The sum of two forces inclined to each other at an angle is 18 kg wt and their resultant which is perpendicular to the smaller force is 12 kg wt find the forces and the angle between them?
To find the forces and the angle between them, we can use vector addition and trigonometry.
Let's assume the two forces are F1 and F2, and the angle between them is θ.
Given that the sum of the two forces is 18 kg wt, we can write the vector addition equation:
F1 + F2 = 18 kg wt ...(Equation 1)
We are also given that the resultant force, which is perpendicular to the smaller force, is 12 kg wt. So, we have:
F2 = 12 kg wt ...(Equation 2)
Now, let's find the magnitude and direction of F1 and F2.
From Equation 1, we can solve for F1:
F1 = 18 kg wt - F2
F1 = 18 kg wt - 12 kg wt
F1 = 6 kg wt ...(Equation 3)
Now, we can use trigonometry to find the angle θ.
Since the resultant force is perpendicular to the smaller force, we can consider a right-angle triangle. The smaller force F2 can be taken as the side opposite to the angle θ, and the resultant force can be taken as the hypotenuse.
We know that:
sin(θ) = Opposite / Hypotenuse
sin(θ) = F2 / 18 kg wt
Substituting the values:
sin(θ) = 12 kg wt / 18 kg wt
sin(θ) = 2/3
Now, we can find θ by taking the inverse sin of both sides:
θ = sin^(-1)(2/3)
Using a calculator, θ ≈ 41.81 degrees.
Therefore, the two forces are F1 = 6 kg wt and F2 = 12 kg wt, and the angle between them is approximately 41.81 degrees.