1ª
a)
[tex]|FR| = \sqrt{ Fr_{x}^2 + Fr_{y}^2 } = \sqrt{ 2^2 + 3.1^2 } = \sqrt{4+9.61} = \sqrt{13,61} [/tex]
[tex]|FR| = 3.689173349 [/tex]
[tex]\boxed{\boxed{|FR| \approx 3.7N}}[/tex]
magnitude: 3.7 N
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[tex]\Theta = tg^{-1} | \frac{ Fr_{x} }{ Fr_{y} } | [/tex]
[tex]\Theta = tg^{-1} ( \frac{2}{3.1} )[/tex]
[tex]\Theta = 32.82854179[/tex]
[tex]\boxed{\boxed{\Theta \approx 33^0anticlockwise/horizontal}}[/tex]
b)
[tex]|FR| = \sqrt{ Fr_{x}^2 + Fr_{y}^2 } = \sqrt{ 16^2 + 6^2 } = \sqrt{256+36} = \sqrt{292} [/tex]
[tex]|FR| = 17.08800749 [/tex]
[tex]\boxed{\boxed{|FR| \approx 17.1N}}[/tex]
magnitude: 17.1 N
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[tex]\Theta = tg^{-1} | \frac{ Fr_{x} }{ Fr_{y} } | [/tex]
[tex]\Theta = tg^{-1} ( \frac{6}{16} )[/tex]
[tex]\Theta = 20.55604522[/tex]
[tex]\boxed{\boxed{\Theta \approx 20.6^0anticlockwise/horizontal}}[/tex] or [tex]\boxed{\boxed{\Theta \approx 21^0anticlockwise/horizontal}}[/tex]
c)
[tex]|FR| = \sqrt{ Fr_{x}^2 + Fr_{y}^2 } = \sqrt{ (3-2)^2 + 1^2 } = \sqrt{1^2+1^2} = \sqrt{2} [/tex]
[tex]|FR| = 1.414213562 [/tex]
[tex]\boxed{\boxed{|FR| \approx 1.4N}}[/tex]
magnitude: 1.4 N
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Watch the picture:
We have: 45º (isosceles) below horizontal (to 3N and 1N).
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4ª
a)
[tex]Cos40^0 = \frac{y}{350}[/tex]
[tex]0.7660444431 = \frac{y}{350} [/tex]
[tex]y = 0.7660444431*350[/tex]
[tex]y= 268.1155551[/tex]
[tex]\boxed{\boxed{y \approx 268 N}}[/tex]
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b)
In opposite
directions
[tex]|FR| = \sqrt{ Fr_{x}^2 - Fr_{y}^2 } = \sqrt{ 350^2 - 268^2 } = \sqrt{122500 - 71824} = \sqrt{50676} [/tex]
[tex]|FR| = 225.1133048 [/tex]
[tex]\boxed{\boxed{|FR| \approx 225N}}[/tex]
