Question

Relativity According to the theory of relativity, the mass $m$ of a particle depends on its velocity $v .$ That is, $m=\frac{m_{0}}{\sqrt{1-\left(v^{2} / c^{2}\right)}},$ where $m_{0}$ is the mass when the particle is at rest and $c$ is the speed of light. Find the limit of the mass as $v$ approaches $c$ from the left.

Name: Problem 58, Chapter 1: Calculus of a Single Variable
Uploaded: 2019-07-24T21:21:41-08:00
Duration: 4 min 44 s
Channel: Carlos Pinilla
Description: Relativity According to the theory of relativity, the mass m of a particle depends on its velocity v . That is, m=(m0)/(√(1-(v^2 / c^2))), where m0 is the mass when the particle is at rest and c is the speed of light. Find the limit of the mass as v approaches c from the left.

   Relativity According to the theory of relativity, the mass $m$ of a particle depends on its velocity $v .$ That is, $m=\frac{m_{0}}{\sqrt{1-\left(v^{2} / c^{2}\right)}},$ where $m_{0}$ is the mass when the particle is at rest and $c$ is the speed of light. Find the limit of the mass as $v$ approaches $c$ from the left.

Calculus of a Single Variable

Ron Larson 11th Edition

Chapter 1, Problem 58

Instant Answer

Solved by Expert Carlos Pinilla

07/24/2019

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Step 1: We are given the equation $m=\frac{m_{0}}{\sqrt{1-\left(v^{2} / c^{2}\right)}}$ and we are asked to find the limit of the mass as $v$ approaches $c$ from the left. Show more…

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Relativity According to the theory of relativity, the mass $m$ of a particle depends on its velocity $v .$ That is, $m=\frac{m_{0}}{\sqrt{1-\left(v^{2} / c^{2}\right)}},$ where $m_{0}$ is the mass when the particle is at rest and $c$ is the speed of light. Find the limit of the mass as $v$ approaches $c$ from the left.

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Key Concepts

Special Relativity

Special relativity is a theory that fundamentally redefines concepts of space, time, and mass at high velocities. One of its key predictions is that as an object’s velocity approaches the speed of light, its relativistic mass increases according to the equation m = m0 / ?(1 - v²/c²). This reflects the idea that it requires increasingly large amounts of energy to accelerate an object as it nears the speed limit posed by the speed of light, c.

Calculus Limit

The concept of a limit in calculus is used to describe the behavior of a function as its input approaches a particular value. In this context, the limit is taken as the velocity v approaches the speed of light c from values less than c. It illustrates how the function representing the relativistic mass explodes, or tends towards infinity, indicating the physical impossibility of reaching the speed of light for massive objects.

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