Answer :
To find the x-component of the total force acting on the chair, follow these steps:
1. Understand the problem:
We have two forces acting on a chair, each at a specific angle. We need to determine the x-component (horizontal part) of each force and then find the total x-component by summing them up.
2. Identify the forces and angles:
- The first force is 122 N, applied at an angle of 43.6°.
- The second force is 97.6 N, applied at an angle of 49.9°.
3. Calculate the x-component of each force:
The formula for calculating the x-component of a force at an angle is:
[tex]\[
F_x = F \cdot \cos(\theta)
\][/tex]
where [tex]\( F \)[/tex] is the force, and [tex]\( \theta \)[/tex] is the angle.
- For the first force:
[tex]\[
F_{x1} = 122 \cdot \cos(43.6^\circ) \approx 88.35 \, \text{N}
\][/tex]
- For the second force:
[tex]\[
F_{x2} = 97.6 \cdot \cos(49.9^\circ) \approx 62.87 \, \text{N}
\][/tex]
4. Calculate the total x-component of the forces:
Add the x-components of the two forces to find the total x-component:
[tex]\[
F_{x\_total} = F_{x1} + F_{x2} \approx 88.35 + 62.87 = 151.22 \, \text{N}
\][/tex]
Therefore, the x-component of the total force acting on the chair is approximately [tex]\( 151.22 \, \text{N} \)[/tex].
1. Understand the problem:
We have two forces acting on a chair, each at a specific angle. We need to determine the x-component (horizontal part) of each force and then find the total x-component by summing them up.
2. Identify the forces and angles:
- The first force is 122 N, applied at an angle of 43.6°.
- The second force is 97.6 N, applied at an angle of 49.9°.
3. Calculate the x-component of each force:
The formula for calculating the x-component of a force at an angle is:
[tex]\[
F_x = F \cdot \cos(\theta)
\][/tex]
where [tex]\( F \)[/tex] is the force, and [tex]\( \theta \)[/tex] is the angle.
- For the first force:
[tex]\[
F_{x1} = 122 \cdot \cos(43.6^\circ) \approx 88.35 \, \text{N}
\][/tex]
- For the second force:
[tex]\[
F_{x2} = 97.6 \cdot \cos(49.9^\circ) \approx 62.87 \, \text{N}
\][/tex]
4. Calculate the total x-component of the forces:
Add the x-components of the two forces to find the total x-component:
[tex]\[
F_{x\_total} = F_{x1} + F_{x2} \approx 88.35 + 62.87 = 151.22 \, \text{N}
\][/tex]
Therefore, the x-component of the total force acting on the chair is approximately [tex]\( 151.22 \, \text{N} \)[/tex].