4.3 Conservation of Linear Momentum

• The formula for linear momentum is p = mv.


  True
• The Law of Conservation of Linear Momentum states that in a closed system, the total linear momentum remains constant.
• What is the Law of Conservation of Linear Momentum in a closed system?

  Total momentum remains constant
• What is linear momentum defined as?

  Product of mass and velocity
• Newton's Third Law states that for every action, there is an equal and opposite reaction


  True
• The mathematical formula for conservation of momentum in one-dimensional collisions is m_{1}v_{1} + m_{2}v_{2} = m_{1}v'_{1} + m_{2}v'_{2}
• How does the Law of Conservation of Linear Momentum apply to two-dimensional collisions?

  Considers momentum in x and y
• What do $p_{y1}$ and $p_{y2}$ represent in two-dimensional collisions?


  Initial y-momenta
• In a two-dimensional collision, the total momentum in the x-direction before the collision equals the total momentum in the x-direction after the collision

  True
• Vector addition is used to analyze momentum in two-dimensional collisions

  True
• The final velocity of the 3 kg object in the example is approximately 2.8 m/s at an angle of 116.6° from the positive x-axis.


  True
• In the conservation of momentum equations, $p_{x1}$ represents the initial x-momentum of the first object.
• The final velocity of the 3 kg object in the example is approximately 2.8 m/s at 116.6° from the positive x-axis.


  True
• Kinetic energy is not conserved in inelastic collisions.


  True
• In the worked example, the conservation of linear momentum results in the equation -2 = $2v'_{1} +$$3v'_{2}$.
• In the inelastic collision example, the final velocity of the joined carts is approximately 2.86 m/s.
• In elastic collisions, both linear momentum and kinetic energy are conserved.
• The equation for kinetic energy conservation in elastic collisions involves squares of velocities.
• A 2 kg skateboard moving at 5 m/s collides with a stationary 3 kg backpack. If the skateboard slows to 2 m/s, what is the backpack's final velocity?

  2 m/s
• Newton's Third Law states that for every action force, there is an equal and opposite reaction force.
• Newton's Third Law states that for every action force, there is an equal and opposite reaction force.
• The Law of Conservation of Linear Momentum states that in a closed system, the total linear momentum remains constant.
• Two identical carts, each with a mass of 3 kg, collide and stick together. If one cart is moving at 2 m/s and the other is stationary, what is their combined velocity after the collision?

  1 m/s
• A 2 kg skateboard moving at 5 m/s collides with a stationary 3 kg backpack. If the skateboard slows to 2 m/s after the collision, what is the backpack's final velocity?

  2 m/s
• In a two-dimensional collision, if object A moves at a 45° angle after the collision, its x and y components of velocity are equal if their magnitudes are the same.


  True
• What is the Law of Conservation of Linear Momentum applied to two-dimensional collisions?

  Conserves momentum in x and y directions
• In an elastic collision, kinetic energy is conserved
• What happens to the objects during an elastic collision?

  No deformation occurs
• What is conserved along with linear momentum in elastic collisions?

  Kinetic energy
• Match the collision type with its characteristic:

  Elastic Collision ↔️ Kinetic energy conserved

  Inelastic Collision ↔️ Kinetic energy not conserved
• The equation for linear momentum conservation is m_{1}v_{1} + m_{2}v_{2} = m_{1}v'_{1} + m_{2}v'_{2}</latex>

  True
• In inelastic collisions, the equation for kinetic energy conservation can be used.

  False
• The conservation of momentum equation is m_{1}v_{1} + m_{2}v_{2} = m_{1}v'_{1} + m_{2}v'_{2}
• What is the final velocity of the 3 kg object in the practice example?

  2 m/s
• What is the formula for the conservation of linear momentum in one dimension?

  $m_{1}v_{1} +$$m_{2}v_{2} =$$m_{1}v'_{1} +$$m_{2}v'_{2}$
• The Law of Conservation of Linear Momentum applies to both one-dimensional and two-dimensional collisions.
• In a two-dimensional collision, we must consider the momentum in both the x and y directions.
• In a two-dimensional collision, the Law of Conservation of Linear Momentum applies to both the x and y components of momentum.
• The total momentum before a collision is equal to the total momentum after the collision in a closed system.

  True
• What is the mass of object 1 in Practice Example 2?

  2 kg