The fictional starship Enterprise obtains its power by...

The fictional starship Enterprise obtains its power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of the Enterprise is approximately $6 \times 10^{9} \mathrm{kg}$ , how much mass must be converted into kinetic energy to accelerate it from rest to one-tenth the speed of light?

Key Concepts

Mass?Energy Equivalence

This fundamental principle of modern physics, encapsulated by Einstein’s equation E = mc², relates mass and energy. It implies that a small amount of mass can be completely converted into a large amount of energy, and is a key concept for understanding processes where matter is annihilated to produce energy, such as in certain theoretical propulsion systems or particle interactions.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion. In mechanics, it is typically calculated using the formula (1/2)mv² for non-relativistic speeds, but at speeds approaching a significant fraction of the speed of light, slight relativistic corrections may be needed. Understanding how to compute kinetic energy is essential for determining the energy required to accelerate an object to a given speed.

Relativistic Mechanics

Relativistic mechanics deals with the behavior of objects when they move at speeds that are a significant fraction of the speed of light. Although classical equations for kinetic energy can be applied at lower speeds, corrections from special relativity become important as velocities increase. This concept is crucial for accurate energy calculations when dealing with high-speed scenarios in physics.

Energy Conversion Efficiency

Energy conversion efficiency in this context refers to the ability to convert matter completely into energy, such as through matter-antimatter annihilation. This concept is pivotal when considering theoretical propulsion methods and energy requirements, as it determines how much mass must be converted to achieve a desired amount of kinetic energy for acceleration.

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