9.2 Impulse and Collisions
2 min read•june 24, 2024
and are key concepts in physics, describing how forces change an object's motion over time. Understanding these ideas helps explain collisions and interactions between objects, from car crashes to billiard balls colliding.
Collisions can be elastic or inelastic, depending on whether is conserved. This distinction is crucial for predicting outcomes in real-world scenarios, from sports to engineering. Mastering these concepts unlocks deeper insights into how objects interact and exchange energy.
Impulse and Momentum
Physical significance of impulse
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- measures the change in momentum of an object during a collision or interaction
- Larger impulses lead to greater changes in momentum
- Impulse vector direction determines the direction of momentum change
- Impulse is related to through the
Applications of impulse-momentum theorem
- Impulse-momentum theorem equates impulse to change in momentum:
- Change in momentum calculated as (final momentum minus initial momentum)
- Solve problems by identifying initial and final momenta, calculating change in momentum, and using impulse-momentum theorem to find impulse or average force
- Utilizes to determine the direction and magnitude of impulse and momentum changes
Impulse and momentum changes
- During interactions (collisions), impulse experienced by each object is equal in magnitude but opposite in direction due to Newton's Third Law
- Total system momentum conserved during interaction assuming no external forces
- Impulse magnitude determines magnitude of momentum change for each object
- Impulse vector direction for each object determines direction of momentum change for that object
Types of Collisions
Elastic vs inelastic collisions
- Collisions classified as elastic or inelastic based on conservation of kinetic energy and momentum
- Elastic collisions:
- Conserve kinetic energy and momentum (hard, rigid objects like billiard balls)
- Total impulse experienced by objects is zero (impulses equal in magnitude, opposite in direction)
- Inelastic collisions:
- Kinetic energy not conserved, some converted to other forms (heat, sound, )
- Momentum still conserved (soft objects or objects that stick together after collision)
- Total impulse experienced by objects is not zero (some initial kinetic energy converted to other forms)
- Perfectly inelastic collisions:
- Special case of where objects stick together after collision and move with common
- Kinetic energy not conserved, but momentum conserved
- Total impulse experienced by objects equals change in momentum of combined object after collision
Fundamental Principles
- form the foundation for understanding impulse and collisions
- Velocity changes during collisions are directly related to the applied impulse
- is a key principle in analyzing collisions
- Kinetic energy may or may not be conserved, depending on the type of collision
Key Terms to Review (28)
Action-at-a-distance force: An action-at-a-distance force is a force exerted by an object on another object that is not in physical contact with it, acting over a distance through space. Examples include gravitational, electromagnetic, and nuclear forces.
Airbag: An airbag is a safety device in vehicles that inflates rapidly during a collision to prevent occupants from striking interior objects. It reduces the force of impact by increasing the time over which the occupant comes to a stop.
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.
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.
Collision Analysis: Collision analysis is the study of the interactions and dynamics that occur when two or more objects collide. It involves the examination of the forces, momentum, and energy changes that take place during the collision process.
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.
Deformation: Deformation is the change in shape or size of an object due to applied forces. It can be temporary (elastic) or permanent (plastic) based on the material properties and magnitude of the force.
Deformation: Deformation is the change in the shape or size of an object due to the application of a force or stress. It is a fundamental concept in physics that describes how materials respond to external forces, and it is essential for understanding various topics, including friction, collisions, and the behavior of solids under stress.
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.
Force: Force is a vector quantity that represents the interaction between two objects, causing a change in the motion or shape of the objects. It is the fundamental concept that underlies many of the physical principles studied in college physics, including Newton's laws of motion, work, energy, and more.
Impact Force: Impact force is the force exerted on an object when it collides with another object. It is the change in momentum experienced by an object during a collision, which can cause significant damage or deformation to the colliding objects.
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.
Impulse-Momentum Theorem: The impulse-momentum theorem states that the impulse, or the change in momentum, of an object is equal to the net force acting on the object multiplied by the time over which the force acts. This theorem establishes a fundamental relationship between the concepts of impulse and momentum, which are crucial in understanding the dynamics of collisions and the conservation of linear momentum.
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.
IPhone: An iPhone is a smartphone developed by Apple Inc. that integrates mobile computing and communication functions. It features various sensors and components that can be analyzed in the context of physics, particularly mechanics and collisions.
Kilogram-Meter per Second: Kilogram-meter per second is a unit of momentum, which is the product of an object's mass and its velocity. It represents the quantity of motion possessed by an object and is a fundamental concept in the study of impulse and collisions.
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.
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.
Momentum: 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. Momentum is a fundamental concept in physics that is closely related to other important topics such as forces, energy, and collisions.
Newton-Second: The newton-second (N⋅s) is a unit of impulse, which is the product of force and the time over which it is applied. It represents the change in momentum of an object and is a fundamental concept in the study of mechanics, particularly in the topics of impulse and collisions.
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 in the physical world. These laws form the foundation of classical mechanics and are essential in understanding the behavior of objects in various contexts, including the Scope and Scale of Physics, Algebra of Vectors, Free Fall, Newton's First Law, Impulse and Collisions, and Center of Mass.
Perfectly Inelastic Collision: A perfectly inelastic collision is a type of collision where the colliding objects stick together after impact, resulting in a single object with a combined mass and a shared velocity. In this type of collision, the total momentum of the system is conserved, but the kinetic energy is not.
Rebound: Rebound refers to the return or bounce-back of an object after it collides with another surface or object. It is a fundamental concept in the study of impulse and collisions, describing the change in an object's motion and direction following an impact or interaction.
Seatbelt: A seatbelt is a safety device designed to secure the occupant of a vehicle against harmful movement that may result from a collision or sudden stop. It reduces the force of impact and helps distribute the forces over stronger parts of the body.
Vector Analysis: Vector analysis is a branch of mathematics that deals with the study and application of vectors, which are quantities that have both magnitude and direction. It is a fundamental tool in physics, particularly in the areas of mechanics, electromagnetism, and fluid dynamics.
Velocity: Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the speed and the direction of an object's motion, making it a more complete description of an object's movement compared to just speed alone.