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.
thats crazy
To determine which of the statements are true, let's examine 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.
This statement is true. The center of mass of a system of fragments will continue to move along the same parabolic trajectory as the original shell until the last fragment touches the ground. This is because the force of gravity acting on each individual fragment will cause them to follow the same path as the original projectile.
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 because it occurs within the system of fragments. According to Newton's third law of motion, internal forces do not change the total momentum of a system. Therefore, the total momentum of the system of fragments will remain constant.
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 false. As stated in the previous explanation, the force of the explosion is an internal force and does not alter the total momentum of the system. Therefore, the momentum of the shell 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 false. The center of mass of the system of fragments will continue to move on the same parabolic trajectory as the original shell until the last fragment touches the ground, not the first fragment.
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 trajectory of the center of mass of the system of fragments will depend on the number of fragments and their velocities immediately after the explosion. The individual velocities and masses of the fragments will affect the overall motion of the center of mass.
Based on the explanations above, the true statements are A, B, and E. Therefore, the correct answer is: A, B, and E.