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 $c^{-}$ .

Name: Problem 65, Chapter 1: Calculus of a Single Variable
Uploaded: 2020-11-17T07:49:41-08:00
Duration: 1 min 35 s
Channel: Sriram Soundarrajan
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^- .

   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 $c^{-}$ .

Calculus of a Single Variable

Ron Larson, Bruce… 9th Edition

Chapter 1, Problem 65

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Solved by Expert Sriram Soundarrajan

11/17/2020

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Step 1: We are given the equation for the mass of a particle according to the theory of relativity: $$m=\frac{m_{0}}{\sqrt{1-\left(v^{2} / c^{2}\right)}}$$ 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 $c^{-}$ .

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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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