Solution 4.7b
From Mechanics
(Difference between revisions)
(New page: <math>\begin{align} & \mathbf{F}1= & =86\textrm{.}6\mathbf{i}+50\mathbf{j}\ \text{N}\\ \end{align}</math> <math>\begin{align} & \mathbf{F}2= & =-30\textrm{.}8\mathbf{i}+84\textrm{.}6\mat...) |
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<math>\begin{align} | <math>\begin{align} | ||
| - | & \mathbf{F}1= | + | & \mathbf{F}1 = |
| - | & | + | & 86\textrm{.}6\mathbf{i}+50\mathbf{j}\ \text{N}\\ |
\end{align}</math> | \end{align}</math> | ||
<math>\begin{align} | <math>\begin{align} | ||
& \mathbf{F}2= | & \mathbf{F}2= | ||
| - | & | + | & -30\textrm{.}8\mathbf{i}+84\textrm{.}6\mathbf{j} \ \text{N}\\ |
\end{align}</math> | \end{align}</math> | ||
<math>\begin{align} | <math>\begin{align} | ||
& \mathbf{F}3= | & \mathbf{F}3= | ||
| - | & | + | & -80\mathbf{j}\ \text{N}\\ |
\end{align}</math> | \end{align}</math> | ||
| + | |||
| + | Summing these vectors give their resultant | ||
| + | |||
| + | <math>\begin{align} | ||
| + | & \mathbf{R}= | ||
| + | & 55\textrm{.}8\mathbf{i}+54\textrm{.}6\mathbf{j} \ \text{N}\\ | ||
| + | \end{align}</math> | ||
| + | |||
| + | The magnitude of this resultant is | ||
| + | |||
| + | |||
| + | <math>\sqrt{{{\left( 55\textrm{.}8 \right)}^{2}}+{{\left( 54\textrm{.}6 \right)}^{2}}}=78\textrm{.}1\ \text{N}</math> | ||
Current revision
\displaystyle \begin{align} & \mathbf{F}1 = & 86\textrm{.}6\mathbf{i}+50\mathbf{j}\ \text{N}\\ \end{align}
\displaystyle \begin{align} & \mathbf{F}2= & -30\textrm{.}8\mathbf{i}+84\textrm{.}6\mathbf{j} \ \text{N}\\ \end{align}
\displaystyle \begin{align} & \mathbf{F}3= & -80\mathbf{j}\ \text{N}\\ \end{align}
Summing these vectors give their resultant
\displaystyle \begin{align} & \mathbf{R}= & 55\textrm{.}8\mathbf{i}+54\textrm{.}6\mathbf{j} \ \text{N}\\ \end{align}
The magnitude of this resultant is
\displaystyle \sqrt{{{\left( 55\textrm{.}8 \right)}^{2}}+{{\left( 54\textrm{.}6 \right)}^{2}}}=78\textrm{.}1\ \text{N}
