Glossary

8.3 Elastic and Inelastic Collisions

3 min read•june 24, 2024

Collisions are key to understanding how objects interact. They come in two types: elastic, where kinetic energy is conserved, and inelastic, where it's not. Both types always conserve momentum, which is crucial for predicting outcomes.

Understanding collisions helps us analyze everything from subatomic particles to car crashes. We'll explore how momentum and energy behave in different scenarios, and how to use these principles to solve real-world problems.

Elastic and Inelastic Collisions

Elastic vs inelastic collisions

Top images from around the web for Elastic vs inelastic collisions

  • Inelastic Collisions in One Dimension | Physics View original

    Is this image relevant?

  • Inelastic Collisions in One Dimension | Physics View original

    Is this image relevant?

  • Inelastic Collisions in One Dimension | Physics View original

    Is this image relevant?

1 of 3

Top images from around the web for Elastic vs inelastic collisions

  • Inelastic Collisions in One Dimension | Physics View original

    Is this image relevant?

  • Inelastic Collisions in One Dimension | Physics View original

    Is this image relevant?

  • Inelastic Collisions in One Dimension | Physics View original

    Is this image relevant?

1 of 3
  • Elastic collisions involve no loss of kinetic energy, with the total kinetic energy before and after the collision remaining the same (bouncing tennis balls)
    • Momentum is also conserved in elastic collisions
    • Commonly observed in collisions between atomic and subatomic particles or in idealized systems ()
  • Inelastic collisions involve a loss of kinetic energy, with some of the energy being converted into other forms such as heat, sound, or deformation (clay balls colliding and sticking together)
    • Momentum is still conserved in inelastic collisions, even though kinetic energy is not
    • Perfectly inelastic collisions occur when objects stick together after the collision (two lumps of clay merging)
    • Partially inelastic collisions occur when objects separate after the collision but still lose kinetic energy (car bumpers deforming during a collision)
    • The between surfaces can affect the energy loss in inelastic collisions

Conservation of momentum in collisions

  • The law of states that the total momentum of a closed system remains constant, expressed as m1v1+m2v2=m1v1′+m2v2′m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'
    • m1m_1 and m2m_2 represent the masses of the objects
    • v1v_1 and v2v_2 represent the initial velocities
    • v1′v_1' and v2′v_2' represent the final velocities
  • In , objects move along a straight line, and the conservation of momentum equation can be used to solve for unknown velocities (two cars colliding head-on)
  • involve objects moving in a plane with both x and y components (billiard balls colliding at an angle)
    1. Resolve the velocity vectors into their x and y components using techniques
    2. Apply the conservation of momentum separately for the x and y components
    3. Combine the resulting components to determine the final velocity and direction of the objects

Momentum and kinetic energy relationships

  • Momentum is defined as the product of an object's mass and velocity, expressed as p=mvp = mv
  • Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE=12mv2KE = \frac{1}{2}mv^2
  • In elastic collisions, both momentum and kinetic energy are conserved, satisfying the equation 12m1v12+12m2v22=12m1v1′2+12m2v2′2\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 = \frac{1}{2}m_1v_1'^2 + \frac{1}{2}m_2v_2'^2 (two identical balls colliding head-on)
  • Inelastic collisions conserve momentum but not kinetic energy, with some energy being converted into other forms, resulting in 12m1v12+12m2v22>12m1v1′2+12m2v2′2\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 > \frac{1}{2}m_1v_1'^2 + \frac{1}{2}m_2v_2'^2 (a ball of putty hitting a wall and deforming)
  • In perfectly inelastic collisions, objects stick together after the collision, and the final velocity can be calculated using the conservation of momentum: vf=m1v1+m2v2m1+m2v_f = \frac{m_1v_1 + m_2v_2}{m_1 + m_2} (two carts with velcro pads colliding and sticking together)
  • The can be applied to analyze the energy transfer during collisions

Reference frames and relative motion

  • The is useful for analyzing collisions, as it simplifies calculations by treating the system as if it were at rest
  • between colliding objects is important in determining the outcome of a collision

Key Terms to Review (17)

Center of Mass: The center of mass is a point within an object or system of objects where the object's entire mass can be considered to be concentrated. It is the point at which the object's weight is evenly distributed and acts as the object's effective point of application for any external forces acting on it.
Center of Mass Frame: The center of mass frame, also known as the center of mass reference frame, is a coordinate system that moves with the combined center of mass of a system of objects. It is a particularly useful frame of reference for analyzing the dynamics of collisions between objects.
Coefficient of Friction: The coefficient of friction is a dimensionless scalar quantity that describes the ratio of the frictional force between two surfaces to the normal force pressing them together. It is a crucial parameter in understanding the behavior of objects sliding or rolling on surfaces, particularly in the context of elastic and inelastic collisions.
Coefficient of Restitution: The coefficient of restitution is a measure of the elasticity of a collision between two objects. It quantifies the amount of kinetic energy lost during the collision and is used to determine the outcome of collisions in various contexts, including physics, engineering, and sports.
Conservation of Kinetic Energy: Conservation of kinetic energy is a fundamental principle in physics which states that the total kinetic energy of a closed system is constant, unless energy is transferred into or out of the system. This means that the total kinetic energy of a group of objects remains the same, unless an external force does work on the system.
Conservation of Momentum: Conservation of momentum is a fundamental principle in physics which states that the total momentum of a closed system remains constant unless an external force acts upon it. This principle is a direct consequence of Newton's laws of motion and is applicable to both elastic and inelastic collisions.
Elastic Collision: An elastic collision is a type of collision between two objects in which there is no net loss of kinetic energy. The total kinetic energy of the colliding objects before the collision is equal to the total kinetic energy after the collision, and the objects may bounce off each other.
Impulse: Impulse is the change in momentum of an object caused by the application of a force over a period of time. It is a vector quantity that combines the magnitude of the force and the duration of its application, providing a measure of the total effect of the force on the object's motion.
Inelastic Collision: An inelastic collision is a type of collision in which the total kinetic energy of the colliding objects is not conserved. In an inelastic collision, the colliding objects stick together or undergo a change in shape, resulting in a loss of kinetic energy that is converted into other forms of energy, such as heat or sound.
Newton's Cradle: Newton's cradle is a device that demonstrates the conservation of momentum and energy in a series of swinging balls. It consists of a set of suspended steel balls, known as a pendulum, that when pulled to the side and released, swing back and forth, colliding with each other and demonstrating the transfer of energy and momentum between the balls.
One-Dimensional Collisions: One-dimensional collisions refer to the interactions between two objects that occur along a single axis, where the motion of the objects is restricted to a straight line. These types of collisions are often used in the analysis of elastic and inelastic collisions in physics.
Perfectly Elastic Collision: A perfectly elastic collision is a type of collision between two objects where the total kinetic energy of the system is conserved, and there is no loss of energy due to friction or deformation. In this type of collision, the momentum and kinetic energy of the colliding objects are simply exchanged, without any change in the total energy of the system.
Perfectly Inelastic Collision: A perfectly inelastic collision is a type of collision where two or more objects collide and stick together, resulting in a single object with a combined mass and momentum after the collision. In this type of collision, the kinetic energy of the system is not conserved, as some energy is lost in the deformation of the objects during the impact.
Relative Velocity: Relative velocity is the velocity of an object measured relative to another object, rather than relative to a fixed reference frame. It describes the motion of one object with respect to another, taking into account their individual velocities.
Two-Dimensional Collisions: A two-dimensional collision is a type of collision that occurs in a plane, where the motion of the colliding objects can be described using two spatial dimensions. This is in contrast to one-dimensional collisions, where the motion is restricted to a single axis.
Vector Resolution: Vector resolution is the process of breaking down a vector into its component parts or projections along different axes or directions. This concept is essential in understanding the behavior of vectors in various physical scenarios, including elastic and inelastic collisions.
Work-Energy Theorem: The work-energy theorem states that the work done on an object is equal to the change in the object's kinetic energy. This fundamental principle connects the concepts of work, force, and energy, and is a crucial tool for analyzing the motion and energy transformations of objects in various physical systems.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Back
Practice QuizGlossary
Practice QuizGlossary
Next guide