The figure shows the work done on an object traveling along different paths between 3 different points A, B, and C. If the force on the object is conservative, what is the work done along the path marked with a "?" ? A -30 J -10 J 30 J -20 J +20 J O -40 J

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The diagram illustrates the work done on an object traveling along different pathways between three points labeled A, B, and C. The work values on the paths are indicated in Joules (J).

- The path from A to B shows -30 J.
- The path from B to C shows -10 J.
- The path from C to A shows a question mark (?), indicating the work needs to be determined.

The text asks for the work done along the path marked with a "?" given that the force is conservative.

Options for the work done along the path marked with a "?" are:

- \(-20 \, J\)
- \(+20 \, J\)
- \(-40 \, J\)
- \(+40 \, J\)

### Explanation of Concepts

- **Conservative Force**: A force is said to be conservative if the total work done in moving an object between two points is independent of the path taken. For conservative forces, the total work done around a closed path is zero.

### Calculation

To find the work done along the path marked with a "?", apply the principle of work done by conservative forces:

1. Total work around the closed loop (A to B to C to A) must be zero.
2. \((\text{work from A to B}) + (\text{work from B to C}) + (\text{work from C to A}) = 0\)

Substitute known values:

\(-30 \, J + (-10 \, J) + \text{(work from C to A)} = 0\)

Calculate:

\(\text{work from C to A} = 40 \, J\)

### Answer

The correct answer is \(+40 \, J\).
Transcribed Image Text:The diagram illustrates the work done on an object traveling along different pathways between three points labeled A, B, and C. The work values on the paths are indicated in Joules (J). - The path from A to B shows -30 J. - The path from B to C shows -10 J. - The path from C to A shows a question mark (?), indicating the work needs to be determined. The text asks for the work done along the path marked with a "?" given that the force is conservative. Options for the work done along the path marked with a "?" are: - \(-20 \, J\) - \(+20 \, J\) - \(-40 \, J\) - \(+40 \, J\) ### Explanation of Concepts - **Conservative Force**: A force is said to be conservative if the total work done in moving an object between two points is independent of the path taken. For conservative forces, the total work done around a closed path is zero. ### Calculation To find the work done along the path marked with a "?", apply the principle of work done by conservative forces: 1. Total work around the closed loop (A to B to C to A) must be zero. 2. \((\text{work from A to B}) + (\text{work from B to C}) + (\text{work from C to A}) = 0\) Substitute known values: \(-30 \, J + (-10 \, J) + \text{(work from C to A)} = 0\) Calculate: \(\text{work from C to A} = 40 \, J\) ### Answer The correct answer is \(+40 \, J\).
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