5.7.2 Conservation of Momentum

• Momentum is a measure of an object's motion, defined as the product of its mass and velocity.
• Momentum is conserved in open systems.

  False
• Arrange the mathematical expression for conservation of momentum:

  1️⃣ Total Momentum = m₁v₁ + m₂v₂

  2️⃣ Total Momentum = m₁v₁' + m₂v₂'
• Newton's Third Law states that for every action force, there is an equal and opposite reaction force.
• In a closed system, the total momentum before and after an interaction remains the same.


  True
• What is the mass of object m₁?

  50 kg
• The total momentum before an interaction is expressed as m₁v₁ + m₂v₂.


  True
• What does Newton's Third Law state?

  Action equals reaction
• Momentum is defined as Mass × Velocity.
• Conservation of momentum states that the total momentum of a closed system remains constant unless acted upon by an external force.
• Match the variable with its meaning in the conservation of momentum equation:

  m₁ ↔️ Mass of object 1

  v₂ ↔️ Initial velocity of object 2

  v₁' ↔️ Final velocity of object 1
• The action and reaction forces in Newton's Third Law act on the same object.

  False
• Conservation of momentum states that the total momentum of a closed system remains constant unless acted upon by an external
• Match the variables with their meanings:

  m₁, m₂ ↔️ Masses

  v₁, v₂ ↔️ Initial velocities

  v₁', v₂' ↔️ Final velocities
• Action and reaction forces in Newton's Third Law have the same magnitude but opposite directions.


  True
• What is the conservation of momentum equation?

  m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1}' + m_{2}v_{2}'</latex>
• When solving momentum problems, the system must be treated as a closed system with no external forces.

  True
• What is the conservation of momentum equation in terms of masses and velocities?

  $m_{1}v_{1} +$$m_{2}v_{2} =$$m_{1}v_{1}' +$$m_{2}v_{2}'$
• What is the fourth step in solving momentum problems using conservation equations?

  Solve for the unknown
• Steps to solve momentum problems using conservation equations

  1️⃣ Define the system

  2️⃣ Write the conservation of momentum equation

  3️⃣ Organize the known and unknown values

  4️⃣ Solve for the unknown
• Steps to solve momentum problems using conservation equations

  1️⃣ Define the system as closed

  2️⃣ Write the conservation of momentum equation

  3️⃣ Organize known and unknown values

  4️⃣ Solve for the unknown velocity
• In the example collision, the red ball's final velocity is 3 m/s.
• To solve for an unknown velocity in momentum problems, plug the known values into the conservation of momentum equation.
• Organizing known and unknown values helps to clearly see the states
• The total momentum before the interaction is equal to the total momentum after
• The conservation of momentum equation holds true only for closed systems.


  True
• What do v₁ and v₂ represent in the conservation of momentum equation?

  Initial velocities
• In the example provided, what is the initial velocity of the 0.3 kg ball?

  -2 m/s
• Solving for the unknown final velocity involves plugging known values into the conservation of momentum equation.


  True
• The final velocity of the 0.3 kg ball in the example is 3 m/s
• Match the variables with their meanings in the conservation of momentum equation:

  m₁ and m₂ ↔️ Masses of objects

  v₁ and v₂ ↔️ Initial velocities

  v₁' and v₂' ↔️ Final velocities