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Elastic Collisions

Elastic Collisions. Conservation. Elastic collisions conserve both momentum and kinetic energy. Two equations govern all elastic collisions. m 1. v 1 i. v 1 f. m 1. m 2. v 2 i. m 2. v 2 f. before. after. An elastic head-on collision takes place in one dimension.

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Elastic Collisions

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  1. Elastic Collisions

  2. Conservation • Elastic collisions conserve both momentum and kinetic energy. • Two equations govern all elastic collisions. m1 v1i v1f m1 m2 v2i m2 v2f before after

  3. An elastic head-on collision takes place in one dimension. If the collision is not head-on, the force pair is in a different direction. Head-on Collision v1i v2i v1i v2i m1 m2 m1 m2 force and velocity in a line force and velocity on different lines

  4. Related Velocities momentum in a line solve for velocities v1i v2i kinetic energy conservation m1 m2

  5. Equal Masses • A 150 g ball moves at 1.4 m/s. • The momentum is 0.21 kg m/s • It strikes an equal mass ball at rest. • v1i = 1.4 m/s • v2i = 0 • Therefore, v1f = 0 • and v2f = v1i v1i m1 m2 v2f m1 m2 momentum: kinetic energy:

  6. Striking a Heavy Mass • Let m1 << m2, when a golf ball bounces off the floor. • The floor is at rest. • v2i = 0 • The final velocity is equal and opposite the initial velocity momentum: kinetic energy: combined: v1f m1 v1i

  7. Striking a Light Mass • Let m1 >> m2, when a golf club strikes a ball. • The ball is at rest. • v2i = 0 • For a very heavy m1 , the final velocity of m2 is twice the initial velocity of m1 . momentum: kinetic energy: combined: v2f m2 v1i

  8. Impact Parameter • When collisions are not head on, the objects can come out at an angle. • The masses come out at equal angles. • The distance of the center of the ball to the center of line between them is the impact parameter. v1f m1 m1 v1i v2i m2 m2 v2f next

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