5.7.2 Conservation of Momentum

• Momentum is a measure of the quantity of motion
• The law of conservation of momentum states that the total momentum in a closed system remains constant
• The total momentum before a collision equals the total momentum after the collision in a closed system.
• A closed system is one in which no energy or mass can enter or leave
• What is the formula for momentum?

  p = mv</latex>
• A 2 kg ball moving at 5 m/s has a momentum of 10 kg m/s.
• The law of conservation of momentum applies only to closed systems
• A closed system is one that does not exchange mass or energy with its surroundings
• The law of conservation of momentum applies even if external forces act on the system.

  False
• What happens to the total momentum of a closed system if no external forces act on it?

  Remains constant
• The law of conservation of momentum states that total momentum remains constant in the absence of external forces
• A closed system does not exchange mass or energy with its surroundings.
• The law of conservation of momentum applies only within closed systems.
• What is the mathematical expression for the conservation of momentum in a collision?

  m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}</latex>
• In the conservation of momentum formula, $m_{1}$ and $m_{2}$ represent the masses of objects 1 and 2.
• The initial velocities in the conservation of momentum formula are represented by $u_{1}$ and $u_{2}$.
• The final velocities in the conservation of momentum formula are represented by $v_{1}$ and $v_{2}$.velocities
• What is the final velocity of a 3 kg ball after being hit by a 5 kg ball moving at 2 m/s, where the 5 kg ball slows to 1 m/s?

  $\frac{5}{3} m / s$
• Match the term with its definition:

  Momentum ↔️ Measure of quantity of motion

  Mass ↔️ Amount of matter in an object

  Velocity ↔️ Speed and direction of motion
• In a closed system, total momentum remains constant if no external forces act upon it.
• A closed system is one in which no mass or energy can enter or leave.
• What is the final velocity of a 3 kg ball after being hit by a 2 kg ball moving at 3 m/s, where the 2 kg ball slows to 1 m/s?

  $\frac{4}{3} m / s$
• Order the steps to solve a conservation of momentum problem in a collision.

  1️⃣ Identify the system as closed

  2️⃣ Write the conservation of momentum formula

  3️⃣ Substitute known values

  4️⃣ Solve for the unknown variable
• A closed system does not exchange mass or energy with its surroundings.
• Give an example of a closed system in the study material.

  Insulated container with billiard balls
• A closed system does not exchange mass or energy
• In a closed system, the total mass remains constant.
• External forces can act on a closed system.

  False
• What law is understanding closed systems crucial for?

  Conservation of momentum
• An example of a closed system is a perfectly insulated container with colliding billiard balls
• In a closed system, the total energy remains constant.
• What is the mathematical expression for the law of conservation of momentum?

  $m_{1}u_{1} +$$m_{2}u_{2} =$$m_{1}v_{1} +$$m_{2}v_{2}$
• In the conservation of momentum formula, $m_{1}$ and $m_{2}$ represent the masses of the two objects
• Match the variables in the conservation of momentum formula with their meanings:

  $u_{1}$ ↔️ Initial velocity of object 1

  $v_{2}$ ↔️ Final velocity of object 2

  $m_{2}$ ↔️ Mass of object 2

  $v_{1}$ ↔️ Final velocity of object 1
• What is the final velocity of a 3 kg ball if a 5 kg ball moving at2 m/s hits it, and after the collision the 5 kg ball moves at 1 m/s?

  1.67 m/s
• In the example provided, the total momentum before the collision is greater than the total momentum after the collision.

  False
• In the conservation of momentum formula, $u_{1}$ and $u_{2}$ represent the initial velocities
• What is the numerical value of the total momentum before the collision in the example provided?

  10 kg m/s
• What is the final velocity of the 3 kg ball after the collision in the example provided?

  1.67 m/s
• The final velocity of the 3 kg ball in the collision example is greater than the initial velocity of the 5 kg ball.

  False