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Answer :
Sure, I'd be happy to explain how to find the [tex]\( y \)[/tex]-component of the total force acting on the chair step-by-step!
1. Understanding the Problem:
- We have two forces acting on the chair.
- 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].
- We need to find the total [tex]\( y \)[/tex]-component of these forces.
2. Breaking Down Each Force into its Components:
- To find the [tex]\( y \)[/tex]-component of a force, we use the formula:
[tex]\[
F_y = F \cdot \sin(\theta)
\][/tex]
where [tex]\( F \)[/tex] is the magnitude of the force, and [tex]\( \theta \)[/tex] is the angle the force makes with the horizontal axis.
3. Calculate the [tex]\( y \)[/tex]-component of the First Force:
- For the first force (122 N at [tex]\( 43.6^\circ \)[/tex]):
[tex]\[
F_{y1} = 122 \cdot \sin(43.6^\circ) \approx 84.13 \text{ N}
\][/tex]
4. Calculate the [tex]\( y \)[/tex]-component of the Second Force:
- For the second force (97.6 N at [tex]\( 49.9^\circ \)[/tex]):
[tex]\[
F_{y2} = 97.6 \cdot \sin(49.9^\circ) \approx 74.66 \text{ N}
\][/tex]
5. Finding the Total [tex]\( y \)[/tex]-component:
- Add the [tex]\( y \)[/tex]-components of the two forces to get the total [tex]\( y \)[/tex]-component of the force:
[tex]\[
F_{y\ total} = F_{y1} + F_{y2} \approx 84.13 \text{ N} + 74.66 \text{ N} \approx 158.79 \text{ N}
\][/tex]
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 158.79 \text{ N} \)[/tex].
1. Understanding the Problem:
- We have two forces acting on the chair.
- 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].
- We need to find the total [tex]\( y \)[/tex]-component of these forces.
2. Breaking Down Each Force into its Components:
- To find the [tex]\( y \)[/tex]-component of a force, we use the formula:
[tex]\[
F_y = F \cdot \sin(\theta)
\][/tex]
where [tex]\( F \)[/tex] is the magnitude of the force, and [tex]\( \theta \)[/tex] is the angle the force makes with the horizontal axis.
3. Calculate the [tex]\( y \)[/tex]-component of the First Force:
- For the first force (122 N at [tex]\( 43.6^\circ \)[/tex]):
[tex]\[
F_{y1} = 122 \cdot \sin(43.6^\circ) \approx 84.13 \text{ N}
\][/tex]
4. Calculate the [tex]\( y \)[/tex]-component of the Second Force:
- For the second force (97.6 N at [tex]\( 49.9^\circ \)[/tex]):
[tex]\[
F_{y2} = 97.6 \cdot \sin(49.9^\circ) \approx 74.66 \text{ N}
\][/tex]
5. Finding the Total [tex]\( y \)[/tex]-component:
- Add the [tex]\( y \)[/tex]-components of the two forces to get the total [tex]\( y \)[/tex]-component of the force:
[tex]\[
F_{y\ total} = F_{y1} + F_{y2} \approx 84.13 \text{ N} + 74.66 \text{ N} \approx 158.79 \text{ N}
\][/tex]
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 158.79 \text{ N} \)[/tex].
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