Question

Replace the 880-lb force acting at point A by a force-couple system at (a) point O and (b) point B. 11510200791.jpg

Complex numbers
ANSWERED
asked 2020-11-08
Replace the 880-lb force acting at point A by a force-couple system at
(a) point O
and
(b) point B.
image

Answers (1)

2020-11-09
\(\displaystyle{o}{v}{e}{r}\rightarrow{\left\lbrace{F}\right\rbrace}={800}\ {l}{b}\ {\left[-{\frac{{{2}}}{{\sqrt{{{3}}}}}}{w}{i}{d}{e}\hat{{{i}}}+{\frac{{{1}}}{{\sqrt{{{3}}}}}}{w}{i}{d}{e}\hat{{{i}}}\right]}\)
a) Point O
\(\displaystyle\Rightarrow{o}{v}{e}{r}\rightarrow{\left\lbrace{O}{A}\right\rbrace}={3}{j}\)
\(\displaystyle\therefore{o}{v}{e}{r}\rightarrow{\left\lbrace{C}\right\rbrace}={o}{v}{e}{r}\rightarrow{\left\lbrace{O}{A}\right\rbrace}\times{o}{v}{e}{r}\rightarrow{\left\lbrace{F}\right\rbrace}\)
\(\displaystyle={3}{j}\times{800}\ {l}{b}\ {\left[-{\frac{{{2}}}{{\sqrt{{{3}}}}}}{w}{i}{d}{e}\hat{{{i}}}+{\frac{{{1}}}{{\sqrt{{{3}}}}}}{w}{i}{d}{e}\hat{{{i}}}\right]}\)
\(\displaystyle={2771}\cdot{28}{w}{i}{d}{e}\hat{{{k}}}\ {l}{b}-{f}{t}\)
b) Point B \(\displaystyle\Rightarrow{o}{v}{e}{r}\rightarrow{\left\lbrace{B}{A}\right\rbrace}={4}{i}+{3}{w}{i}{d}{e}\hat{{{j}}}\)
\(\displaystyle\therefore{o}{v}{e}{r}\rightarrow{\left\lbrace{C}\right\rbrace}={o}{v}{e}{r}\rightarrow{\left\lbrace{B}{A}\right\rbrace}\times{o}{v}{e}{r}\rightarrow{\left\lbrace{F}\right\rbrace}\)
\(\displaystyle={\left({4}{w}{i}{d}{e}\hat{{{i}}}+{3}{w}{i}{d}{e}\hat{{{j}}}\right)}\times{800}\ {l}{b}{\left[-{\frac{{{2}}}{{\sqrt{{{3}}}}}}{w}{i}{d}{e}\hat{{{i}}}+{\frac{{{1}}}{{\sqrt{{{3}}}}}}{w}{i}{d}{e}\hat{{{i}}}\right]}\)
\(\displaystyle={4618}\cdot{8}{w}{i}{d}{e}\hat{{{k}}}\ {l}{b}-{f}{t}\)
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