The figure below is a graph of the energy of a system of a planet interacting wi

Question

The figure below 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 solid curve, and plotted along the vertical axis are various values of K+Ug. Suppose that K+Ug of the system is A. Find all of the true statements below. Please explain!

Problem 10. The figure below 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 solid curve, and plotted along the vertical axis are various values of K+Ug. Suppose that K+Ug of the system is A. Find all of the true statements below i 2r, from star to planet 1. The kinetic energy of the system increases as the planet moves from r, to r 2. The kinetic energy of the system decreases as the planet moves from r, to r2 3. When the separation between the two bodies is r2, the kinetic energy of the system is A-B. 4. The system is a bound system; the planet can never escape 5. The path traced by this orbiting system is a circle. A) 1,4, 5 B) 2,3, 5 C) 1,3, 4 D) 2,3, 4 E) 1, 3,5

Explanation / Answer

Okay, As the total energy is given as

K + Ug = A

It means K = A - Ug. ...... At r1 , U(r1) = C

Therefore, K = A - C

For U(r2) , K = A - B , ,

Kinetic energy of system is GREATER when distance between star and planet is r1 and LESSER when distance is r2. Therefore, in going from r1 to r2 , the kinetic energy decreases.

As total energy A is negative, The system is a bound system , planet can never excape.

When separation between two bodies is r2 , Kinetic energy = A - B.

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