Unit 4: Momentum Conservation and Collision Dynamics

Collision

An event where two or more bodies exert strong forces on each other for a short time.

Law of Conservation of Linear Momentum

The principle stating that the total momentum before a collision equals the total momentum after the collision.

Elastic Collision

A collision in which both momentum and kinetic energy are conserved.

Inelastic Collision

A collision in which momentum is conserved, but kinetic energy is not.

Perfectly Inelastic Collision

A collision where the objects stick together after impact, resulting in maximum loss of kinetic energy.

Kinetic Energy (K)

The energy that an object possesses due to its motion, given by the formula K = (1/2)mv^2.

Impulse

The change in momentum of an object when a force is applied over time.

Relative Velocity of Approach

The velocity of one object as observed from another, indicating how fast they are approaching each other.

Center of Mass Frame

A reference frame in which the total momentum of the system is zero.

Momentum Conservation Equation

A mathematical expression that represents the principle that total momentum before a collision equals total momentum after.

Conservation of Kinetic Energy Equation

An equation that equates the total kinetic energy before and after a collision in elastic collisions.

Massive Hits Light

An example scenario in collisions where a large mass collides with a small mass.

Light Hits Massive

An example scenario in collisions where a small mass collides with a large mass.

Two-Dimensional Collisions

Collisions that occur in a plane where momentum must be conserved in both x and y directions.

Equations for 2D Elastic Collisions

Pairs of equations used to find velocities in both x and y directions after a 2D collision.

Ballistic Pendulum

A device that measures the speed of a projectile by analyzing the collision with a pendulum.

Energy Lost in Inelastic Collisions

In inelastic collisions, kinetic energy is transformed into other forms of energy, like sound or heat.

Mass Exchange in Elastic Collisions

In elastic collisions between equal masses, the object at rest receives the velocity of the object in motion.

Sign Convention in Velocity

A designated positive direction for velocity to avoid confusion with direction in 1D problems.

Correcting Energy Conservation Mistakes

In inelastic scenarios, always check if the conservation of kinetic energy applies.

Energy Conversion in Collisions

The process where kinetic energy is converted to other forms during inelastic collisions.

Common Errors in 2D Collisions

Mistakes such as confusing scalar addition with vector addition in momentum calculations.

Final Common Velocity Formula

For perfectly inelastic collisions, the final common velocity is calculated using the formula vf = (m1 v{1i} + m2 v{2i}) / (m1 + m_2).

Deformation in Inelastic Collisions

The physical change in shape of objects involved in an inelastic collision.

Impulse Applied to the System

A measure of the total change in momentum caused by external forces.