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Motion of a Particle Colliding with Massive Objects

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This Demonstration shows the path that a particle would take given an initial position, velocity, and a direction of a constant gravitational field, and how the path changes when the particle collides elastically with an rigid solid with boundary defined by a Cartesian equation. When the gravitational-well model is selected, the solid object serves as the source of gravitational attraction, with a law of force.

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The motion of the particle is determined by Newton's universal law of gravitation. The particle's motion after a collision with the boundary is computed using implicit differentiation and 2D vector reflection.

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Contributed by: Itay Plavin (November 2014)
Open content licensed under CC BY-NC-SA

Snapshots

Details

Snapshot 1: the particle's path inside a parabola subject to a constant downward vector gradient

Snapshot 2: in the absence of any gravity, the particle follows the path of a photon with total internal reflection, shown here for a hyperbolic barrier; this is analogous to Thales's theorem for a circle

Snapshot 3: particle in the gravitational field of a rectangular block

Reference

[1] A. Salga, "Understanding Vector Reflection Visually." (Sep 23, 2013) asalga.wordpress.com/2012/09/23/understanding-vector-reflection-visually.

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