Two forces F1 and F2 ifF1is double that ofF2 and the resultant is perpendicular on F1 then the angle betwee them is
Expain ans with reason and diagram
Imagine that F₂ is along the x-axis, F is along y-axis,
and F₁ is directed to the “north-west”.
The angle between F and F₁ is α.
sin α = F₂/ F₁=1/2
α=30°
Thus, the angle between F₁ and F₂ is
90°+30° = 120°
Thank u soo much
To find the angle between two forces, we can use vector addition to calculate the resultant force and then use trigonometry to find the angle between the resultant force and one of the forces.
Let's denote the magnitude of force F1 as F1 and the magnitude of force F2 as F2.
Given that F1 is double that of F2, we can write the equation as: F1 = 2F2.
Now, if the resultant force is perpendicular to F1, it means that the two forces must be acting at right angles to each other. This forms a right-angled triangle, as shown in the diagram below:
F1
|
Resultant |
|\
| \ F2
----
In this right-angled triangle, F1 represents the hypotenuse, F2 represents one of the legs, and the resultant force represents the other leg.
Using the Pythagorean Theorem, we can write the equation:
(F1)^2 = (F2)^2 + (Resultant)^2
Substituting F1 = 2F2, we have:
(2F2)^2 = (F2)^2 + (Resultant)^2
4(F2)^2 = (F2)^2 + (Resultant)^2
Expanding and simplifying:
3(F2)^2 = (Resultant)^2
Taking square roots for both sides:
sqrt(3)(F2) = Resultant
Now, we have the magnitude of the resultant force in terms of F2.
To find the angle θ between the resultant force and F1, we can use trigonometry. We know that the tangent of an angle in a right-angled triangle is equal to the ratio of the length of the opposite side to the adjacent side.
Therefore, the tangent of θ is given by:
tan(θ) = (Resultant) / F1
Substituting (Resultant) = sqrt(3)(F2) and F1 = 2F2, we have:
tan(θ) = sqrt(3)(F2) / 2F2
Simplifying further:
tan(θ) = sqrt(3) / 2
Now, we can find the value of θ by taking the inverse tangent (arctan) of both sides:
θ = arctan(sqrt(3) / 2)
Using a scientific calculator, we can approximate the value of θ to be approximately 30 degrees.
Therefore, the angle between the forces F1 and F2 is 30 degrees.
Please note that the actual numerical values of the forces (F1 and F2) were not provided, so the final calculated angle is an approximation based on the given conditions.