Elastic Collisions. Momentum and Kinetic Energy  An object in motion has a momentum based on its mass and velocity. p = mvp = mv  The object also has.

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Presentation transcript:

Elastic Collisions

Momentum and Kinetic Energy  An object in motion has a momentum based on its mass and velocity. p = mvp = mv  The object also has kinetic energy. K = ½ mv 2 = p 2 / 2mK = ½ mv 2 = p 2 / 2m

Kinetic Energy at Collision  Energy is conserved only for conservative forces.  Internal forces may be nonconservative.  The force at the collision is not always conservative. energy lost to heat Before: m1m1 v1iv1i v2iv2i m2m2 After: v2fv2f v1fv1f

Elastic Collision  For conservative forces the energy is conserved.  After the collision of contact the potential energy is zero.  The total kinetic energy is conserved – equal before and after the collision.  This an elastic collision. Elastic

Double Conservation  Elastic collisions conserve both momentum and kinetic energy.  Two equations govern all elastic collisions. m1m1 m2m2 v1iv1i v2iv2i before m1m1 m2m2 v1fv1f v2fv2f after

Head-on Collision  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. m1m1 m2m2 v1iv1i v2iv2i m1m1 m2m2 v1iv1i v2iv2i force and velocity in a lineforce and velocity on different lines

Related Velocities m1m1 m2m2 v1iv1i v2iv2i momentum in a line kinetic energy conservation solve for velocities

Equal Masses  A 150 g ball moves at 1.4 m/s. The momentum is 0.21 kg m/sThe momentum is 0.21 kg m/s  It strikes an equal mass ball at rest. v 1i = 1.4 m/sv 1i = 1.4 m/s v 2i = 0v 2i = 0 Therefore, v 1f = 0Therefore, v 1f = 0 and v 2f = v 1iand v 2f = v 1i m1m1 m2m2 v1iv1i m1m1 m2m2 v2fv2f momentum: kinetic energy:

Striking a Heavy Mass  Let m 1 << m 2, when a golf ball bounces off the floor.  The floor is at rest. v 2i = 0v 2i = 0  The final velocity is equal and opposite the initial velocity momentum: kinetic energy: combined: m1m1 v1iv1i v1fv1f

Striking a Light Mass  Let m 1 >> m 2, when a car strikes a ball.  The ball is at rest. v 2i = 0v 2i = 0  For a very heavy m 1, the final velocity of m 2 is twice the initial velocity of m 1. momentum: kinetic energy: combined: v1iv1i v2fv2f m2m2