An artillery shells is moving on a parabolic trayectory, when it explodes in midair. The shell chatters into a very large number of fragments. Which of the following statements is true? (Select all that apply.)
A) A center of mass of the system of fragments will contitnue to move on the initial parabolic trayectory until the last fragment touches the ground.
B) The force of the explosion is an internal force and thus cannot alter the total momentum of the system.
C)The force of the explosion will decrease the momentum of the system of fragments, and so the momentum of the shell is not conserved during explosion.
D) The center of mass of the system of fragments will continue to move on the parabolic trayectory until first fragment touches the ground.
E) The center of mass of the system of fragments will have the trayectory that depends of the number of fragments and their velocities right after the explosion.
F) None of the above.
The correct statements are:
B) The force of the explosion is an internal force and thus cannot alter the total momentum of the system.
C) The force of the explosion will decrease the momentum of the system of fragments, and so the momentum of the shell is not conserved during the explosion.
E) The center of mass of the system of fragments will have the trajectory that depends on the number of fragments and their velocities right after the explosion.
So the answer is:
B) The force of the explosion is an internal force and thus cannot alter the total momentum of the system.
C) The force of the explosion will decrease the momentum of the system of fragments, and so the momentum of the shell is not conserved during the explosion.
E) The center of mass of the system of fragments will have the trajectory that depends on the number of fragments and their velocities right after the explosion.
To determine which of the statements is true, let's analyze each option:
A) A center of mass of the system of fragments will continue to move on the initial parabolic trajectory until the last fragment touches the ground.
For this statement to be true, we need to understand that the center of mass of the system behaves as if all the fragments were concentrated at a single point. This is a result of the conservation of momentum. Since there are no external forces acting on the system of fragments, the momentum of the system remains constant. Thus, until the last fragment touches the ground, the center of mass will continue to move on the initial parabolic trajectory.
B) The force of the explosion is an internal force and thus cannot alter the total momentum of the system.
This statement is true. The explosion force acts between the fragments of the shell and is considered an internal force. According to the law of conservation of momentum, the total momentum of an isolated system remains constant when there are no external forces. Therefore, the force of the explosion does not alter the total momentum of the system.
C) The force of the explosion will decrease the momentum of the system of fragments, and so the momentum of the shell is not conserved during the explosion.
This statement is incorrect. As mentioned before, the total momentum of an isolated system remains constant when there are no external forces. Since the force of the explosion is internal, the momentum of the system of fragments is conserved during the explosion.
D) The center of mass of the system of fragments will continue to move on the parabolic trajectory until the first fragment touches the ground.
This statement is incorrect. According to the conservation of momentum, the center of mass of the system will continue to move on the initial parabolic trajectory until the last fragment touches the ground, as explained in statement A.
E) The center of mass of the system of fragments will have the trajectory that depends on the number of fragments and their velocities right after the explosion.
This statement is true. The trajectory of the center of mass of the system of fragments will depend on the individual velocities and masses of the fragments after the explosion. The center of mass represents the average position of the system, taking into account the distribution of mass and velocities of the fragments.
Based on the analysis above, the correct statements are:
A) A center of mass of the system of fragments will continue to move on the initial parabolic trajectory until the last fragment touches the ground.
B) The force of the explosion is an internal force and thus cannot alter the total momentum of the system.
E) The center of mass of the system of fragments will have the trajectory that depends on the number of fragments and their velocities right after the explosion.
Therefore, the correct answer is A, B, and E.