Answer :
To find the [tex]\( y \)[/tex]-component of the total force acting on the chair, we need to consider the individual [tex]\( y \)[/tex]-components of the two forces applied to the chair and then add them together.
Let's break this down step by step:
1. Identify the forces and angles:
- The first force is 122 N at an angle of [tex]\( 43.6^\circ \)[/tex].
- The second force is 97.6 N at an angle of [tex]\( 49.9^\circ \)[/tex].
2. Calculate the [tex]\( y \)[/tex]-component of each force:
- For any force at an angle, the [tex]\( y \)[/tex]-component can be found using the sine of the angle.
- For the first force:
[tex]\[
F_{y1} = 122 \, \text{N} \times \sin(43.6^\circ)
\][/tex]
- The [tex]\( y \)[/tex]-component of the first force is approximately [tex]\( 84.13 \, \text{N} \)[/tex].
- For the second force:
[tex]\[
F_{y2} = 97.6 \, \text{N} \times \sin(49.9^\circ)
\][/tex]
- The [tex]\( y \)[/tex]-component of the second force is approximately [tex]\( 74.66 \, \text{N} \)[/tex].
3. Add the [tex]\( y \)[/tex]-components to find the total [tex]\( y \)[/tex]-component:
[tex]\[
F_{y\text{ total}} = F_{y1} + F_{y2} = 84.13 \, \text{N} + 74.66 \, \text{N}
\][/tex]
- The total [tex]\( y \)[/tex]-component of the force is approximately [tex]\( 158.79 \, \text{N} \)[/tex].
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is about [tex]\( 158.79 \, \text{N} \)[/tex].
Let's break this down step by step:
1. Identify the forces and angles:
- The first force is 122 N at an angle of [tex]\( 43.6^\circ \)[/tex].
- The second force is 97.6 N at an angle of [tex]\( 49.9^\circ \)[/tex].
2. Calculate the [tex]\( y \)[/tex]-component of each force:
- For any force at an angle, the [tex]\( y \)[/tex]-component can be found using the sine of the angle.
- For the first force:
[tex]\[
F_{y1} = 122 \, \text{N} \times \sin(43.6^\circ)
\][/tex]
- The [tex]\( y \)[/tex]-component of the first force is approximately [tex]\( 84.13 \, \text{N} \)[/tex].
- For the second force:
[tex]\[
F_{y2} = 97.6 \, \text{N} \times \sin(49.9^\circ)
\][/tex]
- The [tex]\( y \)[/tex]-component of the second force is approximately [tex]\( 74.66 \, \text{N} \)[/tex].
3. Add the [tex]\( y \)[/tex]-components to find the total [tex]\( y \)[/tex]-component:
[tex]\[
F_{y\text{ total}} = F_{y1} + F_{y2} = 84.13 \, \text{N} + 74.66 \, \text{N}
\][/tex]
- The total [tex]\( y \)[/tex]-component of the force is approximately [tex]\( 158.79 \, \text{N} \)[/tex].
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is about [tex]\( 158.79 \, \text{N} \)[/tex].