Answer :
To find the [tex]\( y \)[/tex]-component of the total force acting on the chair, we need to determine how each of the given forces contributes in the vertical direction. Here's how we can do it step-by-step:
1. Identify the Forces and Angles:
- The first force is 122 N, applied at an angle of [tex]\( 43.6^\circ \)[/tex] from the horizontal.
- The second force is 97.6 N, applied at an angle of [tex]\( 49.9^\circ \)[/tex] from the horizontal.
2. Calculate the [tex]\( y \)[/tex]-component of Each Force:
- To find the [tex]\( y \)[/tex]-component of a force, we use the sine function, which gives us the vertical component of a force at an angle.
- For the first force:
[tex]\[
F_{y1} = 122 \, \text{N} \times \sin(43.6^\circ) \approx 84.13 \, \text{N}
\][/tex]
- For the second force:
[tex]\[
F_{y2} = 97.6 \, \text{N} \times \sin(49.9^\circ) \approx 74.66 \, \text{N}
\][/tex]
3. Add the [tex]\( y \)[/tex]-components Together:
- The total [tex]\( y \)[/tex]-component of the force is the sum of the individual [tex]\( y \)[/tex]-components from each force.
[tex]\[
F_{y_{\text{total}}} = F_{y1} + F_{y2} \approx 84.13 \, \text{N} + 74.66 \, \text{N} = 158.79 \, \text{N}
\][/tex]
Thus, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 158.79 \, \text{N} \)[/tex].
1. Identify the Forces and Angles:
- The first force is 122 N, applied at an angle of [tex]\( 43.6^\circ \)[/tex] from the horizontal.
- The second force is 97.6 N, applied at an angle of [tex]\( 49.9^\circ \)[/tex] from the horizontal.
2. Calculate the [tex]\( y \)[/tex]-component of Each Force:
- To find the [tex]\( y \)[/tex]-component of a force, we use the sine function, which gives us the vertical component of a force at an angle.
- For the first force:
[tex]\[
F_{y1} = 122 \, \text{N} \times \sin(43.6^\circ) \approx 84.13 \, \text{N}
\][/tex]
- For the second force:
[tex]\[
F_{y2} = 97.6 \, \text{N} \times \sin(49.9^\circ) \approx 74.66 \, \text{N}
\][/tex]
3. Add the [tex]\( y \)[/tex]-components Together:
- The total [tex]\( y \)[/tex]-component of the force is the sum of the individual [tex]\( y \)[/tex]-components from each force.
[tex]\[
F_{y_{\text{total}}} = F_{y1} + F_{y2} \approx 84.13 \, \text{N} + 74.66 \, \text{N} = 158.79 \, \text{N}
\][/tex]
Thus, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 158.79 \, \text{N} \)[/tex].