Answer :
To find the [tex]\( x \)[/tex]-component of the total force acting on the chair, we need to break down each force into its respective [tex]\( x \)[/tex]-component using trigonometry. We'll then add these components together to find the total [tex]\( x \)[/tex]-component.
### Steps to Solve:
1. Identify the Forces and Angles:
- The first force [tex]\( F_1 \)[/tex] is 122 N at an angle of [tex]\( 43.6^\circ \)[/tex].
- The second force [tex]\( F_2 \)[/tex] is 97.6 N at an angle of [tex]\( 49.9^\circ \)[/tex].
2. Calculate the [tex]\( x \)[/tex]-component of Each Force:
- The [tex]\( x \)[/tex]-component of a force can be found using the cosine function, which relates to the adjacent side of a right triangle.
- For the first force [tex]\( F_1 \)[/tex]:
[tex]\[
F_{1x} = 122 \times \cos(43.6^\circ)
\][/tex]
- For the second force [tex]\( F_2 \)[/tex]:
[tex]\[
F_{2x} = 97.6 \times \cos(49.9^\circ)
\][/tex]
3. Add the [tex]\( x \)[/tex]-components Together:
- To find the total [tex]\( x \)[/tex]-component ([tex]\( F_x \)[/tex]) of the forces acting on the chair, add the [tex]\( x \)[/tex]-components of [tex]\( F_1 \)[/tex] and [tex]\( F_2 \)[/tex]:
[tex]\[
F_x = F_{1x} + F_{2x}
\][/tex]
4. Results:
- The [tex]\( x \)[/tex]-component of the first force is approximately 88.35 N.
- The [tex]\( x \)[/tex]-component of the second force is approximately 62.87 N.
- Therefore, the total [tex]\( x \)[/tex]-component of the forces is approximately:
[tex]\[
F_x \approx 151.22 \, \text{N}
\][/tex]
Thus, the [tex]\( x \)[/tex]-component of the total force acting on the chair is about 151.22 N.
### Steps to Solve:
1. Identify the Forces and Angles:
- The first force [tex]\( F_1 \)[/tex] is 122 N at an angle of [tex]\( 43.6^\circ \)[/tex].
- The second force [tex]\( F_2 \)[/tex] is 97.6 N at an angle of [tex]\( 49.9^\circ \)[/tex].
2. Calculate the [tex]\( x \)[/tex]-component of Each Force:
- The [tex]\( x \)[/tex]-component of a force can be found using the cosine function, which relates to the adjacent side of a right triangle.
- For the first force [tex]\( F_1 \)[/tex]:
[tex]\[
F_{1x} = 122 \times \cos(43.6^\circ)
\][/tex]
- For the second force [tex]\( F_2 \)[/tex]:
[tex]\[
F_{2x} = 97.6 \times \cos(49.9^\circ)
\][/tex]
3. Add the [tex]\( x \)[/tex]-components Together:
- To find the total [tex]\( x \)[/tex]-component ([tex]\( F_x \)[/tex]) of the forces acting on the chair, add the [tex]\( x \)[/tex]-components of [tex]\( F_1 \)[/tex] and [tex]\( F_2 \)[/tex]:
[tex]\[
F_x = F_{1x} + F_{2x}
\][/tex]
4. Results:
- The [tex]\( x \)[/tex]-component of the first force is approximately 88.35 N.
- The [tex]\( x \)[/tex]-component of the second force is approximately 62.87 N.
- Therefore, the total [tex]\( x \)[/tex]-component of the forces is approximately:
[tex]\[
F_x \approx 151.22 \, \text{N}
\][/tex]
Thus, the [tex]\( x \)[/tex]-component of the total force acting on the chair is about 151.22 N.