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