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Answer :
To find the [tex]$x$[/tex]-component of the total force acting on the chair, we need to consider each force separately and use trigonometry:
1. Identify the Forces and Angles:
- The first force is 122 N at an angle of 43.6° from the horizontal.
- The second force is 97.6 N at an angle of 49.9° from the horizontal.
2. Calculate the [tex]$x$[/tex]-component for Each Force:
- For the first force, the [tex]$x$[/tex]-component can be found using the cosine of the angle:
[tex]\[
\text{Force 1}_x = 122 \, \text{N} \times \cos(43.6^\circ)
\][/tex]
This calculation results in approximately 88.35 N.
- For the second force, similarly, we use the cosine of the angle:
[tex]\[
\text{Force 2}_x = 97.6 \, \text{N} \times \cos(49.9^\circ)
\][/tex]
This calculation results in approximately 62.87 N.
3. Combine the [tex]$x$[/tex]-components:
- The total [tex]$x$[/tex]-component of the force is the sum of the [tex]$x$[/tex]-components from both forces:
[tex]\[
\overrightarrow{F_{x}} = 88.35 \, \text{N} + 62.87 \, \text{N}
\][/tex]
This results in a total [tex]$x$[/tex]-component of approximately 151.22 N.
Therefore, the [tex]$x$[/tex]-component of the total force acting on the chair is about 151.22 N.
1. Identify the Forces and Angles:
- The first force is 122 N at an angle of 43.6° from the horizontal.
- The second force is 97.6 N at an angle of 49.9° from the horizontal.
2. Calculate the [tex]$x$[/tex]-component for Each Force:
- For the first force, the [tex]$x$[/tex]-component can be found using the cosine of the angle:
[tex]\[
\text{Force 1}_x = 122 \, \text{N} \times \cos(43.6^\circ)
\][/tex]
This calculation results in approximately 88.35 N.
- For the second force, similarly, we use the cosine of the angle:
[tex]\[
\text{Force 2}_x = 97.6 \, \text{N} \times \cos(49.9^\circ)
\][/tex]
This calculation results in approximately 62.87 N.
3. Combine the [tex]$x$[/tex]-components:
- The total [tex]$x$[/tex]-component of the force is the sum of the [tex]$x$[/tex]-components from both forces:
[tex]\[
\overrightarrow{F_{x}} = 88.35 \, \text{N} + 62.87 \, \text{N}
\][/tex]
This results in a total [tex]$x$[/tex]-component of approximately 151.22 N.
Therefore, the [tex]$x$[/tex]-component of the total force acting on the chair is about 151.22 N.
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