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is a fundamental concept in physics, describing an object's motion based on its mass and velocity. It's crucial for understanding collisions, explosions, and the effects of forces on moving objects.

differs from in its vector nature and linear relationship with velocity. The principle is key to analyzing interactions between objects, from simple collisions to complex systems like rockets and explosions.

Linear Momentum

Calculation of momentum

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  • Calculate momentum by multiplying an object's mass and velocity
    • Use the formula [p = mv](https://www.fiveableKeyTerm:p_=_mv) where pp represents momentum (), mm represents mass (kg), and vv represents velocity (m/s)
    • Momentum is a , meaning it has both magnitude and direction
      • Direction of momentum aligns with the direction of velocity
  • Express momentum in various units
    • SI units for momentum are kilogram-meter per second (kg⋅m/s)
    • English system units for momentum are slug-foot per second ()
  • Examples:
    • A 1,000 kg car traveling at 20 m/s has a momentum of 20,000 kg⋅m/s
    • A 0.145 kg baseball pitched at 40 m/s has a momentum of 5.8 kg⋅m/s

Momentum vs kinetic energy

  • Understand the differences between momentum and kinetic energy in representing motion
    • Momentum is a vector quantity (has magnitude and direction) while kinetic energy is a scalar quantity (has only magnitude)
    • Momentum is linearly proportional to velocity (p=mvp = mv) while kinetic energy is proportional to the square of velocity (KE=12mv2KE = \frac{1}{2}mv^2)
    • Momentum is always conserved in closed systems (elastic and inelastic collisions) while kinetic energy is only conserved in elastic collisions
      • The determines the elasticity of a collision
  • Compare the formulas for momentum and kinetic energy
    • Momentum: p=mvp = mv
    • Kinetic energy: KE=12mv2KE = \frac{1}{2}mv^2
  • Examples:
    • A 2 kg object moving at 3 m/s has a momentum of 6 kg⋅m/s and a kinetic energy of 9 J
    • Doubling the velocity of an object doubles its momentum but quadruples its kinetic energy

Conservation of linear momentum

  • Apply the to collisions and explosions
    • In a , total momentum before an interaction equals total momentum after the interaction
      • Use the formula m1v1+m2v2=m1v1′+m2v2′m_1v_1 + m_2v_2 = m_1v'_1 + m_2v'_2 where v1v_1 and v2v_2 are initial velocities and v1′v'_1 and v2′v'_2 are final velocities
  • Distinguish between elastic and inelastic collisions
    1. Elastic collisions conserve both kinetic energy and momentum (colliding billiard balls, certain atomic and subatomic particle interactions)
    2. Inelastic collisions conserve momentum but not kinetic energy, converting some kinetic energy into other forms like heat or sound (colliding vehicles, a ball of clay hitting a wall)
  • Analyze the conservation of momentum in explosions
    • Initial momentum of the system is zero before the
    • After the explosion, the sum of the momenta of all fragments equals zero
  • Examples:
    • In a head-on between two objects of equal mass, they will bounce off each other with the same speed but opposite directions
    • When a firecracker explodes, the fragments fly off in different directions, but the vector sum of their momenta is zero

Impulse and Newton's Second Law

  • Understand as the change in momentum
    • is equal to the force applied multiplied by the time interval of application
    • Impulse is directly related to of Motion
  • Apply Newton's Second Law to momentum problems
    • The law states that the rate of change of momentum is equal to the applied force
    • This relationship is crucial in understanding how forces affect the motion of objects
  • Analyze the concept of in multi-particle systems
    • The is the point where the entire mass of a system can be considered concentrated
    • It's important in calculating the overall motion of complex objects or systems
  • Explore the phenomenon of in various scenarios
    • Recoil occurs due to conservation of momentum when a part of a system is ejected
    • Examples include the kickback of a gun or the thrust of a rocket

Key Terms to Review (23)

Center of mass: The center of mass is the point in an object or system where all its mass can be considered to be concentrated for the purpose of analyzing translational motion. It is the weighted average position of all the mass in the system.
Center of Mass: The center of mass is the point at which an object's entire mass can be considered to be concentrated. It is the average position of the mass of an object, and it is the point around which the object's rotation and motion can be analyzed.
Closed system: A closed system is a physical system that does not exchange matter with its surroundings, but can exchange energy. In mechanics, it is often used to analyze conservation laws such as the conservation of linear momentum.
Closed System: A closed system is a thermodynamic system that does not exchange matter with its surroundings, but may exchange energy. It is an idealized model used to understand the behavior of various physical and chemical processes, particularly in the context of energy conservation and momentum conservation.
Coefficient of Restitution: The coefficient of restitution is a measure of the elasticity of a collision between two objects. It quantifies the ratio of the relative speed of the objects after the collision to the relative speed before the collision, and is a key factor in determining the outcomes of various types of collisions.
Conservation of Momentum: Conservation of momentum is a fundamental principle in physics that states the total momentum of a closed system remains constant unless an external force acts upon it. This principle applies to various topics in mechanics, including Newton's Third Law, linear momentum, impulse and collisions, types of collisions, center of mass, and rocket propulsion.
Elastic Collision: An elastic collision is a type of collision between two objects where the total kinetic energy of the system is conserved. In an elastic collision, there is no net loss of kinetic energy, and the objects simply exchange momentum without any deformation or change in internal energy.
Explosion: An explosion is a rapid and violent release of energy, typically accompanied by the generation of high temperatures and the emission of gases, flames, and debris. It is a sudden and powerful event that can have significant impacts on its surroundings.
Impulse: Impulse is the product of the average force and the time interval over which it acts on an object. It is equal to the change in momentum of the object.
Impulse: Impulse is a quantity that describes the change in momentum of an object over a given time interval. It is the product of the net force acting on an object and the time interval during which that force is applied. Impulse is a fundamental concept in physics that connects the ideas of force, time, and momentum, and is essential for understanding topics such as solving problems in physics, forces, Newton's laws, and collisions.
Inelastic Collision: An inelastic collision is a type of collision where the colliding objects stick together after the collision, or undergo a deformation, resulting in a loss of kinetic energy. In an inelastic collision, the total momentum of the system is conserved, but the total kinetic energy is not.
Kg⋅m/s: kg⋅m/s, or kilogram-meter per second, is a unit that represents linear momentum. It is the product of an object's mass (in kilograms) and its velocity (in meters per second), and it quantifies the amount of motion an object possesses.
Kinetic energy: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object.
Kinetic Energy (KE = ½mv²): Kinetic energy is the energy of motion possessed by an object. It is directly proportional to the mass of the object and the square of its velocity, as described by the formula KE = ½mv², where m is the mass and v is the velocity of the object.
Law of Conservation of Momentum: The Law of Conservation of Momentum states that the total linear momentum of a closed system remains constant if no external forces are acting on it. This principle is fundamental in analyzing collisions and interactions in mechanics.
Linear Momentum: Linear momentum is a vector quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity, and it represents the object's quantity of motion. Linear momentum is a fundamental concept in classical mechanics that is crucial for understanding the behavior of moving objects and the conservation of energy.
M₁v₁ + m₂v₂ = m₁v'₁ + m₂v'₂: The equation $m₁v₁ + m₂v₂ = m₁v'₁ + m₂v'₂$ represents the principle of conservation of linear momentum. It states that the total linear momentum of a closed system before a collision or interaction is equal to the total linear momentum after the collision or interaction.
Momentum: Momentum is the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction.
Newton's Second Law: Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. It describes the relationship between an object's motion and the forces acting upon it, providing a quantitative framework for understanding the dynamics of physical systems.
P = mv: The equation p = mv, where p represents linear momentum, m represents mass, and v represents velocity, is a fundamental relationship in physics that connects the concepts of kinetic energy and linear momentum. This equation describes the quantity of motion possessed by an object, which is a crucial factor in understanding the dynamics of physical systems.
Recoil: Recoil is the backward movement or force that occurs when an object is propelled forward, such as the backward motion of a gun when it is fired. This concept is closely related to Newton's Third Law of Motion, Linear Momentum, and the Conservation of Linear Momentum.
Slug⋅ft/s: The slug-foot per second (slug⋅ft/s) is a unit of linear momentum, which is the product of an object's mass and its velocity. It represents the amount of force required to change the motion of an object by a certain amount.
Vector Quantity: A vector quantity is a physical measurement that has both magnitude and direction, distinguishing it from scalar quantities that have only magnitude. Vector quantities are essential in physics as they provide a complete description of various physical phenomena, such as motion and forces. Understanding vector quantities allows for better analysis of how objects move and interact in space.
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Glossary
Glossary
9.2 Impulse and Collisions