Question
A box sits on a table. A short arrow labeled F subscript N = 100 N points up. A short arrow labeled F subscript g = 100 N points down. A long arrow labeled F subscript P = 75 N points right. A short arrow labeled F subscript f = 10 N points left.
What is the net force acting on the box?
285 N
185 N
85 N
65 N
Answers
GPT-4o mini
To determine the net force acting on the box, we can analyze the forces acting in the vertical (up and down) and horizontal (left and right) directions separately.
**Vertical Forces:**
- \( F_N = 100 \, \text{N} \) (upward)
- \( F_g = 100 \, \text{N} \) (downward)
The net vertical force (\( F_{net, vertical} \)) is:
\[
F_{net, vertical} = F_N - F_g = 100 \, \text{N} - 100 \, \text{N} = 0 \, \text{N}
\]
**Horizontal Forces:**
- \( F_P = 75 \, \text{N} \) (right)
- \( F_f = 10 \, \text{N} \) (left)
The net horizontal force (\( F_{net, horizontal} \)) is:
\[
F_{net, horizontal} = F_P - F_f = 75 \, \text{N} - 10 \, \text{N} = 65 \, \text{N}
\]
**Total Net Force:**
Since there is no net vertical force:
- The net force acting on the box is entirely in the horizontal direction.
Thus, the net force is:
\[
F_{net} = 65 \, \text{N} \, \text{(to the right)}
\]
The correct answer is **65 N**.
**Vertical Forces:**
- \( F_N = 100 \, \text{N} \) (upward)
- \( F_g = 100 \, \text{N} \) (downward)
The net vertical force (\( F_{net, vertical} \)) is:
\[
F_{net, vertical} = F_N - F_g = 100 \, \text{N} - 100 \, \text{N} = 0 \, \text{N}
\]
**Horizontal Forces:**
- \( F_P = 75 \, \text{N} \) (right)
- \( F_f = 10 \, \text{N} \) (left)
The net horizontal force (\( F_{net, horizontal} \)) is:
\[
F_{net, horizontal} = F_P - F_f = 75 \, \text{N} - 10 \, \text{N} = 65 \, \text{N}
\]
**Total Net Force:**
Since there is no net vertical force:
- The net force acting on the box is entirely in the horizontal direction.
Thus, the net force is:
\[
F_{net} = 65 \, \text{N} \, \text{(to the right)}
\]
The correct answer is **65 N**.