when two equal forces of f1 and f2 making an angle of 180 degree with each other the magnitude of their resultant is ................?
A = |f1|
B = |f2|
answer = | A - B |
When two equal forces, F1 and F2, are making an angle of 180 degrees with each other, the magnitude of their resultant can be calculated as follows:
Resultant = √(F1^2 + F2^2 + 2*F1*F2*cos(180°))
Since the angle between the forces is 180 degrees, the cosine of 180 degrees is -1.
Resultant = √(F1^2 + F2^2 - 2*F1*F2)
Since the forces are equal (F1 = F2), we can substitute F for both F1 and F2.
Resultant = √(F^2 + F^2 - 2*F*F)
Simplifying the equation:
Resultant = √(2F^2 - 2F^2)
The squared terms cancel each other out:
Resultant = √0
Therefore, the magnitude of the resultant is 0.
To find the magnitude of the resultant when two equal forces (F1 and F2) are acting at an angle of 180 degrees with each other, you can use the concept of vector addition.
When two forces are acting in opposite directions along the same line, the magnitude of their resultant force is given by the algebraic sum of the two forces.
In this case, since the forces F1 and F2 are equal, the magnitude of their resultant force would be:
Resultant magnitude = F1 + F2
Since F1 and F2 have the same magnitude, we can substitute:
Resultant magnitude = 2F1
Therefore, the magnitude of the resultant force when two equal forces (F1 and F2) are acting at an angle of 180 degrees with each other is twice the magnitude of either force.