9762

Motion of Exploding Projectile

This Demonstration maps the motion of an object with a mass of 10 kg that splits into two pieces at the peak of its flight. The first piece is stopped in midair by a specially contrived explosion in such a way that its subsequent trajectory is straight down to the ground. You can change the mass of the second piece to see how its path and velocity are affected. Note the motion of the center of mass (, the black dot) and how it relates to the two fragments.

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In this specially contrived explosion, one of the pieces (A) becomes momentarily motionless. Having been stopped in midair, this piece falls to the ground in a straight downward path. The other piece (B) continues forward, following a different trajectory than the original projectile. The center of mass of the system (denoted "CM") still follows the original parabolic path after the explosion because no external force has been exerted on the system during its flight (the model ignores air resistance and the variation of gravity over the region of motion). By conservation of linear momentum, the velocities before and after the explosion are related by . Since , piece B travels farther horizontally than it would have in the time that both pieces take to fall to the ground. The two pieces reach the ground at the same time because they start from the same height with zero vertical velocity. The explosion could have been caused by detonation of a small charge or by a spring allowed to suddenly expand between the two fragments.
References
[1] P. A. Tipler, Physics for Scientists and Engineers, New York: W.H. Freeman/Worth, 1999.
[2] J. Walker, D. Halliday, and R. Resnick, Fundamentals of Physics, Hoboken, NJ: Wiley, 2008.
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