Point masses allow for simplified calculations in two-dimensional collisions by focusing only on mass and velocity.
During a collision, the total linear momentum of point masses is conserved if no external forces act on the system.
The equations governing the conservation of momentum can be separated into components: $m_1v_{1x} + m_2v_{2x} = m_1u_{1x} + m_2u_{2x}$ and $m_1v_{1y} + m_2v_{2y} = m_1u_{1y} + m_2u_{2y}$.
Elastic collisions between point masses conserve both kinetic energy and momentum, while inelastic collisions only conserve momentum.
In two-dimensional collisions, angles of deflection and final velocities can be determined using trigonometric relationships.
Review Questions
What conditions must hold true for the conservation of linear momentum in a system of point masses?
How do elastic and inelastic collisions differ when considering point masses?
What are the component forms of the conservation of momentum equations in two-dimensional collisions?
Related terms
Linear Momentum: The product of an object's mass and its velocity, represented as $\mathbf{p} = m\mathbf{v}$.
Elastic Collision: A type of collision where both kinetic energy and linear momentum are conserved.
Inelastic Collision: A type of collision where only linear momentum is conserved, but some kinetic energy is transformed into other forms of energy.