = 15 kN
Thus, the magnitudes of the two forces are 20 kN and 15 kN, respectively.
To find the angle between these forces when the magnitude of the resultant is 5 kN, we need to use the concept of vector addition. The angle can be found using the Law of Cosines:
R^2 = F1^2 + F2^2 - 2 * F1 * F2 * cosθ
Given:
Resultant (R) = 5 kN
F1 = 20 kN
F2 = 15 kN
Let's substitute these values into the Law of Cosines equation:
(5 kN)^2 = (20 kN)^2 + (15 kN)^2 - 2 * (20 kN) * (15 kN) * cosθ
Simplifying this equation will give us the value of cosθ. We can then find θ by taking the inverse cosine (cos^(-1)) of cosθ.
Using the Law of Cosines equation, we can calculate the value of cosθ and then find θ.