n the table below, the directions of the constant force F and the displacement Δr are shown. Write in the sign of the work done by the force (positive "+" or negative "-") or "0" if the work done by the force is zero. Write a brief explanation of why each is correct.

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In the table below, the directions of the constant force F and the displacement Δr are shown. Write in the sign of the work done by the force (positive "+" or negative "-") or "0" if the work done by the force is zero. Write a brief explanation of why each is correct.

The image presents a table with three columns labeled \( \mathbf{F} \), \( \Delta \mathbf{r} \), and "Sign." The table shows five rows labeled from (a) to (e). Here is the detailed content of the table:

- Row (a): 
  - \( \mathbf{F} \): An arrow pointing left.
  - \( \Delta \mathbf{r} \): An arrow pointing left.
  - Sign: No entry.

- Row (b): 
  - \( \mathbf{F} \): An arrow pointing diagonally left and upwards.
  - \( \Delta \mathbf{r} \): An arrow pointing up.
  - Sign: No entry.

- Row (c): 
  - \( \mathbf{F} \): An arrow pointing up.
  - \( \Delta \mathbf{r} \): An arrow pointing right.
  - Sign: No entry.

- Row (d): 
  - \( \mathbf{F} \): An arrow pointing diagonally right and upwards.
  - \( \Delta \mathbf{r} \): An arrow pointing down.
  - Sign: No entry.

- Row (e): 
  - \( \mathbf{F} \): An arrow pointing right.
  - \( \Delta \mathbf{r} \): An arrow pointing diagonally right and downwards.
  - Sign: No entry.

This table can be used to analyze the relationship between force (\( \mathbf{F} \)) and displacement (\( \Delta \mathbf{r} \)), potentially in the context of determining the sign (positive, negative, or neutral) of the work done in various scenarios.
Transcribed Image Text:The image presents a table with three columns labeled \( \mathbf{F} \), \( \Delta \mathbf{r} \), and "Sign." The table shows five rows labeled from (a) to (e). Here is the detailed content of the table: - Row (a): - \( \mathbf{F} \): An arrow pointing left. - \( \Delta \mathbf{r} \): An arrow pointing left. - Sign: No entry. - Row (b): - \( \mathbf{F} \): An arrow pointing diagonally left and upwards. - \( \Delta \mathbf{r} \): An arrow pointing up. - Sign: No entry. - Row (c): - \( \mathbf{F} \): An arrow pointing up. - \( \Delta \mathbf{r} \): An arrow pointing right. - Sign: No entry. - Row (d): - \( \mathbf{F} \): An arrow pointing diagonally right and upwards. - \( \Delta \mathbf{r} \): An arrow pointing down. - Sign: No entry. - Row (e): - \( \mathbf{F} \): An arrow pointing right. - \( \Delta \mathbf{r} \): An arrow pointing diagonally right and downwards. - Sign: No entry. This table can be used to analyze the relationship between force (\( \mathbf{F} \)) and displacement (\( \Delta \mathbf{r} \)), potentially in the context of determining the sign (positive, negative, or neutral) of the work done in various scenarios.
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