We appreciate your visit to A chair is pulled by two horizontal forces The first force is 122 N at an angle of tex 43 6 circ tex and the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve this problem, we need to find the [tex]\( y \)[/tex]-components of the two forces acting on the chair and sum them to get the total [tex]\( y \)[/tex]-component of the force.
Let's go step-by-step:
1. Identify the Given Forces and Angles
- Force 1 ([tex]\(F_1\)[/tex]): 122 N at an angle of [tex]\(43.6^\circ\)[/tex]
- Force 2 ([tex]\(F_2\)[/tex]): 97.6 N at an angle of [tex]\(49.9^\circ\)[/tex]
2. Convert Angles from Degrees to Radians
Angles need to be in radians for trigonometric calculations. The conversion formula from degrees to radians is:
[tex]\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\][/tex]
- For the first angle ([tex]\(43.6^\circ\)[/tex]):
[tex]\[
43.6 \times \frac{\pi}{180} \approx 0.7618 \, \text{radians}
\][/tex]
- For the second angle ([tex]\(49.9^\circ\)[/tex]):
[tex]\[
49.9 \times \frac{\pi}{180} \approx 0.8704 \, \text{radians}
\][/tex]
3. Calculate the [tex]\( y \)[/tex]-component of Each Force
The [tex]\( y \)[/tex]-component of a force can be calculated using the sine function:
[tex]\[
F_{y} = F \times \sin(\theta)
\][/tex]
- For Force 1:
[tex]\[
F_{1y} = 122 \times \sin(0.7618) \approx 84.13 \, \text{N}
\][/tex]
- For Force 2:
[tex]\[
F_{2y} = 97.6 \times \sin(0.8704) \approx 74.66 \, \text{N}
\][/tex]
4. Calculate the Total [tex]\( y \)[/tex]-Component of the Force
The total [tex]\( y \)[/tex]-component is simply the sum of the [tex]\( y \)[/tex]-components of the individual forces:
[tex]\[
\overrightarrow{F_y} = F_{1y} + F_{2y}
\][/tex]
[tex]\[
\overrightarrow{F_y} = 84.13 + 74.66 \approx 158.79 \, \text{N}
\][/tex]
So, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 158.79 \, \text{N} \)[/tex].
Let's go step-by-step:
1. Identify the Given Forces and Angles
- Force 1 ([tex]\(F_1\)[/tex]): 122 N at an angle of [tex]\(43.6^\circ\)[/tex]
- Force 2 ([tex]\(F_2\)[/tex]): 97.6 N at an angle of [tex]\(49.9^\circ\)[/tex]
2. Convert Angles from Degrees to Radians
Angles need to be in radians for trigonometric calculations. The conversion formula from degrees to radians is:
[tex]\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\][/tex]
- For the first angle ([tex]\(43.6^\circ\)[/tex]):
[tex]\[
43.6 \times \frac{\pi}{180} \approx 0.7618 \, \text{radians}
\][/tex]
- For the second angle ([tex]\(49.9^\circ\)[/tex]):
[tex]\[
49.9 \times \frac{\pi}{180} \approx 0.8704 \, \text{radians}
\][/tex]
3. Calculate the [tex]\( y \)[/tex]-component of Each Force
The [tex]\( y \)[/tex]-component of a force can be calculated using the sine function:
[tex]\[
F_{y} = F \times \sin(\theta)
\][/tex]
- For Force 1:
[tex]\[
F_{1y} = 122 \times \sin(0.7618) \approx 84.13 \, \text{N}
\][/tex]
- For Force 2:
[tex]\[
F_{2y} = 97.6 \times \sin(0.8704) \approx 74.66 \, \text{N}
\][/tex]
4. Calculate the Total [tex]\( y \)[/tex]-Component of the Force
The total [tex]\( y \)[/tex]-component is simply the sum of the [tex]\( y \)[/tex]-components of the individual forces:
[tex]\[
\overrightarrow{F_y} = F_{1y} + F_{2y}
\][/tex]
[tex]\[
\overrightarrow{F_y} = 84.13 + 74.66 \approx 158.79 \, \text{N}
\][/tex]
So, the [tex]\( y \)[/tex]-component of the total force acting on the chair is approximately [tex]\( 158.79 \, \text{N} \)[/tex].
Thanks for taking the time to read A chair is pulled by two horizontal forces The first force is 122 N at an angle of tex 43 6 circ tex and the. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
