Use the following information for problems (1) and (2): The figure on the right is a graph of the energy of a system of a planet interacting with a star. The gravitational potential energy Ug is shown as the thick curve, and plotted along the vertical axis are various values of K + Ug 1. A B r1 r2 r, from star to planet Suppose that K+ Ug of the system is A. Which of the following statements are true? Explain your reasoning. a. The potential energy of the system decreases as the planet moves from ₁ to ₂. b. When the two bodies are separated by amount r2, the kinetic energy of the system is (A - B). c. The system is a bound system; the planet can never escape. d. The planet will escape. e. When the separation between the two bodies is r2, the kinetic energy of the system is (B-C). The kinetic energy of the system is greater when the distance between the star and planet is ₁ than when the distance between the two bodies is r2. f.
Use the following information for problems (1) and (2): The figure on the right is a graph of the energy of a system of a planet interacting with a star. The gravitational potential energy Ug is shown as the thick curve, and plotted along the vertical axis are various values of K + Ug 1. A B r1 r2 r, from star to planet Suppose that K+ Ug of the system is A. Which of the following statements are true? Explain your reasoning. a. The potential energy of the system decreases as the planet moves from ₁ to ₂. b. When the two bodies are separated by amount r2, the kinetic energy of the system is (A - B). c. The system is a bound system; the planet can never escape. d. The planet will escape. e. When the separation between the two bodies is r2, the kinetic energy of the system is (B-C). The kinetic energy of the system is greater when the distance between the star and planet is ₁ than when the distance between the two bodies is r2. f.
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Transcribed Image Text:**Use the following information for problems (1) and (2):**
The figure on the right is a graph of the energy of a system of a planet interacting with a star. The gravitational potential energy \( U_g \) is shown as the thick curve, and plotted along the vertical axis are various values of \( K + U_g \).
1. Suppose that \( K + U_g \) of the system is \( A \). Which of the following statements are true? Explain your reasoning.
a. The potential energy of the system decreases as the planet moves from \( r_1 \) to \( r_2 \).
b. When the two bodies are separated by amount \( r_2 \), the kinetic energy of the system is \( (A - B) \).
c. The system is a bound system; the planet can never escape.
d. The planet will escape.
e. When the separation between the two bodies is \( r_2 \), the kinetic energy of the system is \( (B - C) \).
f. The kinetic energy of the system is greater when the distance between the star and planet is \( r_1 \) than when the distance between the two bodies is \( r_2 \).
2. Suppose that \( K + U_g \) of the system is \( B \). Which of the following statements is true? Explain your reasoning.
a. When the separation between the planet and star is \( r_2 \), the kinetic energy of the system is zero.
b. The planet and star cannot get farther apart than \( r_2 \).
c. This system is not a bound system; the planet can escape.
d. When the separation between the planet and star is \( r_2 \), the potential energy of the system is zero.
**Graph Explanation:**
The graph plots the total energy \( K + U_g \) of a system on the vertical axis with \( r \), the distance from the star to the planet, on the horizontal axis. The thick curve represents the gravitational potential energy \( U_g \). Points \( A \), \( B \), and \( C \) indicate different levels of total energy for the system, with specific separations at \( r_1 \) and \( r_2 \).
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