8.3 Conservation of Momentum
3 min read•june 18, 2024
conservation is a fundamental principle in physics, stating that the total momentum of a remains constant. This concept is crucial for understanding collisions, explosions, and various interactions between objects, from everyday scenarios to atomic-level events.
The principle applies to one-dimensional and two-dimensional collisions, as well as explosions. It's used to predict object motion after collisions, explain , and analyze particle interactions in physics experiments. Understanding momentum conservation is key to grasping many physical phenomena.
Conservation of Momentum
Conservation of momentum principle
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- Fundamental physics principle states total momentum of closed system remains constant over time
- Closed system has no external forces acting on objects within system
- In , vector sum of momenta of all objects remains unchanged before and after or interaction
- Momentum is product of object's mass and velocity ()
- Vector quantity has both magnitude and direction
- is direct consequence of
- Derived from which states for every action, there is equal and opposite reaction
- Crucial in understanding and analyzing collisions and interactions between objects
- Allows prediction of motion of objects after collision or , given initial momenta and type of collision (elastic or inelastic)
- Involves vector addition of individual momenta to determine total system momentum
Applications in collisions and explosions
- In one-dimensional collisions, total momentum before collision equals total momentum after collision
- , where and represent initial and final velocities
- Equation can be used to solve for unknown velocities or masses in collision (car crash, billiard balls)
- In two-dimensional collisions, applies to both x and y components of momentum vector
- (x-component)
- (y-component)
- Equations can be used to solve for unknown velocities or angles in (football tackle, asteroid impact)
- In explosions, initial momentum of system is zero, and final momenta of fragments must sum to zero to conserve momentum
- , where is number of fragments and is velocity of each fragment (fireworks, supernova)
- , the change in momentum, is equal to the force applied over time in collisions
Real-world momentum conservation scenarios
- Rocket propulsion relies on conservation of momentum
- As rocket expels fuel in one direction, it experiences equal and opposite thrust force causing acceleration
- Momentum of expelled fuel is equal in magnitude and opposite in direction to momentum gained by rocket
- Billiard ball collisions demonstrate conservation of momentum in nearly elastic system
- When one ball strikes another, momentum is transferred from striking ball to struck ball
- Total momentum of system remains constant before and after collision, neglecting friction and dissipative forces
- Other examples include:
- of gun when fired
- Motion of object when hit by moving object (baseball bat hitting ball)
- Behavior of objects in zero-gravity environment (astronauts in space)
Momentum in atomic interactions
- Conservation of momentum is fundamental principle in and
- In particle collisions, like those studied in accelerator experiments, total momentum of system is conserved
- Momenta of incoming particles must equal sum of momenta of outgoing particles, including newly created particles (Large Hadron Collider experiments)
- In nuclear reactions, like or , total momentum of system is conserved
- Momentum of parent nucleus equals sum of momenta of daughter nuclei and emitted particles (alpha particles, beta particles, gamma rays)
- Essential in understanding behavior and properties of subatomic particles and outcomes of nuclear reactions
- Helps scientists predict trajectories and energies of particles in experiments
- Key factor in designing particle detectors and interpreting experimental results (neutrino detectors, dark matter searches)
Momentum and energy in collisions
- Conservation of momentum always applies in collisions, while conservation of depends on collision type
- of a system continues to move at constant velocity unless acted upon by external forces
- In elastic collisions, both momentum and kinetic energy are conserved
- In inelastic collisions, momentum is conserved but kinetic energy is not fully conserved due to deformation or heat generation
Key Terms to Review (27)
Center of mass: The center of mass is the point in a body or system of bodies where the entire mass can be considered to be concentrated for the purpose of analyzing translational motion. It is the average location of all the mass in a system.
Center of Mass: The center of mass is a point within an object or system of objects where the object's mass is concentrated. It is the point at which the object's weight can be considered to act, and it is the point around which the object's rotational motion is determined.
Closed System: A closed system is a thermodynamic system that does not exchange matter with its surroundings, but may exchange energy. It is isolated from the transfer of matter but can interact with its environment through the transfer of energy, such as heat or work.
Collision: A collision is an event where two or more objects come into contact with each other, resulting in an exchange of energy and momentum. Collisions can be elastic, where kinetic energy is conserved, or inelastic, where kinetic energy is not conserved. Understanding collisions helps in analyzing the behavior of moving objects and the forces acting upon them.
Conservation of Momentum: Conservation of momentum is a fundamental principle in physics which states that the total momentum of a closed system is constant unless an external force acts on the system. This means that the total momentum before an event, such as a collision, is equal to the total momentum after the event.
Conservation of momentum principle: The principle of conservation of momentum states that the total linear momentum of an isolated system remains constant if no external forces are acting on it. This means that the momentum before and after a collision or interaction is the same.
Elastic Collision: An elastic collision is a type of collision in which there is no net loss of kinetic energy. The total kinetic energy before the collision is equal to the total kinetic energy after the collision, and the momentum of the colliding objects is conserved.
Explosion: An explosion is a rapid and violent release of energy, typically accompanied by the generation of high temperatures, pressure, and the expansion of gases. It is a sudden, intense, and forceful event that can have significant impacts on the surrounding environment.
Impulse: Impulse is the product of the average force applied to an object and the time duration over which it is applied. It is also equal to the change in momentum of the object.
Impulse: Impulse is a vector quantity that represents the change in momentum experienced by an object over a given time interval. It is the product of the force acting on an object and the time interval over which that force is applied.
Inelastic collision: An inelastic collision is a type of collision where the colliding objects stick together or deform, resulting in a loss of kinetic energy. However, the total momentum of the system is conserved.
Inelastic Collision: An inelastic collision is a type of collision between two or more objects where the total kinetic energy of the system is not conserved. In an inelastic collision, the colliding objects stick together or undergo deformation, resulting in the conversion of some of the initial kinetic energy into other forms of energy, such as heat or sound.
Internal kinetic energy: Internal kinetic energy is the sum of the kinetic energies of all particles within a system. It plays a crucial role in understanding how energy is distributed and conserved during elastic collisions.
Isolated system: An isolated system is a physical system that does not exchange matter or energy with its surroundings. This means that the total energy and momentum within the system remain constant over time, as there are no external forces or influences acting on it. Such systems are theoretical constructs that help in understanding the principles of conservation laws.
Kinetic Energy: Kinetic energy is the energy of motion possessed by an object. It is the energy an object has by virtue of being in motion and is directly proportional to the mass of the object and the square of its velocity. Kinetic energy is a crucial concept in physics, as it relates to the work done on an object, the conservation of energy, and various other physical phenomena.
Momentum: Momentum is a vector quantity that represents the product of an object's mass and velocity. It is a measure of an object's quantity of motion and is conserved in a closed system, meaning the total momentum of a system remains constant unless acted upon by an external force.
Newton's Laws of Motion: Newton's Laws of Motion are a set of three fundamental principles that describe the relationship between an object and the forces acting upon it, governing the motion of objects and the interactions between them. These laws form the foundation of classical mechanics and are crucial in understanding various topics in introductory college physics.
Newton's Third Law: Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object exerts an equal and opposite force on the first. This principle of action and reaction forces is fundamental to understanding the dynamics of various physical systems, from collisions to rocket propulsion.
Nuclear fission: Nuclear fission is the process in which a nucleus of a heavy atom splits into two or more smaller nuclei, along with the release of energy. This reaction is often initiated by the absorption of a neutron.
Nuclear Fission: Nuclear fission is the process of splitting heavy atomic nuclei, such as uranium or plutonium, into lighter nuclei. This process releases a large amount of energy that can be harnessed for various applications, including nuclear power generation and the development of nuclear weapons.
Nuclear reactions: Nuclear reactions are processes in which atomic nuclei collide and interact, resulting in the transformation of elements and the release or absorption of energy. These reactions can lead to the creation of new isotopes, fission or fusion of nuclei, and are governed by the principles of conservation of mass-energy and momentum. Understanding nuclear reactions is crucial for exploring energy production, radioactive decay, and the behavior of particles at high speeds.
One-Dimensional Collision: A one-dimensional collision is a type of collision that occurs when two objects interact along a single axis, with no motion in any other direction. This type of collision is often used in the study of conservation of momentum, as the principles of momentum conservation can be easily applied in a one-dimensional scenario.
Particle Physics: Particle physics is the study of the most fundamental constituents of matter and energy, and the interactions between them. It seeks to understand the nature of the universe at the most basic level, exploring the smallest known particles and the forces that govern their behavior.
Radioactive Decay: Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This process is a fundamental aspect of nuclear physics and has important implications across various fields, including the four basic forces, conservation of momentum, nuclear radioactivity, the substructure of the nucleus, half-life and activity, and the four basic forces.
Recoil: Recoil is the backward movement experienced by an object when it expels another object, typically observed in firearms or rockets. This phenomenon occurs due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In essence, when a projectile is fired forward, the gun or rocket experiences an equal force pushing it backward, which is known as recoil.
Rocket Propulsion: Rocket propulsion is a method of propulsion that uses the principle of action and reaction to generate thrust. It involves the expulsion of matter from a rocket engine at high speed to produce a forward force that propels the rocket forward.
Two-Dimensional Collision: A two-dimensional collision is an interaction between two objects in which the motion of the objects is described by both the magnitude and direction of their velocities in a two-dimensional plane. This type of collision involves the conservation of momentum in both the x and y dimensions.