Consider the path of a comet orbiting a star, the system of the comet plus the star. Which of the following statements are correct? Select all that are True. 1) As the comet slows down, the kinetic energy of the system decreases. 2) As the comet's kinetic energy increases, the gravitational potential energy of the system also increases. 3) External work must be done on the system to speed up the comet. 4) As the kinetic energy of the system increases, the gravitational potential energy of the system decreases. 5) As the comet slows down, energy is lost from the system.

True  1, 4

False 2, 3, 5

Explanation:

The system is formed by the Sun that is fixed at a point (focus of movement) and the comet that rotates around in styptic orbits. The only force involved is the force of attraction between the two bodies, if we write the energy of the system

         Em = K + U

         Em = ½ m v2 + G m Ms / r2

where m is the mass of the comet, Ms the mass of the Sun and r the distance between them.

This system is isolated so the energy is conserved throughout the movement, it only transforms from kinetic to gravitational potential.

Let's review the different claims;

1) True. The speed of the comet determines its kinetic energy, so when decreasing the speed decreases the kinetic energy, there is also a decrease due to the lost mass

2) False. The total energy is constant, so if the kinetic energy increases, the power energy must decrease

3) False. The comet's speed changes are due to changes in gravitational energy, so no external work is needed to change the speed.

4) True. Correct because the sum of the two must be constant

5) False. When the comet loses speed, the energy increases, the power would gravitate, so there is no loss of energy, we are ignoring the loss of mass of the comet.