Question
Two workers are pushing on the same large crate. One worker pushes east with a force of 875 N, while the other worker pushes north with a force of 960 N. Friction between the crate and the floor is directed west with a force of 80 N and south with a force of 105 N. Assuming drag due to air resistance is negligible, what are the total north-south net forces and the total east-west net forces acting on the crate, causing it to accelerate across the floor?(1 point)
Responses
795 N to the south and 855 N to the west
795 N to the south and 855 N to the west
795 N to the north and 855 N to the east
795 N to the north and 855 N to the east
855 N to the south and 759 N to the west
855 N to the south and 759 N to the west
855 N to the north and 795 N to the east
Responses
795 N to the south and 855 N to the west
795 N to the south and 855 N to the west
795 N to the north and 855 N to the east
795 N to the north and 855 N to the east
855 N to the south and 759 N to the west
855 N to the south and 759 N to the west
855 N to the north and 795 N to the east
Answers
GPT-4o mini
To find the net forces acting on the crate, we need to separately calculate the net forces in the north-south direction and the east-west direction.
### North-South Forces:
1. **Force to the north**: 960 N (pushing force by the second worker)
2. **Force to the south**: 105 N (friction force)
Net North-South Force:
\[
\text{Net Force}_{NS} = \text{Force}_{\text{north}} - \text{Force}_{\text{south}}
\]
\[
\text{Net Force}_{NS} = 960\, \text{N} - 105\, \text{N} = 855\, \text{N} \text{ to the north}
\]
### East-West Forces:
1. **Force to the east**: 875 N (pushing force by the first worker)
2. **Force to the west**: 80 N (friction force)
Net East-West Force:
\[
\text{Net Force}_{EW} = \text{Force}_{\text{east}} - \text{Force}_{\text{west}}
\]
\[
\text{Net Force}_{EW} = 875\, \text{N} - 80\, \text{N} = 795\, \text{N} \text{ to the east}
\]
### Summary of Net Forces:
- North-South Net Force: 855 N to the north
- East-West Net Force: 795 N to the east
Thus, based on the calculations, there seems to have been an error in interpreting the direction of forces initially provided. The correct net forces are:
- **Net North-South force**: 855 N to the north
- **Net East-West force**: 795 N to the east
However, aligning with the responses provided:
- The correct choice based on the calculated net forces is **855 N to the north and 795 N to the east**.
None of the provided answers match this conclusion perfectly, so you might need to confirm the available responses, but this is how you would calculate the forces accurately.
### North-South Forces:
1. **Force to the north**: 960 N (pushing force by the second worker)
2. **Force to the south**: 105 N (friction force)
Net North-South Force:
\[
\text{Net Force}_{NS} = \text{Force}_{\text{north}} - \text{Force}_{\text{south}}
\]
\[
\text{Net Force}_{NS} = 960\, \text{N} - 105\, \text{N} = 855\, \text{N} \text{ to the north}
\]
### East-West Forces:
1. **Force to the east**: 875 N (pushing force by the first worker)
2. **Force to the west**: 80 N (friction force)
Net East-West Force:
\[
\text{Net Force}_{EW} = \text{Force}_{\text{east}} - \text{Force}_{\text{west}}
\]
\[
\text{Net Force}_{EW} = 875\, \text{N} - 80\, \text{N} = 795\, \text{N} \text{ to the east}
\]
### Summary of Net Forces:
- North-South Net Force: 855 N to the north
- East-West Net Force: 795 N to the east
Thus, based on the calculations, there seems to have been an error in interpreting the direction of forces initially provided. The correct net forces are:
- **Net North-South force**: 855 N to the north
- **Net East-West force**: 795 N to the east
However, aligning with the responses provided:
- The correct choice based on the calculated net forces is **855 N to the north and 795 N to the east**.
None of the provided answers match this conclusion perfectly, so you might need to confirm the available responses, but this is how you would calculate the forces accurately.