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 horizontal component. Here’s how you can do it step-by-step:
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:
- To find the [tex]\( x \)[/tex]-component of a force, we use the cosine of the angle since we need the adjacent side of the right triangle formed by the force vector.
- 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. Sum the [tex]\( x \)[/tex]-components:
- Add the [tex]\( x \)[/tex]-components of both forces to get the total [tex]\( x \)[/tex]-component of the force on the chair.
[tex]\[
F_x = F_{1x} + F_{2x}
\][/tex]
4. Numerical Result:
- From the calculations, the [tex]\( x \)[/tex]-components are approximately:
- [tex]\( F_{1x} \approx 88.35 \, \text{N} \)[/tex]
- [tex]\( F_{2x} \approx 62.87 \, \text{N} \)[/tex]
- Therefore, the total [tex]\( x \)[/tex]-component of the force [tex]\( F_x \approx 151.22 \, \text{N} \)[/tex].
So, the [tex]\( x \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 151.22 \, \text{N} \)[/tex].
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:
- To find the [tex]\( x \)[/tex]-component of a force, we use the cosine of the angle since we need the adjacent side of the right triangle formed by the force vector.
- 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. Sum the [tex]\( x \)[/tex]-components:
- Add the [tex]\( x \)[/tex]-components of both forces to get the total [tex]\( x \)[/tex]-component of the force on the chair.
[tex]\[
F_x = F_{1x} + F_{2x}
\][/tex]
4. Numerical Result:
- From the calculations, the [tex]\( x \)[/tex]-components are approximately:
- [tex]\( F_{1x} \approx 88.35 \, \text{N} \)[/tex]
- [tex]\( F_{2x} \approx 62.87 \, \text{N} \)[/tex]
- Therefore, the total [tex]\( x \)[/tex]-component of the force [tex]\( F_x \approx 151.22 \, \text{N} \)[/tex].
So, the [tex]\( x \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 151.22 \, \text{N} \)[/tex].