f the force in the figure below is the net force on the particle, find the change in the particle's kinetic energy as it moves as follows. Fx (N) 12.0 X (m) 3.0 6.0 9.0 12.0 -12.0 (a) From x, = 0 to x,= 6.0 m 24 Your response differs from the correct answer by more than 10%. Double check your calculations. J (b) From x; = 6.0 to xf = 12.0 m -48 Your response differs from the correct answer by more than 10%. Double check your calculations. J (c) From x; = 0 to xf = 12.0 m -24 Your response differs from the correct answer by more than 10%. Double check your calculations. J

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### Net Force Analysis on a Particle

The problem involves finding the change in a particle's kinetic energy as it moves, given the net force acting on it. The force, \( F_x \), is plotted against the position, \( x \).

#### Graph Explanation

- **X-axis (Position, x):** Measures the particle's displacement in meters (m), ranging from 0 to 12 m.
- **Y-axis (Force, \( F_x \)):** Represents the net force in newtons (N), ranging from -12 N to 12 N.

The force varies with position:
- From 0 m to 3 m, \( F_x = 12 \, \text{N} \).
- From 3 m to 9 m, \( F_x = -12 \, \text{N} \).
- From 9 m to 12 m, \( F_x = 0 \, \text{N} \).

### Calculations:

For each segment, calculate the change in kinetic energy (\( \Delta KE \)).

#### (a) From \( x_i = 0 \) to \( x_f = 6.0 \, \text{m} \)

User Response: 24 J  
Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations.

#### (b) From \( x_i = 6.0 \) to \( x_f = 12.0 \, \text{m} \)

User Response: -48 J  
Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations.

#### (c) From \( x_i = 0 \) to \( x_f = 12.0 \, \text{m} \)

User Response: -24 J  
Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations.

### Notes

Calculate the work done for each section of the graph by finding the area under the curve within the specified limits. The changes in kinetic energy can be directly related to these calculations according to the work-energy principle.
Transcribed Image Text:### Net Force Analysis on a Particle The problem involves finding the change in a particle's kinetic energy as it moves, given the net force acting on it. The force, \( F_x \), is plotted against the position, \( x \). #### Graph Explanation - **X-axis (Position, x):** Measures the particle's displacement in meters (m), ranging from 0 to 12 m. - **Y-axis (Force, \( F_x \)):** Represents the net force in newtons (N), ranging from -12 N to 12 N. The force varies with position: - From 0 m to 3 m, \( F_x = 12 \, \text{N} \). - From 3 m to 9 m, \( F_x = -12 \, \text{N} \). - From 9 m to 12 m, \( F_x = 0 \, \text{N} \). ### Calculations: For each segment, calculate the change in kinetic energy (\( \Delta KE \)). #### (a) From \( x_i = 0 \) to \( x_f = 6.0 \, \text{m} \) User Response: 24 J Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations. #### (b) From \( x_i = 6.0 \) to \( x_f = 12.0 \, \text{m} \) User Response: -48 J Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations. #### (c) From \( x_i = 0 \) to \( x_f = 12.0 \, \text{m} \) User Response: -24 J Feedback: Your response differs from the correct answer by more than 10%. Double check your calculations. ### Notes Calculate the work done for each section of the graph by finding the area under the curve within the specified limits. The changes in kinetic energy can be directly related to these calculations according to the work-energy principle.
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