the sum of magnitudes of two forces acting at a point is 18n and the magnitude of their resultant is 12n. if the resultant makes an angle of 90 degree with the force of smaller magnitude,what are the magnitude of two forces
To solve this problem, we can use the concept of vector addition.
Let's assume the magnitudes of the two forces are F1 and F2, with F1 being the smaller magnitude.
According to the problem, the sum of the magnitudes of the two forces is 18N. Therefore, we can write the equation:
F1 + F2 = 18 ---(Equation 1)
We are also given that the magnitude of their resultant is 12N and that the resultant force makes a 90-degree angle with the force of smaller magnitude.
In a vector addition diagram, the magnitude of the resultant is given by the Pythagorean theorem:
Resultant magnitude = √(F1^2 + F2^2) = 12N
Since the resultant makes a 90-degree angle with F1, we can use the trigonometric relationship:
tan(90 deg) = F2 / F1
Since tan(90 deg) is undefined, we can conclude that F2 / F1 is equal to infinity. This implies that F2 is infinitely larger than F1.
Given that F1 is the smaller magnitude of the two forces, we can assume F1 is approaching zero and F2 is approaching 18N.
Therefore, the magnitude of the two forces are approximately:
F1 ≈ 0N
F2 ≈ 18N
Draw right triangle ABC with right angle at A.
As sides of the triangle, a^2 = b^2+c^2
a^2 = 12^2 + (18-a)^2
a = 13
You have a 5-12-13 triangle.