Two forces whose resultant is 10N,are perpendicular to each other.if one of them makes an angle of 60 with the resultant,calculate its magnitude
To solve this problem, we can use the concept of vector addition and trigonometry.
Let's consider the two perpendicular forces as vectors, F1 and F2.
Given that the resultant of these two forces is 10N, we can represent it as the vector sum of F1 and F2:
Resultant = F1 + F2
Since the forces are perpendicular, we can use the Pythagorean theorem to find the magnitude of the resultant:
Resultant^2 = F1^2 + F2^2
Substituting the given values:
10^2 = F1^2 + F2^2
Now, we are also given that one of the forces, let's say F1, makes an angle of 60 degrees with the resultant. To find the magnitude of F1, we need to use trigonometry.
Using the cosine function, we can relate the adjacent side (F1) and the hypotenuse (Resultant):
cos(60) = F1 / Resultant
Substituting the values:
cos(60) = F1 / 10
Rearranging the equation to solve for F1:
F1 = 10 * cos(60)
F1 = 10 * (1/2)
F1 = 5N
Therefore, the magnitude of the force that makes an angle of 60 degrees with the resultant is 5N.