A single conservative force acts on a 5.30-kg particle within a system due to its interaction with the rest of the system. The equation Fx = 2x + 4 describes the force, where F is in newtons and x is in meters. As the particle moves along the x axis from x = 1.06 m to x = 7.35 m, calculate the following. (a) the work done by this force on the particle 80.99 J (b) the change in the potential energy of the system -80.88 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. J (c) the kinetic energy the particle has at x = 7.35 m if its speed is 3.00 m/s at x = 1.06 m 6.28 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. J

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Description:**  
A single conservative force acts on a 5.30-kg particle within a system due to its interaction with the rest of the system. The equation \( F_x = 2x + 4 \) describes the force, where \( F_x \) is in newtons and \( x \) is in meters. As the particle moves along the x-axis from \( x = 1.06 \, \text{m} \) to \( x = 7.35 \, \text{m} \), calculate the following:

**(a) The work done by this force on the particle**  
- Answer: \( 80.99 \, \text{J} \)

**(b) The change in the potential energy of the system**  
- Answer: \( -80.88 \, \text{J} \) (Incorrect)  
- Feedback: Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.

**(c) The kinetic energy the particle has at \( x = 7.35 \, \text{m} \) if its speed is \( 3.00 \, \text{m/s} \) at \( x = 1.06 \, \text{m} \)**  
- Answer: \( 6.28 \, \text{J} \) (Incorrect)  
- Feedback: Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.
Transcribed Image Text:**Problem Description:** A single conservative force acts on a 5.30-kg particle within a system due to its interaction with the rest of the system. The equation \( F_x = 2x + 4 \) describes the force, where \( F_x \) is in newtons and \( x \) is in meters. As the particle moves along the x-axis from \( x = 1.06 \, \text{m} \) to \( x = 7.35 \, \text{m} \), calculate the following: **(a) The work done by this force on the particle** - Answer: \( 80.99 \, \text{J} \) **(b) The change in the potential energy of the system** - Answer: \( -80.88 \, \text{J} \) (Incorrect) - Feedback: Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. **(c) The kinetic energy the particle has at \( x = 7.35 \, \text{m} \) if its speed is \( 3.00 \, \text{m/s} \) at \( x = 1.06 \, \text{m} \)** - Answer: \( 6.28 \, \text{J} \) (Incorrect) - Feedback: Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.
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