Option 1 : F1 = 15N, F2 = 25N
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Option(1)
CONCEPT:
- Force is a vector quantity that has both magnitude and direction, to calculate the magnitude of a vector quantity we apply vector law .
- Triangle law of vector addition state that if two vectors can be represented both in magnitude and direction by the two sides of a triangle taken in the same order, then their resultant is represented completely, both in magnitude and direction, by the third side of the triangle taken in the opposite order.
- Vectors can be added geometrically by the vector law of addition.
Vector Law of Addition:
R = \(\sqrt{A^2+B^2 +2ABcosθ }\)
EXPLANATION:
If F1 and F2 are the two forces whose magnitude are in the ratio of 3 : 5 ,
Let assume F1 = 3x N and F2 = 5x Newton, R = 35, θ = 60°
we already know that R = \(\sqrt{A^2+B^2 +2ABcosθ }\)
35 = \(\sqrt{(3x)^2+(5x)^2 +2× 3x × 5x cosθ } \)
35 = 7x, or x = 35/7 = 5
hence F1 = 3x N = 3 × 5 = 15 N and F2 = 5x N = 5 × 5 = 25 N
Additional Information
Special case:
- If two vectors \(\vec A\) and \(\vec B\) are acting along the same direction, θ = 0. Therefore the magnitude of the resultant is given by mathematically:
- \(R =\sqrt{A^2 + B^2 + 2ABcosθ }\) = \(\sqrt{A^2+ B^2 +2AB}\) = \(\sqrt{(A+ B)^2 } \)
R = A + B
- If two vectors \(\vec A\) and \(\vec B\) are acting along the opposite direction, θ = 180°. Therefore the magnitude of the resultant is given by mathematically
- \(R =\sqrt{A^2 + B^2 + 2ABcosθ }\) = \(\sqrt{A^2+B^2+2ABcos180}=\sqrt{A^2+B^2-2AB}\)
R = A - B
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