4.2 Conservation of Momentum

• What is linear momentum defined as?

  Mass times velocity
• A 2 kg object moving at 5 m/s has a linear momentum of 10 kg·m/s
• The net force on an object is equal to the rate of change of its linear momentum.


  True
• The mathematical representation of linear momentum is $p =$$mv$.


  True
• How is Newton's Second Law expressed in terms of momentum?

  $F =$$\frac{dp}{dt}$
• What does the Law of Conservation of Momentum state?

  Total momentum is conserved
• In an inelastic collision, some kinetic energy is lost to other forms.


  True
• What does the principle of conservation of momentum state in a closed system?

  Total momentum remains constant
• Kinetic energy is conserved in elastic collisions.


  True
• Linear momentum is the product of an object's mass and its velocity
• How is Newton's Second Law expressed in terms of momentum?

  $F =$$\frac{dp}{dt}$
• The Law of Conservation of Momentum states that in a closed system, the total linear momentum before an interaction is equal to the total linear momentum after
• In an example of two cars colliding, the final velocity of the combined mass is calculated as 17 m/s.


  True
• In an inelastic collision, kinetic energy is always conserved.

  False
• The initial momentum in a one-dimensional collision is calculated using the equation p_{i} = m_{1}v_{1i} + m_{2}v_{2i}
• What is the equation for final momentum in a one-dimensional collision when two objects move together as a single mass?

  $p_{f} =$$(m_{1} +$$m_{2})v_{f}$
• The momentum equation in a two-dimensional collision is separated into x and y components
• Steps to solve a two-dimensional collision problem using conservation of momentum

  1️⃣ Separate the momentum equation into x and y components

  2️⃣ Resolve velocities into x and y components

  3️⃣ Apply conservation of momentum equations for each axis

  4️⃣ Solve for unknowns
• What is the x-component of a velocity of 5 m/s at an angle of 30°?

  $4.33 \text{ m / s}$
• The direction of the final velocity in a two-dimensional collision can be found using the $\arctan$ function.


  True
• In one-dimensional collisions, objects move along a single axis
• To solve one-dimensional collision problems, the equation used is p_{i} = p_{f}.
• In one-dimensional collisions, objects move along a single axis
• What happens to kinetic energy in inelastic collisions?

  It is converted to other forms
• A 2 kg object moving at 5 m/s has a momentum of 10 kg·m/s.


  True
• Match the type of collision with its characteristic:

  Elastic collision ↔️ Kinetic energy conserved

  Inelastic collision ↔️ Kinetic energy not conserved
• What is the formula for the total initial momentum in a one-dimensional collision involving two objects?

  $p_{i} =$$m_{1}v_{1i} +$$m_{2}v_{2i}$
• In an elastic collision, both momentum and kinetic energy are conserved
• What equation is used to solve problems involving the conservation of momentum in one-dimensional collisions?

  $p_{i} =$$p_{f}$
• Steps to solve a one-dimensional collision problem using conservation of momentum

  1️⃣ Calculate the initial momentum $p_{i}$

  2️⃣ Calculate the final momentum $p_{f}$

  3️⃣ Set $p_{i} =$$p_{f}$

  4️⃣ Solve for the unknown final velocity
• In a two-dimensional collision, the total linear momentum is conserved along both the x and y axes.

  True
• Match the velocity component with its corresponding trigonometric function:

  $v_{x}$ ↔️ $v \cos(\theta)$

  $v_{y}$ ↔️ $v \sin(\theta)$
• In a two-dimensional collision, if one object is initially at rest, its momentum equation along both axes simplifies.


  True
• In a two-dimensional collision, the magnitude of the final velocity is found using the Pythagorean theorem.
• A 5 kg bowling ball moving at 10 m/s strikes a 1 kg pin at rest. After the collision, the ball slows to 8 m/s. What is the final velocity of the pin?

  $10 \text{ m / s}$