Physics Chapter on Elastic Collisions

Elastic Collisions

• An elastic collision conserves internal kinetic energy
• Internal kinetic energy is the sum of the kinetic energies of the objects in the system
• Elastic collisions can only be achieved with subatomic particles, like electrons striking nuclei.
• Macroscopic collisions can be nearly, but not quite, elastic.
• Some kinetic energy is always converted into other forms of energy, such as heat transfer due to friction and sound.
• Two steel blocks on ice and two carts with spring bumpers on an air track demonstrate nearly elastic collisions.
• Icy surfaces and air tracks are nearly frictionless, allowing nearly elastic collisions on them.

Conservation of Internal Kinetic Energy

• The equation for conservation of momentum for two objects in a one-dimensional collision can be expressed as:
  • m1v1+m2v2=m1v1′+m2v2′m_1v_1+m_2v_2=m_1v_1'+m_2v_2'm1​v1​+m2​v2​=m1​v1′​+m2​v2′​
  • Where the primes (') indicate values after the collision.
• The sum of kinetic energies before the collision equals the sum after the collision in an elastic collision.
• This can be expressed with 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'^221​m1​v12​+21​m2​v22​=21​m1​v1′2​+21​m2​v2′2​

Inelastic Collisions

• An inelastic collision is one that does not conserve internal kinetic energy, and some energy is lost to heat transfer due to friction and sound.
• Collisions where objects stick together are perfectly inelastic
• Potential energy can be converted to internal kinetic energy during a collision, like in a collision between two carts on an air track.

Two-Dimensional Collisions

• In a two-dimensional collision, momentum is conserved in both the x and y directions.
• Conservation of momentum can be applied to analyze collision events in two dimensions with two independent equations for the x and y directions.

Momentum, Sports, and Collisions

• Momentum, not force, is important in collisions.
• A heavier object has an advantage in a collision.
• The location and timing of impact are important in sports collisions.

Importance of Studying Collisions

• Two-dimensional collision experiments have provided insight into subatomic particles.
• Ernest Rutherford discovered the nature of the atomic nucleus through these experiments.

Rocket Propulsion

• Rocket propulsion utilizes Newton's third law of motion.
• Matter is forcefully ejected from a system, producing an equal and opposite reaction on what remains.
• Examples include fireworks, jet engines, deflating balloons, and even squids and octopuses.
• The recoil of a gun also demonstrates this principle.

Space Shuttles and Rocket Launches

• The space shuttle was an attempt at an economical vehicle with reusable parts like the solid fuel boosters and the orbiter.
• The shuttle's reliance on human operation made it costly for launching satellites.
• Rockets carrying satellites can also be launched from airplanes, maximizing initial velocity and avoiding atmospheric resistance.

This quiz explores the concept of elastic collisions and the conservation of internal kinetic energy. It covers the principles of momentum and kinetic energy in both microscopic and macroscopic systems. You'll gain insights into how these principles apply to various physical scenarios, such as collisions involving steel blocks and carts on air tracks.