F = ma doesn't work when aproaching c

  • Context: Undergrad 
  • Thread starter Thread starter Jacob_hull
  • Start date Start date
  • Tags Tags
    Work
Click For Summary

Discussion Overview

The discussion centers around the implications of special relativity on the classical equation F = ma, particularly as an object's velocity approaches the speed of light (c). Participants explore concepts such as mass increase, the inability of massive objects to reach c, and the validity of F = ma at relativistic speeds.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why mass increases as an object approaches c and whether this makes it impossible for the object to reach c, expressing a desire for a clearer explanation.
  • Another participant describes two approaches to understanding mass in relativity: the older view where mass increases (m = γm₀) and the more recent view where mass is treated as constant (F = mγa), noting that both lead to the same predictions.
  • A different participant asserts that mass increases due to the relationship m = E/c² and E = 1/2mv², suggesting that increased velocity leads to increased energy and thus increased mass.
  • This participant also states that a massive object cannot reach the speed of light and argues that F = ma does not apply at that speed because it would imply infinite force and mass.
  • One participant expresses gratitude for the clarification, indicating that such concepts were not covered in their previous education.

Areas of Agreement / Disagreement

Participants express various interpretations of mass and force in the context of relativity, with no consensus reached on the best way to describe these phenomena. Some participants support the idea of mass increase, while others suggest alternative frameworks that do not rely on this concept.

Contextual Notes

Participants reference different definitions and interpretations of mass and force, highlighting the complexity of reconciling classical mechanics with relativistic physics. The discussion includes unresolved assumptions about the nature of mass and energy at relativistic speeds.

Jacob_hull
Messages
2
Reaction score
0
Hello all,

Im only a student, taking physics in college in september, However I have read up on the level of physics I will be studying. One thing that I couldn't get my head round, Why when an object aproaches c does its mass increase? Am I right in saying this also makes it impossible from the object to reach c? Also why does this cancel out f = ma?

Sorry if this seems like a stupid question, but it just sparked an interest in my mind and I couldn't find an explanation that actually fully explained it to me. Thanks all.
 
Physics news on Phys.org
Welcome to Physics Forums!

There are basically two ways of describing this in relativity.

The more old-fashioned way is to write F=ma, and say that [itex]m=\gamma m_o[/itex], where [itex]m_o[/itex] is the mass the object has when it's at rest.

More recently (roughly within the last 50 years), it's been more common to write [itex]F=m\gamma a[/itex], and treat m as a constant.

So depending on which description you prefer, you can either say that mass increases or it doesn't increase, but either way the prediction is the same.

It doesn't cancel out F=ma completely. At velocities that are small compared to the speed of light, [itex]\gamma[/itex] is very close to 1, so F=ma is approximately right. That's why people believed F=ma was exact for hundreds of years.

Yes, this is one way of seeing that an object can't reach c. As its velocity gets close to c, [itex]\gamma[/itex] approaches infinity, so the force required in order to maintain the same acceleration also approaches infinity.

For an explanation of why this happens: http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html#Section1.3
 
Last edited by a moderator:
Jacob_hull said:
Hello all,

Im only a student, taking physics in college in september, However I have read up on the level of physics I will be studying. One thing that I couldn't get my head round, Why when an object aproaches c does its mass increase? Am I right in saying this also makes it impossible from the object to reach c? Also why does this cancel out f = ma?

Sorry if this seems like a stupid question, but it just sparked an interest in my mind and I couldn't find an explanation that actually fully explained it to me. Thanks all.

The mass increases because m = e/c^2 and E = 1/2mv^2

This means that if your velocity increases your energy increases your mass increases.

You are correct, a massive object can't reach the speed c.

Also f=ma does not work at speed c because the force would be infinite along with the mass which essentially states 1=1 since "a" now equals next to 0. Perhaps it works it is just not very interesting.
 
Thanks for the reply, this sort of stuff doesn't get explained to you in Secondary school it was basically f=ma end of. But I understand now so thanks a lot :)
 

Similar threads

'F=ma' Physics competition preparation help
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Series Expansion of the Infinitesimal Spacetime Interval
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Relational event horizons?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Explain Relativistic Mass: Special Relativity & F=ma
  • · Replies 7 ·
Replies
7
Views
2K
F=ma Prep and Resources for High School Students
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Is Acceleration an Invariant? (Taylor & Wheeler)
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Question about geometrical engineering (placeholder name)
  • · Replies 32 ·
2
Replies
32
Views
2K
High School A Scenic Trip as a Spaceship at 0.999...c, and questions that arise
  • · Replies 36 ·
2
Replies
36
Views
4K
Undergrad Synchronizing clocks at different locations to measure speed of light
  • · Replies 58 ·
2
Replies
58
Views
6K
High School Can an Object Exceed the Speed of Light?
  • · Replies 12 ·
Replies
12
Views
2K