diagram below is a graph of the energy of a system of a planet interacting with
ID: 1789512 • Letter: D
Question
diagram below is a graph of the energy of a system of a planet interacting with a star. The gravitational potential energy Ug is s r1 r2 r, from star to planet Suppose that K+Ug of the system is A. Which of the following statements are true? The system is a bound system; the planet can never escape when the separation between the two bodies is r2, the kinetic energy of the system is (A-B). When the separation between the two bodies is r2, the kinetic energy of the system is (B-C) The potential energy of the system decreases as the planet moves from r to r2 The kinetic energy of the system is greater when the distance between the star and planet is r1 than when the distance -The planet will escape Suppose instead that K+Ug of the system is B. Which of the following statements are true? When the separation between the planet and star is r2, the kinetic energy of the system is zero The planet and star cannot get farther apart than r2. when the separation between the planet and star is 2, the potential energy of the system is zero. O This is not a bound system; the planet can escapeExplanation / Answer
A)
Kinetic energy of the system when the separation between star and planet is r2 is given as K = A-B. Since the total energy of the system is negative, the system is said to be in a bound state.
Since magnitude of energy A-C is greater than A-B, the kinetic energy of the system is greater when the distance between the star and planet is r1 than when the distance is r2
Potential energy of the system when the separation between star and planet is r2 which is given as, U(r2) = B
Total energy of the system is given as A
Kinetic energy of the system when the separation between star and planet is r2 is given as K = A-B
The total energy is negative as it is 4th quadrant. Thus, the system is a bound system; the planet can never escape.
B)
Potential energy of the system when the separation between star and planet is r2 which is given as,
U(r2) = B
Total energy of the system is given as B
Kinetic energy of the system when the separation between star and planet is r2 which is given as,
K = B-B = 0
As the kinetic energy of the system becomes zero, they can’t get farther apart than r2
Potential energy of the system when the separation between star and planet is r2 which is given as,
U(r2) = B
Total energy of the system is given as B
Kinetic energy of the system when the separation between star and planet is r2 which is given as,
K = B-B = 0
So, planet and star can’t get farther apart than r2
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