Explosions in one dimension: A shell explodes into two fragments, one fragment 25 times heavier than the other. If any gas from the explosion has negligible mass, then

Question

Quizplus · Accepted Answer

EC) In an explosion, the total momentum of the system (shell) must be conserved. Before the explosion, the shell's momentum is zero (assuming it's at rest), so the total momentum after the explosion must also be zero. This means the momentum gained by the lighter fragment must be equal in magnitude and opposite in direction to the momentum gained by the heavier fragment, making their momentum changes exactly the same.E) The kinetic energy change of the lighter fragment is greater than that of the heavier fragment because, for a given momentum change, lighter objects acquire a higher velocity than heavier objects. Since kinetic energy depends on the square of the velocity ($KE = \frac{1}{2}mv^2$), the lighter fragment, having a higher velocity for the same momentum change, will have a disproportionately larger increase in kinetic energy. However, the exact ratio of their kinetic energy changes depends on their velocities and cannot be determined to be exactly 25 times greater without additional information. This choice is included based on the options provided, but it's important to note the explanation for why the kinetic energy change of the lighter fragment is greater, not necessarily exactly 25 times as great.

Explosions in One Dimension: a Shell Explodes into Two Fragments