Question

what would the fractional change of kinetic energy of the system be if, instead of sticking to the end of the rod, the projectile continued its motion in the horizontal direction with a speed vi 2 after the collision?

Answer 1

The fractional change of kinetic energy for a projectile continuing its motion after a collision would depend on whether the final speed post-collision is the same or different from its initial speed.

Step-by-step explanation:

When considering the fractional change of kinetic energy of a system when a projectile continues its motion after a collision instead of sticking to the end of the rod, the scenario implies an elastic collision where kinetic energy is conserved. The initial kinetic energy (KEinitial) can be calculated using the formula KE = 0.5 * m * v2, where m is the mass of the projectile and v is the initial speed vi. The final kinetic energy (KEfinal) would be calculated using the mass and the final speed vi 2 post-collision.

If we assume that all other conditions remain constant, and only the speed changes after the collision, the fractional change in kinetic energy is given by the difference between KEinitial and KEfinal, divided by KEinitial. If the speed after the collision remains the same as before (vi 2 = vi), then the fractional change in kinetic energy would be zero, illustrating the principle of conservation of kinetic energy in elastic collisions. Conversely, if the speed vi 2 is different from the initial speed vi, the fractional change would need to be calculated using the final kinetic energy expression that includes the changed velocity.