4.3 Elastic and Inelastic Collisions

• An elastic collision is one in which both momentum and kinetic energy are conserved
• Two carts on a frictionless track colliding elastically is an example of an elastic collision.
• What is the formula for conservation of momentum in collisions?

  $m_{1}v_{1i} +$$m_{2}v_{2i} =$$m_{1}v_{1f} +$$m_{2}v_{2f}$
• The formula for conservation of kinetic energy in elastic collisions involves the term \frac{1}{2}
• Solving the system of equations in the example yields final velocities of approximately 1 m/s and 2 m/s.
• In an elastic collision, both momentum and kinetic energy remain unchanged.
• What are the approximate final velocities of the two carts in the example after the elastic collision?

  1 m/s and 2 m/s
• In an elastic collision, the total kinetic energy before the collision equals the total kinetic energy after the collision
• Match the collision type with its properties:

  Elastic ↔️ Momentum and KE conserved

  Inelastic ↔️ Momentum conserved, KE lost
• What type of track are the two carts colliding on in the example provided?

  Frictionless track
• An elastic collision conserves both momentum and kinetic
• Which type of collision does not conserve kinetic energy?

  Inelastic
• The formula for conservation of momentum in a collision is $m_{1}v_{1i} +$$m_{2}v_{2i} =$$m_{1}v_{1f} +$$m_{2}v_{2f}$.
• Is momentum conserved in an inelastic collision?

  Yes
• In an elastic collision, the total momentum before the collision equals the total momentum after the collision.
• Match the collision type with its properties:

  Elastic ↔️ Momentum and kinetic energy conserved

  Inelastic ↔️ Momentum conserved, kinetic energy not
• What is the mass of Cart 1 in the example given?

  2 kg
• In the example, the initial velocity of Cart2 is -2
• What is the final velocity of Cart 1 if it collides elastically with Cart 2 on a frictionless track?

  Approximately 1 m/s
• Arrange the steps to solve for the final velocities in an elastic collision using conservation laws.

  1️⃣ Apply conservation of momentum

  2️⃣ Apply conservation of kinetic energy

  3️⃣ Solve the system of equations
• Which type of collision has the property that both momentum and kinetic energy are conserved?

  Elastic
• In an inelastic collision, the total kinetic energy after the collision is less than the total kinetic energy before the collision.
• In the example, the total kinetic energy before the collision is 11
• What is the final kinetic energy of the system after the elastic collision in the example?

  11 Joules
• Match the variable with its description in the context of conservation laws:

  v_{1i} ↔️ Initial velocity of Cart 1

  m_2 ↔️ Mass of Cart 2

  v_{1f} ↔️ Final velocity of Cart 1
• An elastic collision is one in which both momentum and kinetic energy are conserved.
• In an elastic collision, both momentum and kinetic energy are conserved.
• Using conservation of kinetic energy, we can write the equation 11 = v_{1f}^2 + \frac{1}{2}v_{2f}^2</latex>.
• What is conserved in an elastic collision?

  Momentum and kinetic energy
• In an elastic collision, kinetic energy is conserved.
• An inelastic collision is one where momentum is conserved but kinetic energy is not.
• What happens to the lost kinetic energy in an inelastic collision?

  Transformed into heat or sound
• In an inelastic collision, kinetic energy is conserved.

  False
• What equation represents the conservation of momentum in a collision?

  $m_{1}v_{1i} +$$m_{2}v_{2i} =$$m_{1}v_{1f} +$$m_{2}v_{2f}$
• Momentum is conserved in both elastic and inelastic collisions.
• Match the collision type with its properties:

  Elastic collision ↔️ Momentum and kinetic energy conserved

  Inelastic collision ↔️ Momentum conserved, kinetic energy lost
• An elastic collision conserves both momentum and kinetic energy.
• What is conserved in elastic collisions?

  Kinetic energy
• Kinetic energy is conserved in inelastic collisions.

  False
• An elastic collision is one where both momentum and kinetic energy are conserved