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Types of Collisions

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Types of Collisions. Perfectly Elastic Collisions. KE workelastic potential energyworkKE.

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perfectly elastic collisions
Perfectly Elastic Collisions

KEworkelastic potential energyworkKE

Work is accomplished on each by ball from the other. The work converts the kinetic energy into elastic potential energy which is stored in the deformations of the objects. The objects then do work on each other converting the stored elastic potential energy back into kinetic energy.

  • Conditions for a perfectly elastic collision:
  • The conversion from kinetic energy to elastic potential energy back to kinetic is complete without any energy losses of any form.
  • Separation of the objects after the collision.
  • The objects return to their initial shapes.
  • Practically, perfectly elastic collisions do not exist.
elastic collisions
Elastic Collisions

Sound and Heat Energy

Sound and Heat Energy

  • Conditions for an elastic collision:
  • The conversion from kinetic energy to elastic potential energy back to kinetic is incomplete due to energy losses of some type.
  • Separation of the objects after the collision.
  • The objects return to their initial shapes.
  • Example: Collisions between billiard balls.
inelastic collisions
Inelastic Collisions

Sound and Heat Energy

Sound and Heat Energy

  • Conditions for an inelastic collision:
  • The conversion from kinetic to elastic potential back to kinetic is incomplete due to energy losses of some type.
  • Separation of the objects after the collision.
  • One or both objects remain deformed after the collision.
  • Example: A crash between vehicles that dent and separate after the collision.
perfectly inelastic collisions
Perfectly Inelastic Collisions

Sound and Heat Energy

Sound and Heat Energy

  • Conditions for a perfectly inelastic collision:
  • The conversion from kinetic to elastic potential energy back to kinetic energy is incomplete due to energy losses of some type.
  • The objects remain conjoined after the collision.
  • One or both objects remain deformed after the collision.
  • Examples: Coupling of trains cars, a bullet striking and becoming embedded in an object, catching a ball.
kinetic energy in inelastic perfectly inelastic collisions
Kinetic Energy in Inelastic/Perfectly Inelastic Collisions

The final kinetic energy of the system after the collision is less than the initial kinetic energy of the system before the collision.

KEf= final kinetic energy KEi = initial kinetic energy

KEf= KEA’+KEB’ KEi=KEA+KEB

ΔKE=KEf-KEi

KEf

ΔKE is negative for inelastic and perfectly inelastic collisions.

ΔKE=0 for elastic/perfectly elastic collisions.

(Again treat elastic as perfectly elastic collisions for problem-solving.)

kinetic energy and momentum in elastic and perfectly elastic collisions
Kinetic Energy and Momentum in Elastic and Perfectly Elastic Collisions

KEA+KEB=KEA’+KEB’

½ mAvA2+ ½ mBvB2= ½ mA(vA’)2+ ½ mB(vB’)2

1:

mAvA+mBvB=mAvA’+mBvB’

2:

Plugging equation 2 into 1 yields the following equations:

velocities in collisions
Velocities in Collisions

The following equations are used to obtain velocities for

elastic and perfectly elastic collisions:

  • If the collision is inelastic or perfectly inelastic then conservation of momentum must be used to obtain velocity.
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