What is the resultant of two equal forces of magnitude f,acting at right angles to each other
Fr = Sqrt(F^2 + F^2) = Sqrt(2F^2) = 1.414F.
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Physics question
To find the resultant of two equal forces of magnitude \(f\), acting at right angles to each other, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the two forces are the sides of the right triangle, and the resultant force is the hypotenuse.
Let's label the forces as \(F_1\) and \(F_2\), both having a magnitude of \(f\):
|\
| \ F1
| \
Resultant |___\
(hypotenuse) F2
According to the Pythagorean theorem, the square of the resultant force (\(R\)) is equal to the sum of the squares of the individual forces:
R^2 = F1^2 + F2^2
Since both forces have the same magnitude (\(f\)), we can simplify the equation:
R^2 = f^2 + f^2
R^2 = 2f^2
To find the resultant force, \(R\), we take the square root of both sides:
R = √(2f^2)
R = f√2
Therefore, the resultant of two equal forces of magnitude \(f\), acting at right angles to each other, is \(f\) times the square root of 2 (\(f√2\)).