Elastic collision
Collision where total kinetic energy is conserved.
In physics, an elastic collision is one where the total kinetic energy of the two objects involved stays the same before and after they hit. In a perfect elastic collision, no kinetic energy is turned into heat, sound, or potential energy. During the collision of small objects, kinetic energy first changes into potential energy linked to a repulsive or attractive force between the particles (when the particles move against this force, meaning the angle between the force and relative velocity is obtuse), and then that potential energy changes back into kinetic energy (when the particles move with this force, meaning the angle is acute). Collisions between atoms, like in Rutherford backscattering, are elastic. A handy special case is when the two bodies have the same mass—they simply swap their momenta. Molecules in a gas or liquid, unlike atoms, rarely have perfectly elastic collisions because kinetic energy gets swapped between their translational motion and their internal degrees of freedom with each hit. At any moment, about half the collisions are inelastic (the pair has less translational kinetic energy after the collision) and the other half are "super-elastic" (they have more translational kinetic energy after). Averaged over the whole sample, molecular collisions can be treated as essentially elastic as long as black-body radiation is negligible or doesn't escape. For macroscopic objects, perfectly elastic collisions are an ideal never fully achieved, but they are approximated by things like billiard balls. Rotational energy before or after a collision may also matter.
In any collision without an external force, momentum is conserved; in an elastic one, kinetic energy is also conserved. For particles A and B with masses mA, mB, and velocities vA1, vB1 before the collision, and vA2, vB2 after, the conservation of momentum is: mA vA1 + mB vB1 = mA vA2 + mB vB2. The conservation of kinetic energy is: ½ mA vA1² + ½ mB vB1² = ½ mA vA2² + ½ mB vB2². These equations can be solved directly to find vA2 and vB2 when vA1 and vB1 are known: vA2 = ((mA - mB) / (mA + mB)) vA1 + ((2 mB) / (mA + mB)) vB1, and vB2 = ((2 mA) / (mA + mB)) vA1 + ((mB - mA) / (mA + mB)) vB1.
- field
- Physics
- known_for
- Conservation of kinetic energy in collisions
- type
- Physical process
- key_equation
- m_A v_A1 + m_B v_B1 = m_A v_A2 + m_B v_B2 (momentum); 1/2 m_A v_A1^2 + 1/2 m_B v_B1^2 = 1/2 m_A v_A2^2 + 1/2 m_B v_B2^2 (kinetic energy)
Lore & Background
During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive or attractive force between the particles (when the particles move against this force, i.e. the angle between the force and the relative velocity is obtuse), then this potential energy is converted back to kinetic energy (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute). Collisions of atoms are elastic, for example Rutherford backscattering. A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta.
Reader's Guide
Elastic collisions serve as a key idealization in physics, allowing the conservation laws of momentum and kinetic energy to be applied simultaneously. In one-dimensional Newtonian mechanics, the equations for conservation of momentum and kinetic energy can be solved directly to find the velocities after collision when the masses and initial velocities are known. While perfectly elastic collisions are never fully realized for macroscopic bodies, they are approximated by interactions such as those between billiard balls. The concept is essential for understanding atomic collisions, as atoms undergo elastic collisions, and it provides a baseline for analyzing inelastic and super-elastic collisions in molecular systems, where kinetic energy may be exchanged with internal degrees of freedom. The equations derived for elastic collisions are foundational in fields ranging from particle physics to engineering.
Did You Know?
- In an elastic collision, the total kinetic energy of the two bodies remains the same before and after the collision.
- Collisions of atoms are elastic, for example Rutherford backscattering.
- When two bodies have equal mass in an elastic collision, they will simply exchange their momenta.
- Macroscopic bodies never fully realize perfectly elastic collisions, but billiard balls approximate them.
Frequently Asked Questions
What is an elastic collision?
An elastic collision is a physical interaction between two bodies where the combined kinetic energy measured before impact equals the combined kinetic energy measured after impact. No energy is lost to heat, sound, or deformation in the ideal case, making it a clean energy-conservation scenario.
How does an elastic collision differ from an inelastic one?
In an inelastic collision, some kinetic energy is converted into other forms like thermal energy or structural deformation, so the post-collision kinetic energy is lower than the pre-collision value. An elastic collision, by definition, preserves the total kinetic energy exactly, which is why it serves as a simpler analytical model.
What equations govern an elastic collision?
Two conservation laws apply simultaneously: momentum is conserved (m_A·v_A1 + m_B·v_B1 = m_A·v_A2 + m_B·v_B2) and total kinetic energy is conserved (½m_A·v_A1² + ½m_B·v_B1² = ½m_A·v_A2² + ½m_B·v_B2²). Solving these two equations together yields the final velocities of both objects.
Why is the elastic collision concept important in physics?
It provides a foundational idealized model in mechanics and particle physics for studying how objects exchange momentum without energy loss. Many more complex interactions—billiard-ball strikes, gas-molecule scattering, and certain nuclear reactions—are approximated as elastic to make the mathematics tractable.
Do perfectly elastic collisions occur in the real world?
Strictly speaking, no real macroscopic collision is perfectly elastic because some kinetic energy always dissipates as heat, sound, or microscopic deformation. However, interactions at the atomic and subatomic level—such as idealized gas-molecule bounces or certain particle scatterings—come very close to the elastic limit, which is why the model remains physically meaningful.
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