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Answer :
To find the [tex]\( y \)[/tex]-component of the total force acting on the chair, we need to calculate the contribution of each force's [tex]\( y \)[/tex]-component and then add them together. Here's how we can do it:
1. Identify the forces and their angles:
- The first force, [tex]\( F_1 \)[/tex], has a magnitude of 122 N and is applied at an angle of [tex]\( 43.6^\circ \)[/tex].
- The second force, [tex]\( F_2 \)[/tex], has a magnitude of 97.6 N and is applied at an angle of [tex]\( 49.9^\circ \)[/tex].
2. Calculate the [tex]\( y \)[/tex]-component of each force:
- To find the [tex]\( y \)[/tex]-component of a force, you use the sine of the angle because it gives the vertical (or [tex]\( y \)[/tex]-axis) component when an angle is measured from the horizontal.
- For [tex]\( F_1 \)[/tex]:
[tex]\[
\text{Fy1} = 122 \times \sin(43.6^\circ) \approx 84.13 \, \text{N}
\][/tex]
- For [tex]\( F_2 \)[/tex]:
[tex]\[
\text{Fy2} = 97.6 \times \sin(49.9^\circ) \approx 74.66 \, \text{N}
\][/tex]
3. Sum the [tex]\( y \)[/tex]-components to find the total [tex]\( y \)[/tex]-component:
[tex]\[
\text{Fy\_total} = \text{Fy1} + \text{Fy2} \approx 84.13 \, \text{N} + 74.66 \, \text{N} = 158.79 \, \text{N}
\][/tex]
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately 158.79 N.
1. Identify the forces and their angles:
- The first force, [tex]\( F_1 \)[/tex], has a magnitude of 122 N and is applied at an angle of [tex]\( 43.6^\circ \)[/tex].
- The second force, [tex]\( F_2 \)[/tex], has a magnitude of 97.6 N and is applied at an angle of [tex]\( 49.9^\circ \)[/tex].
2. Calculate the [tex]\( y \)[/tex]-component of each force:
- To find the [tex]\( y \)[/tex]-component of a force, you use the sine of the angle because it gives the vertical (or [tex]\( y \)[/tex]-axis) component when an angle is measured from the horizontal.
- For [tex]\( F_1 \)[/tex]:
[tex]\[
\text{Fy1} = 122 \times \sin(43.6^\circ) \approx 84.13 \, \text{N}
\][/tex]
- For [tex]\( F_2 \)[/tex]:
[tex]\[
\text{Fy2} = 97.6 \times \sin(49.9^\circ) \approx 74.66 \, \text{N}
\][/tex]
3. Sum the [tex]\( y \)[/tex]-components to find the total [tex]\( y \)[/tex]-component:
[tex]\[
\text{Fy\_total} = \text{Fy1} + \text{Fy2} \approx 84.13 \, \text{N} + 74.66 \, \text{N} = 158.79 \, \text{N}
\][/tex]
Therefore, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately 158.79 N.
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