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Answer :
To find the [tex]\( y \)[/tex]-component of the total force acting on the chair, we need to consider the contributions from both forces, taking into account their respective angles. Here's how you can do it step-by-step:
1. Understand the Setup:
- We have two forces acting on a 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].
2. Calculate the [tex]\( y \)[/tex]-Component of Each Force:
- The [tex]\( y \)[/tex]-component of a force can be found using the formula:
[tex]\[ F_y = F \cdot \sin(\theta) \][/tex]
- For the first force:
[tex]\[ F_{y1} = 122 \cdot \sin(43.6^\circ) \][/tex]
This gives the [tex]\( y \)[/tex]-component of the first force as approximately 84.13 N.
- For the second force:
[tex]\[ F_{y2} = 97.6 \cdot \sin(49.9^\circ) \][/tex]
This gives the [tex]\( y \)[/tex]-component of the second force as approximately 74.66 N.
3. Add the [tex]\( y \)[/tex]-Components to Get the Total [tex]\( y \)[/tex]-Component:
- The total [tex]\( y \)[/tex]-component of the force is the sum of the [tex]\( y \)[/tex]-components from both forces:
[tex]\[ F_{y\_total} = F_{y1} + F_{y2} \][/tex]
- Thus, the total [tex]\( y \)[/tex]-component is approximately:
[tex]\[ F_{y\_total} = 84.13 + 74.66 = 158.79 \, \text{N} \][/tex]
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately 158.79 N.
1. Understand the Setup:
- We have two forces acting on a 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].
2. Calculate the [tex]\( y \)[/tex]-Component of Each Force:
- The [tex]\( y \)[/tex]-component of a force can be found using the formula:
[tex]\[ F_y = F \cdot \sin(\theta) \][/tex]
- For the first force:
[tex]\[ F_{y1} = 122 \cdot \sin(43.6^\circ) \][/tex]
This gives the [tex]\( y \)[/tex]-component of the first force as approximately 84.13 N.
- For the second force:
[tex]\[ F_{y2} = 97.6 \cdot \sin(49.9^\circ) \][/tex]
This gives the [tex]\( y \)[/tex]-component of the second force as approximately 74.66 N.
3. Add the [tex]\( y \)[/tex]-Components to Get the Total [tex]\( y \)[/tex]-Component:
- The total [tex]\( y \)[/tex]-component of the force is the sum of the [tex]\( y \)[/tex]-components from both forces:
[tex]\[ F_{y\_total} = F_{y1} + F_{y2} \][/tex]
- Thus, the total [tex]\( y \)[/tex]-component is approximately:
[tex]\[ F_{y\_total} = 84.13 + 74.66 = 158.79 \, \text{N} \][/tex]
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately 158.79 N.
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