Two forces of resultant 100N are perpendicular to each other. If one of them makes angle 60 degree with the resultant. Calculate the magnitude of forces
this is just the usual 30-60-90 right triangle, with hypotenuse 100. Now just find the sides.
unknown
Use a diagram to solve it please
To find the magnitude of the forces, let's break down the given information.
We have two forces that are perpendicular to each other, resulting in a resultant force of 100N. Let's call the magnitudes of these forces F1 and F2.
We also know that one of the forces makes an angle of 60 degrees with the resultant force. Let's call this force F1.
To find the magnitudes of the forces, we can use trigonometry. Since F1 makes an angle with the resultant force, we can use the cosine function to relate the magnitudes.
Cosine(theta) = adjacent/hypotenuse
In this case, the adjacent side is F1 and the hypotenuse is the resultant force of 100N.
Cos(60 degrees) = F1/100N
Taking the inverse cosine of both sides, we can find the value of F1.
F1 = 100N * cos(60 degrees)
F1 = 100N * 0.5
F1 = 50N
So, one of the forces, F1, has a magnitude of 50N.
Since the two forces are perpendicular to each other, the other force, F2, can be found using the Pythagorean theorem.
Pythagorean theorem: a^2 + b^2 = c^2
In this case, a is F1 (50N), b is F2, and c is the resultant force (100N).
(50N)^2 + F2^2 = (100N)^2
2500N^2 + F2^2 = 10000N^2
F2^2 = 10000N^2 - 2500N^2
F2^2 = 7500N^2
F2 = √7500N^2
F2 ≈ 86.60N (rounded to two decimal places)
So, the magnitude of the other force, F2, is approximately 86.60N.