An artillery shell is moving on a parabolic trajectory when it explodes in midair. The shell shatters into a very large number of fragments. Which of the following statements is true (select all that apply)? a) The force of the explosion will increase the momentum of the system of fragments, and so the momentum of the shell is not conserved during the explosion. b) The force of the explosion is an internal force and thus cannot alter the total momentum of the system. c) The center of mass of the system of fragments will continue to move on the initial parabolic trajectory until the last fragment touches the ground. d) The center of mass of the system of fragments will continue to move on the initial parabolic trajectory until the first fragment touches the ground. 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.

Step by step solution

01

Statement a

The force of the explosion will increase the momentum of the system of fragments, and so the momentum of the shell is not conserved during the explosion. This statement is false. The total momentum of a closed system is always conserved. The force of the explosion is an internal force, and internal forces cannot change the total momentum of the system.

02

Statement b

The force of the explosion is an internal force and thus cannot alter the total momentum of the system. This statement is true. As mentioned before, the forces involved in the explosion are internal forces. These forces can change the individual momenta of the fragments but not the total momentum of the system.

03

Statement c

The 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 true. The center of mass of a system of particles moves as if all the mass of the system were concentrated at that point. Since the total momentum of the system is conserved during the explosion, the center of mass will continue moving along the initial parabolic trajectory until the last fragment touches the ground.

04

Statement d

The center of mass of the system of fragments will continue to move on the initial parabolic trajectory until the first fragment touches the ground. This statement is false. As explained in the analysis of statement c, the center of mass will continue moving along the initial parabolic trajectory until the last fragment touches the ground, not the first.

05

Statement 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 false. The trajectory of the center of mass only depends on the initial parabolic trajectory and does not depend on the number of fragments or their individual velocities. In conclusion, the statements b and c are true.

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