Question

The kinetic energy of a particle is equal to the rest energy of the particle. What is the speed of the particle?

   The kinetic energy of a particle is equal to the rest energy of the particle. What is the speed of the particle?

College Physics: Reasoning and Relationships

College Physics: Reasoning and Relationships

Nicholas J.… 2nd Edition

Chapter 27, Problem 40

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Solved by Expert Raj Bala

02/12/2022

Step 1

The kinetic energy of the particle is given by the relation: \[ KE = \frac{M_0c^2}{\sqrt{1-\frac{v^2}{c^2}}} - M_0c^2 \] Show more…

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The kinetic energy of a particle is equal to the rest energy of the particle. What is the speed of the particle?

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Key Concepts

Special Relativity

A theory introduced by Einstein that governs the behavior of objects at velocities close to the speed of light, indicating that measurements of time, length, and energy differ for observers in different inertial frames.

Lorentz Factor

A dimensionless quantity, denoted as gamma, that accounts for time dilation, length contraction, and the increase in mass as objects move near the speed of light. It is defined as 1/sqrt(1 - v²/c²).

Rest Energy

The intrinsic energy of an object due to its mass, formulated by the equation E = mc², representing the energy content when the object is at rest.

Relativistic Kinetic Energy

The kinetic energy of an object moving at relativistic speeds, calculated as K = (gamma - 1)mc², which illustrates how the energy increases disproportionately as the object’s speed approaches the speed of light.

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