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.
To determine which statements are true, we need to consider the principles of conservation of momentum and the motion of the center of mass.
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.
This statement is false. The explosion will alter the trajectory of the fragments, and the center of mass will not necessarily continue on the initial parabolic trajectory. Therefore, A is not true.
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 force of the explosion is an internal force within the system of fragments, and according to the law of conservation of momentum, the total momentum of an isolated system remains constant. Since the explosion is an internal force, it does not affect the total momentum of the system. Therefore, B is true.
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.
This statement is false. As mentioned in statement B, the force of the explosion is an internal force, and internal forces do not alter the total momentum of the system. Therefore, C is not true.
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 false. Similar to statement A, the explosion will alter the trajectory of the fragments, and the center of mass will not necessarily continue on the initial parabolic trajectory. Therefore, D is not true.
E) The center of mass of the system of fragments will have a trajectory that depends on the number of fragments and their velocities right after the explosion.
This statement is true. The motion of the center of mass is determined by the combined effects of the masses and velocities of the fragments. If the explosion creates fragments with different masses and velocities, the center of mass will follow a trajectory that reflects those factors. Therefore, E is true.
F) None of the above.
This statement is false because multiple statements above were found to be true (B and E). Therefore, F is not true.
To summarize, the true statements are B) The force of the explosion is an internal force and thus cannot alter the total momentum of the system and E) The center of mass of the system of fragments will have a trajectory that depends on the number of fragments and their velocities right after the explosion.