Two forces of resultant 100N are prependicular to each other. If one of them makes angle 60degree with the resultant, calculate the magnitude of the forces. (Sin60degree=0.87, cos60degree=0.5)
F1 = 100*Cos60 = 50 N.
F2 = 100*sin60 = 87 N.
Assuming both angles are p and q thereford cos60=Q/100, Q=100*0.5=86.6N
Physcis Assaghment
To solve this problem, we can use vector addition and trigonometry.
Let's denote the magnitudes of the two forces as F1 and F2. Since the resultant force is 100N and it is perpendicular to both forces, we can use the Pythagorean theorem to find the relationship between F1 and F2.
According to the Pythagorean theorem, the square of the magnitude of the resultant force is equal to the sum of the squares of the magnitudes of the individual forces:
(Resultant force)^2 = (Force 1)^2 + (Force 2)^2
(100N)^2 = F1^2 + F2^2
Now, let's consider the angle between Force 1 and the resultant force. We know that sin(60 degrees) = opposite/hypotenuse. In this case, the opposite side is F1, which means we can rearrange the equation to solve for F1:
F1 = sin(60 degrees) * Resultant force
F1 = 0.87 * 100N
F1 = 87N
Similarly, we can find the magnitude of Force 2 using the angle between Force 2 and the resultant force:
Force 2 = cos(60 degrees) * Resultant force
Force 2 = 0.5 * 100N
Force 2 = 50N
Therefore, the magnitude of Force 1 is 87N and the magnitude of Force 2 is 50N.