- #1
- 46
- 10
- Homework Statement
- The uniform bar is bent in the form of a parabola and has a weight per unit length of 6 lb>ft. parabola and has a weight per unit length of 6 lb>ft. Determine the reactions at the fixed support A.
- Relevant Equations
- ## dL=\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy ##
## \overline{x}=\frac{\int _{ }^{ }\tilde{x}dL}{\int _{ }^{ }dL} ##
My solution is
![<math xmlns=http://www.w3.org/1998/Math/MathML display=block data-is-equatio=1 data-latex=\begin{array}{l}Data\\
\begin{array}{l}\left(dL\right)^2=\left(dx\right)^2+\left(dy\right)^2\\
dL=\sqrt{\left(dx\right)^2+\left(dy\right)^2}\\
dL=\sqrt{\left(\left(\frac{dx}{dy}\right)^2dy^2+\left(1\right)\left(dy\right)^2\right)}\\
dL=\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy\\
y^2=3x\\
\frac{y^2}{3}=x\ →\frac{2y}{3}dy=dx\\
\frac{y^2}{3}=x\ →\frac{2y}{3}=\frac{dx}{dy}\\
\overline{x}=\frac{\int_0^3\tilde{x}dL}{\int_0^3dL}\ →\left[\textcolor{#E94D40}{\ dL=\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy}\right]\\
\overline{x}=\frac{\int_0^3\tilde{x}\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy}{\int_0^3\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy}\ →\left[\textcolor{#E94D40}{\ \frac{dx}{dy}=\frac{2y}{3}}\right]\end{array}\\
\overline{x}=\frac{\int_0^3x\sqrt{\left(\frac{2y}{3}\right)^2+1}dy\ →\ \left[\textcolor{#E94D40}{\frac{y^2}{3}=x}\ \right]\ }{\int_0^3\sqrt{\left(\frac{2y}{3}\right)^2+1}dy}\\
\overline{x}=\frac{\int_0^3\frac{y^2}{3}\sqrt{\left(\frac{2y}{3}\right)^2+1}dy\ \ }{\int_0^3\sqrt{\left(\frac{2y}{3}\right)^2+1}dy}\\
\overline{x}=\frac{5.46}{4.44}p\\
\overline{x}\approx1.23p\\
w=\int_0^36\sqrt{\left(\frac{2y}{3}\right)^2+1}dy\\
w=\textcolor{#28AE61}{\frac{6}{3}}\int_{ }^{ }\sqrt{4y^2+9}dy\ \left(y=\frac{3}{2}\tan\theta,\ dy=\frac{3}{2}\sec^2\theta\ d\theta\right)\\
w=2\int_{ }^{ }\sqrt{9\tan^2\theta+9}\frac{3}{2}\sec^2\theta\ d\theta\\
w=\frac{\cancel{\textcolor{#E94D40}{2}}\cdot3\cdot3}{\cancel{\textcolor{#E94D40}{2}}}\int_0^3\sqrt{\tan^2\theta+1}\sec^2\theta\ d\theta\\
w=9\int_{ }^{ }\sec^3\theta\ d\theta\ \left(u=\sec\theta,\ du=\sec\theta\tan\theta,\ dv=\sec^2\theta,\ v=\tan\theta\right)\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\sec\theta\tan\theta\tan\theta d\theta\right\}\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\sec\theta\tan^2\theta d\theta\right\}\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\left(\sec^3\theta-\sec\theta\right)d\theta\right\}\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\sec^3\theta d\theta+\int_{ }^{ }\sec\theta d\theta\right\}\\
w=\frac{9}{2}\sec\theta\tan\theta+\frac{9}{2}\ln\left|\sec\theta+\tan\theta\right|\ \left[y=\frac{3}{2}\tan\theta,\ \theta=\arctan\left(\frac{2y}{3}\right)\right]\\
w=\frac{9}{2}\frac{\sqrt{4y^2+9}}{3}\frac{2y}{3}+\frac{9}{2}\ln\left|\frac{\sqrt{4y^2+9}}{3}+\frac{2y}{3}\right|\\
w=y\sqrt{4y^2+9}+\frac{9}{2}\ln\left|\frac{2y+\sqrt{4y^2+9}}{3}\right|\ \begin{bmatrix}3\\
0\end{bmatrix}\\
w=3\sqrt{4\left(3\right)^2+9}+\frac{9}{2}\ln\left|\frac{2\left(3\right)+\sqrt{4\left(3\right)^2+9}}{3}\right|-\left(\cancel{\textcolor{#E94D40}{0\sqrt{4\left(0\right)^2+9}}}+\frac{9}{2}\ln\left|\frac{\cancel{\textcolor{#E94D40}{2\left(0\right)}}+\sqrt{\cancel{\textcolor{#E94D40}{4\left(0\right)^2}}+9}}{3}\right|\right)\\
w=9\sqrt{5}+\frac{9\ln\left(2+\sqrt{5}\right)}{2}-\left(\textcolor{#E94D40}{\cancel{\frac{9}{2}\ln\left|1\right|}}\right)\\
w=26.62lb\end{array}><mtable columnalign=left columnspacing=1em rowspacing=4pt><mtr><mtd><mi>D</mi><mi>a</mi><mi>t</mi><mi>a</mi></mtd></mtr><mtr><mtd><mtable columnspacing=1em rowspacing=4pt><mtr><mtd><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>L</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo>=</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>x</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>y</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>d</mi><mi>L</mi><mo>=</mo><msqrt><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>x</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>y</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mi>d</mi><mi>L</mi><mo>=</mo><msqrt><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mi>d</mi><mi>y</mi></mrow></mfrac><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mi>d</mi><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mn>1</mn><mo data-mjx-texclass=CLOSE>)</mo></mrow><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>y</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo data-mjx-texclass=CLOSE>)</mo></mrow></msqrt></mtd></mtr><mtr><mtd><mi>d<](https://lh5.googleusercontent.com/VT6GutAdkVXhuDnL3smY7ui5KBx4ORHztbT046vn4TKYK87mqPToV0k9UDzwXCSqOPIsbPT81SXU7WSCLN_3P1G62ZkdnuBK-YbI9SIygPWTUjELey8g4rC-Xdu0jJsvsmHKuaw5=s1600 "<math xmlns=http://www.w3.org/1998/Math/MathML display=block data-is-equatio=1 data-latex=\begin{array}{l}Data\\
\begin{array}{l}\left(dL\right)^2=\left(dx\right)^2+\left(dy\right)^2\\
dL=\sqrt{\left(dx\right)^2+\left(dy\right)^2}\\
dL=\sqrt{\left(\left(\frac{dx}{dy}\right)^2dy^2+\left(1\right)\left(dy\right)^2\right)}\\
dL=\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy\\
y^2=3x\\
\frac{y^2}{3}=x\ →\frac{2y}{3}dy=dx\\
\frac{y^2}{3}=x\ →\frac{2y}{3}=\frac{dx}{dy}\\
\overline{x}=\frac{\int_0^3\tilde{x}dL}{\int_0^3dL}\ →\left[\textcolor{#E94D40}{\ dL=\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy}\right]\\
\overline{x}=\frac{\int_0^3\tilde{x}\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy}{\int_0^3\sqrt{\left(\frac{dx}{dy}\right)^2+1}dy}\ →\left[\textcolor{#E94D40}{\ \frac{dx}{dy}=\frac{2y}{3}}\right]\end{array}\\
\overline{x}=\frac{\int_0^3x\sqrt{\left(\frac{2y}{3}\right)^2+1}dy\ →\ \left[\textcolor{#E94D40}{\frac{y^2}{3}=x}\ \right]\ }{\int_0^3\sqrt{\left(\frac{2y}{3}\right)^2+1}dy}\\
\overline{x}=\frac{\int_0^3\frac{y^2}{3}\sqrt{\left(\frac{2y}{3}\right)^2+1}dy\ \ }{\int_0^3\sqrt{\left(\frac{2y}{3}\right)^2+1}dy}\\
\overline{x}=\frac{5.46}{4.44}p\\
\overline{x}\approx1.23p\\
w=\int_0^36\sqrt{\left(\frac{2y}{3}\right)^2+1}dy\\
w=\textcolor{#28AE61}{\frac{6}{3}}\int_{ }^{ }\sqrt{4y^2+9}dy\ \left(y=\frac{3}{2}\tan\theta,\ dy=\frac{3}{2}\sec^2\theta\ d\theta\right)\\
w=2\int_{ }^{ }\sqrt{9\tan^2\theta+9}\frac{3}{2}\sec^2\theta\ d\theta\\
w=\frac{\cancel{\textcolor{#E94D40}{2}}\cdot3\cdot3}{\cancel{\textcolor{#E94D40}{2}}}\int_0^3\sqrt{\tan^2\theta+1}\sec^2\theta\ d\theta\\
w=9\int_{ }^{ }\sec^3\theta\ d\theta\ \left(u=\sec\theta,\ du=\sec\theta\tan\theta,\ dv=\sec^2\theta,\ v=\tan\theta\right)\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\sec\theta\tan\theta\tan\theta d\theta\right\}\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\sec\theta\tan^2\theta d\theta\right\}\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\left(\sec^3\theta-\sec\theta\right)d\theta\right\}\\
w=9\left\{\sec\theta\tan\theta-\int_{ }^{ }\sec^3\theta d\theta+\int_{ }^{ }\sec\theta d\theta\right\}\\
w=\frac{9}{2}\sec\theta\tan\theta+\frac{9}{2}\ln\left|\sec\theta+\tan\theta\right|\ \left[y=\frac{3}{2}\tan\theta,\ \theta=\arctan\left(\frac{2y}{3}\right)\right]\\
w=\frac{9}{2}\frac{\sqrt{4y^2+9}}{3}\frac{2y}{3}+\frac{9}{2}\ln\left|\frac{\sqrt{4y^2+9}}{3}+\frac{2y}{3}\right|\\
w=y\sqrt{4y^2+9}+\frac{9}{2}\ln\left|\frac{2y+\sqrt{4y^2+9}}{3}\right|\ \begin{bmatrix}3\\
0\end{bmatrix}\\
w=3\sqrt{4\left(3\right)^2+9}+\frac{9}{2}\ln\left|\frac{2\left(3\right)+\sqrt{4\left(3\right)^2+9}}{3}\right|-\left(\cancel{\textcolor{#E94D40}{0\sqrt{4\left(0\right)^2+9}}}+\frac{9}{2}\ln\left|\frac{\cancel{\textcolor{#E94D40}{2\left(0\right)}}+\sqrt{\cancel{\textcolor{#E94D40}{4\left(0\right)^2}}+9}}{3}\right|\right)\\
w=9\sqrt{5}+\frac{9\ln\left(2+\sqrt{5}\right)}{2}-\left(\textcolor{#E94D40}{\cancel{\frac{9}{2}\ln\left|1\right|}}\right)\\
w=26.62lb\end{array}><mtable columnalign=left columnspacing=1em rowspacing=4pt><mtr><mtd><mi>D</mi><mi>a</mi><mi>t</mi><mi>a</mi></mtd></mtr><mtr><mtd><mtable columnspacing=1em rowspacing=4pt><mtr><mtd><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>L</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo>=</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>x</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>y</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>d</mi><mi>L</mi><mo>=</mo><msqrt><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>x</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>y</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mi>d</mi><mi>L</mi><mo>=</mo><msqrt><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mi>d</mi><mi>y</mi></mrow></mfrac><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mi>d</mi><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mn>1</mn><mo data-mjx-texclass=CLOSE>)</mo></mrow><msup><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>(</mo><mi>d</mi><mi>y</mi><mo data-mjx-texclass=CLOSE>)</mo></mrow><mn>2</mn></msup><mo data-mjx-texclass=CLOSE>)</mo></mrow></msqrt></mtd></mtr><mtr><mtd><mi>d<")
![<math xmlns=http://www.w3.org/1998/Math/MathML display=block data-is-equatio=1 data-latex=\begin{array}{l}↶_+ΣM_A=0\\
M_A-\overline{x}\cdot26.6=0\\
M_A-1.23\cdot26.6=0\\
\left[\textcolor{#E94D40}{M_A=32.72↶_+}\right]\\
\overrightarrow{+}Σfx=0\\
\left[\textcolor{#E94D40}{A_x=\overrightarrow{0}}\right]\\
_+↑Σfy=0\\
A_y-26.6=0\\
\left[\textcolor{#E94D40}{A_y=26.6_+↑}\right]\\
Solutions\\
\left[\textcolor{#E94D40}{A_x=\overrightarrow{0}}\right]\left[\textcolor{#E94D40}{A_y=26.6_+↑}\right]\\
\left[\textcolor{#E94D40}{M_A=32.72↶_+}\right]\end{array}><mtable columnalign=left columnspacing=1em rowspacing=4pt><mtr><mtd><msub><mo>↶</mo><mo>+</mo></msub><mi>Σ</mi><msub><mi>M</mi><mi>A</mi></msub><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>M</mi><mi>A</mi></msub><mo>−</mo><mover><mi>x</mi><mo accent=true>―</mo></mover><mo>⋅</mo><mn>26.6</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>M</mi><mi>A</mi></msub><mo>−</mo><mn>1.23</mn><mo>⋅</mo><mn>26.6</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>M</mi><mi>A</mi></msub><mo>=</mo><mn>32.72</mn><msub><mo>↶</mo><mo>+</mo></msub></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><mover><mo>+</mo><mo>→</mo></mover><mi>Σ</mi><mi>f</mi><mi>x</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>x</mi></msub><mo>=</mo><mover><mn>0</mn><mo>→</mo></mover></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><msub><mi/><mo>+</mo></msub><mo stretchy=false>↑</mo><mi>Σ</mi><mi>f</mi><mi>y</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>A</mi><mi>y</mi></msub><mo>−</mo><mn>26.6</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>y</mi></msub><mo>=</mo><msub><mn>26.6</mn><mo>+</mo></msub><mo stretchy=false>↑</mo></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><mi>S</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>x</mi></msub><mo>=</mo><mover><mn>0</mn><mo>→</mo></mover></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>y</mi></msub><mo>=</mo><msub><mn>26.6</mn><mo>+</mo></msub><mo stretchy=false>↑</mo></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>M</mi><mi>A</mi></msub><mo>=</mo><mn>32.72</mn><msub><mo>↶</mo><mo>+</mo></msub></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr></mtable></math>](https://lh6.googleusercontent.com/eh33mZuwrGdw08zZMT9-XQRNEds6-8zvswUKFxr8ed8vpIAKsCy-QQ-ah63HsRLpYPX4QJuE8nszTzoIGdfGq--DZMZAQqd6-UywrnLtXbqjo8FAzp7d8hiTCFvvqOy-HY23ZUMX=s1600 "<math xmlns=http://www.w3.org/1998/Math/MathML display=block data-is-equatio=1 data-latex=\begin{array}{l}↶_+ΣM_A=0\\
M_A-\overline{x}\cdot26.6=0\\
M_A-1.23\cdot26.6=0\\
\left[\textcolor{#E94D40}{M_A=32.72↶_+}\right]\\
\overrightarrow{+}Σfx=0\\
\left[\textcolor{#E94D40}{A_x=\overrightarrow{0}}\right]\\
_+↑Σfy=0\\
A_y-26.6=0\\
\left[\textcolor{#E94D40}{A_y=26.6_+↑}\right]\\
Solutions\\
\left[\textcolor{#E94D40}{A_x=\overrightarrow{0}}\right]\left[\textcolor{#E94D40}{A_y=26.6_+↑}\right]\\
\left[\textcolor{#E94D40}{M_A=32.72↶_+}\right]\end{array}><mtable columnalign=left columnspacing=1em rowspacing=4pt><mtr><mtd><msub><mo>↶</mo><mo>+</mo></msub><mi>Σ</mi><msub><mi>M</mi><mi>A</mi></msub><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>M</mi><mi>A</mi></msub><mo>−</mo><mover><mi>x</mi><mo accent=true>―</mo></mover><mo>⋅</mo><mn>26.6</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>M</mi><mi>A</mi></msub><mo>−</mo><mn>1.23</mn><mo>⋅</mo><mn>26.6</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>M</mi><mi>A</mi></msub><mo>=</mo><mn>32.72</mn><msub><mo>↶</mo><mo>+</mo></msub></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><mover><mo>+</mo><mo>→</mo></mover><mi>Σ</mi><mi>f</mi><mi>x</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>x</mi></msub><mo>=</mo><mover><mn>0</mn><mo>→</mo></mover></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><msub><mi/><mo>+</mo></msub><mo stretchy=false>↑</mo><mi>Σ</mi><mi>f</mi><mi>y</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>A</mi><mi>y</mi></msub><mo>−</mo><mn>26.6</mn><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>y</mi></msub><mo>=</mo><msub><mn>26.6</mn><mo>+</mo></msub><mo stretchy=false>↑</mo></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><mi>S</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>x</mi></msub><mo>=</mo><mover><mn>0</mn><mo>→</mo></mover></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>A</mi><mi>y</mi></msub><mo>=</mo><msub><mn>26.6</mn><mo>+</mo></msub><mo stretchy=false>↑</mo></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass=INNER><mo data-mjx-texclass=OPEN>[</mo><mstyle mathcolor=#E94D40><msub><mi>M</mi><mi>A</mi></msub><mo>=</mo><mn>32.72</mn><msub><mo>↶</mo><mo>+</mo></msub></mstyle><mo data-mjx-texclass=CLOSE>]</mo></mrow></mtd></mtr></mtable></math>")
However can someone explain in detail why
will be equal to the weight? and why does it have to be multiplied by 6?
