8.1 Linear Momentum and Force
3 min read•june 18, 2024
is a crucial concept in physics, describing an object's motion based on its mass and velocity. It's calculated by multiplying these two factors, resulting in a vector quantity with both magnitude and direction. Understanding momentum is key to grasping how objects interact and move.
Momentum plays a central role in Newton's laws of motion and the principle of conservation. In collisions and interactions, the total momentum of a closed system remains constant. This fundamental concept helps explain everything from everyday collisions to complex particle interactions in physics.
Linear Momentum
Definition of linear momentum
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- () calculated by multiplying an object's mass () and velocity ()
- Formula:
- SI unit: kilogram-meter per second (kg⋅m/s)
- Larger mass or velocity results in greater momentum (bowling ball, bullet)
- Momentum is a vector quantity with both magnitude and direction
- Momentum direction same as velocity direction (car moving north)
- is the point where the entire mass of an object can be considered concentrated for momentum calculations
Momentum in Newton's second law
- : net force () equals rate of change of momentum ()
- Formula:
- For constant mass: , is acceleration
- Net force acting on an object changes its momentum (pushing a shopping cart)
- Change in momentum directly proportional to net force and time interval ()
- Formula:
- Change in momentum directly proportional to net force and time interval ()
- () is product of net force and time interval
- Formula:
- SI unit: newton-second (N⋅s)
- equals change in momentum (hitting a tennis ball)
- relates the work done by net force to change in kinetic energy, complementing momentum analysis
Conservation of Momentum
Momentum analysis in collisions
- Colliding or interacting objects experience momentum changes due to mutual forces
- Elastic collisions: conserved kinetic energy, total momentum remains constant
- Examples: billiard balls, certain atomic and subatomic particle interactions
- Inelastic collisions: kinetic energy not conserved, total momentum remains constant
- Examples: colliding vehicles, clay ball hitting a wall
- Perfectly inelastic collisions: objects stick together after collision with common velocity
- Maximum kinetic energy loss in these collisions (two lumps of clay colliding)
- measures the elasticity of a collision, ranging from 0 (perfectly inelastic) to 1 (perfectly elastic)
Conservation of momentum in systems
- : total momentum of closed system remains constant
- Closed system has no external forces acting on objects within (space probe)
- Without external forces, total momentum before interaction equals total momentum after
- Formula: , and are initial and final velocities
- solves problems involving collisions and explosions (rocket launch)
- Equating total momentum before and after interaction calculates unknown velocities or masses
- Law of conservation of momentum is fundamental physics principle for all isolated systems (particles to planets)
Force and Momentum Interactions
- states that for every action, there is an equal and opposite reaction
- occurs when objects interact, exchanging momentum between them
- The total momentum of the system remains constant due to these equal and opposite forces
Key Terms to Review (19)
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.
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 velocity of the objects after the collision to the relative velocity before the collision, and is used to determine the energy lost during the impact.
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.
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.
Law of Conservation of Momentum: The law of conservation of momentum 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 interaction is equal to the total momentum after the interaction, assuming no external forces are present.
Linear momentum: Linear momentum is the product of an object's mass and its velocity. It is a vector quantity, possessing both magnitude and direction.
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 resistance to changes in its motion.
Momentum Transfer: Momentum transfer is the exchange of momentum between objects during a collision or interaction. It describes how the momentum of one object is transferred to another object, resulting in changes in their respective velocities and/or directions of motion.
Newton's Second Law: Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. This law describes the relationship between an object's motion and the forces acting upon it, providing a fundamental principle for understanding the dynamics of physical systems.
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.
Perfectly Inelastic Collision: A perfectly inelastic collision is a type of collision in which the colliding objects stick together after the impact, resulting in a single object with a combined mass moving at a common velocity. In this type of collision, the total momentum of the system is conserved, but the kinetic energy is not.
Second law of motion: The second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, this is expressed as $F = ma$ where $F$ is the net force, $m$ is the mass, and $a$ is the acceleration.
Work-Energy Theorem: The Work-Energy Theorem states that the work done by all forces acting on an object equals the change in its kinetic energy. This relationship highlights how work and energy are interchangeable; when work is done on an object, it results in a change in that object's energy state. Understanding this theorem is crucial because it connects the concept of work with energy, showing how forces impact motion and energy transformations.