4.3 Elastic and Inelastic Collisions

• In inelastic collisions, kinetic energy is not conserved but converted into other forms such as heat or deformation
• In an elastic collision, kinetic energy is conserved.


  True
• Inelastic collisions can result in permanent deformation
• The law of conservation of momentum applies only in closed systems.


  True
• What happens to momentum in a collision according to the law of conservation of momentum?

  It is redistributed
• The law of conservation of momentum is expressed mathematically as p_before = p_after.
• What does the law of conservation of momentum state in a closed system?

  Total momentum is constant
• The formula for conservation of momentum is m_A v_A + m_B v_B = m_A v_A' + m_B v_B'</latex>


  True
• The formula $m_{1} v_{1i} +$$m_{2} v_{2i} =$$m_{1} v_{1f} +$$m_{2} v_{2f}$ describes the conservation of momentum
• Inelastic collisions conserve kinetic energy

  False
• The equation \frac{1}{2} m_{1} v_{1i}^{2} + \frac{1}{2} m_{2} v_{2i}^{2} = \frac{1}{2} m_{1} v_{1f}^{2} + \frac{1}{2} m_{2} v_{2f}^{2}</latex> describes the conservation of kinetic energy.
• What is the initial velocity of the 3 kg ball in the example problem?

  0 m/s
• In an elastic collision, objects permanently deform after impact.

  False
• What type of collisions conserve kinetic energy?

  Elastic collisions
• Summarize the differences between elastic and inelastic collisions based on their properties.

  1️⃣ Kinetic energy is conserved in elastic collisions but not in inelastic collisions

  2️⃣ Momentum is conserved in both elastic and inelastic collisions

  3️⃣ Elastic collisions have no permanent deformation, while inelastic collisions do

  4️⃣ Examples of elastic collisions include billiard ball collisions, while inelastic collisions include explosions
• What is an example of a perfectly elastic collision?

  Perfectly elastic bouncing
• What does the law of conservation of momentum state?

  Total momentum is constant
• In an example of momentum conservation, if Ball A stops after colliding with Ball B, Ball B's velocity is approximately 3.33 m/s.
• Match the type of collision with its property:

  Elastic Collision ↔️ Kinetic energy is conserved

  Inelastic Collision ↔️ Kinetic energy is not conserved

  Perfectly Elastic Collision ↔️ Perfectly elastic bouncing

  Perfectly Inelastic Collision ↔️ Objects stick together
• What does the law of conservation of momentum imply about the total momentum of a system?

  It remains constant
• The law of conservation of momentum states that momentum is neither gained nor lost
• What happens to momentum in a collision if one object stops completely?

  Redistributed to other objects
• In which type of collision is kinetic energy conserved?

  Elastic collision
• What two quantities are conserved in an elastic collision?

  Momentum and kinetic energy
• In an elastic collision, if one object comes to rest after the collision, what is the final velocity of the other object?

  4 m/s
• In an elastic collision, both momentum and kinetic energy are conserved.
• What happens to the kinetic energy in an inelastic collision?

  Decreases
• Momentum can be gained or lost in a closed system during a collision.

  False
• Steps to solve an elastic collision problem using conservation laws

  1️⃣ Apply momentum conservation

  2️⃣ Apply kinetic energy conservation

  3️⃣ Solve the equations simultaneously

  4️⃣ Find the final velocities
• What is the final velocity of the 3 kg ball if the 2 kg ball stops after the collision?

  3.33 m/s
• In an elastic collision, the total kinetic energy before and after the collision remains the same.

  True
• What happens to momentum in a closed system during a collision?

  Redistributed
• The formula for momentum conservation is m_{1} v_{1i} + m_{2} v_{2i} = m_{1} v_{1f} + m_{2} v_{2f}</latex>


  True
• What happens to kinetic energy in an inelastic collision?

  It is not conserved
• In an elastic collision, both momentum and kinetic energy remain constant.

  True
• In an elastic collision, the total kinetic energy before equals the total kinetic energy after
• What is the final velocity of the 2 kg ball in the example problem after colliding elastically with the 3 kg ball?

  -1 m/s
• In an elastic collision, both momentum and kinetic energy are conserved
• The equation for momentum conservation in an inelastic collision is the same as in an elastic collision.


  True
• Since the ball starts at rest, $v_{2f} =$$0 m / s$ is chosen.


  False