Two forces whose resultants is 100N are perpendicular to each other. If one of them makes an angle of 60 degree with the horinzontal. Calculate its magnitude
Answer the question
100n 60
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Two force whose resultant force is 100N are perpendicular to each other. if one of them make an angle of 60 with resultant force. what is the angle made with other force?
To calculate the magnitude of the force, we can use the concept of vector addition.
Let's call the two forces F1 and F2. It is given that the resultant of these two forces is 100N, and they are perpendicular to each other.
If one of the forces makes an angle of 60 degrees with the horizontal, we can consider the other force to be vertical.
To find the magnitude of F1, we can use the right-angle triangle formed by the forces. The vertical component of F1 will cancel out the vertical component of F2, resulting in the vertical component of the resultant force being zero.
Using trigonometry, we can determine the magnitude of F1:
sin(60°) = F1/F2
Rearranging the equation, we get:
F1 = F2 * sin(60°)
Since the two forces have a resultant of 100N, we have:
F1 + F2 = 100N
Substituting the value of F1, we get:
F2 * sin(60°) + F2 = 100N
Simplifying the equation:
2F2 * sin(60°) = 100N
sin(60°) = √3/2, so:
2F2 * (√3/2) = 100N
Multiplying both sides by 2/(√3):
F2 = (100N * 2) / (√3)
Calculating the value of F2:
F2 ≈ 115.47N
Substituting the value of F2 back into the equation for F1:
F1 = F2 * sin(60°)
F1 = 115.47N * (√3/2)
Calculating the value of F1:
F1 ≈ 99.99N
Therefore, the magnitude of the force making an angle of 60 degrees with the horizontal is approximately 99.99N.