How do I calculate acceleration with a mass of Zero

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Discussion Overview

The discussion revolves around the calculation of acceleration for an object with zero mass when a force is applied, particularly in a vacuum. Participants explore theoretical implications, including nonrelativistic and relativistic perspectives, and the challenges posed by the concept of massless objects.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant asks how to calculate acceleration and speed for an object with zero mass when a force is applied.
  • Another participant states that calculating acceleration leads to a division by zero, implying that the scenario is problematic.
  • Some participants mention that massless particles travel at the speed of light, referencing Einstein's Theory of Relativity.
  • There is a discussion about the implications of applying force to increasingly smaller masses, leading to infinite acceleration as mass approaches zero.
  • A participant expresses a desire for a formula that ignores the speed of light to calculate acceleration and speed for a massless object.
  • Another participant challenges the feasibility of the scenario, suggesting that if the laws of physics are disregarded, the outcome becomes arbitrary.
  • One participant emphasizes that the laws of physics cannot be intentionally made to fail and questions the validity of the proposed scenario.

Areas of Agreement / Disagreement

Participants express disagreement regarding the treatment of massless objects and the implications of applying force in such scenarios. There is no consensus on how to approach the calculations or the validity of the underlying assumptions.

Contextual Notes

The discussion highlights limitations in the assumptions made about mass and force, particularly in relation to established physical laws. The scenario presented raises questions about the applicability of classical mechanics and relativity.

casio69
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Hi all,

If I have an object with zero mass in a vacuum and apply say 1n of force to the object how
can I calculate its acceleration, and current speed at any time?

Thanks all.
 
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You can't. You'll have a division by zero.
 
all massless particles travel at the speed of light.
 
As Vanadium50 pointed out, a = F/m gets you in trouble. You can understand this more clearly by considering what happens if you apply this same force to a succession of increasingly smaller masses. Look at the curve of a = F/m (a hyperbola), and you see that the lighter the mass, the higher the acceleration, which goes to infinity as the mass goes to zero.

That's the nonrelativistic answer, i.e. what Newton would have told you. Cragar's response comes from Einstein's Theory of Relativity, where there are no infinite speeds (or accelerations). The speed of light is the absolute speed limit, so massless particles must all move at that speed (they can't ever be at rest, or they would appear to be moving at a speed less than c to some observers).
 
belliott4488 said:
As Vanadium50 pointed out, a = F/m gets you in trouble. You can understand this more clearly by considering what happens if you apply this same force to a succession of increasingly smaller masses. Look at the curve of a = F/m (a hyperbola), and you see that the lighter the mass, the higher the acceleration, which goes to infinity as the mass goes to zero.

That's the nonrelativistic answer, i.e. what Newton would have told you. Cragar's response comes from Einstein's Theory of Relativity, where there are no infinite speeds (or accelerations). The speed of light is the absolute speed limit, so massless particles must all move at that speed (they can't ever be at rest, or they would appear to be moving at a speed less than c to some observers).

thanks. I was getting a div zero, and needed a fix for it. I also don't subscribe to the absolute speed limit thing. I need a formula that ignores the speed of light and gives me the acceleration and speed of a mass-less object.

Basically I need a way of working out the following scenrio.

An object with a mass of say 10kg is sat in geo stationary orbit.
The object has a way to reduce it's mass to zero.
It applies some thrust say 1n for 1 second
It then returns to normal mass
How far has it traveled?
 
casio69 said:
I also don't subscribe to the absolute speed limit thing. [...]
Fail.

(How were you going to push so hard against something that doesn't resist being pushed against, anyway?)
 
casio69 said:
Basically I need a way of working out the following scenrio.

An object with a mass of say 10kg is sat in geo stationary orbit.
The object has a way to reduce it's mass to zero.
It applies some thrust say 1n for 1 second
It then returns to normal mass
How far has it traveled?

The laws of physics will fail if you intentionally make them fail. What more do you want? If you want to pretend the laws of physics need not apply, your object has traveled to the planet infinity. Or it fell to the ground. Who knows? You make up the rules.
 
casio69 said:
I also don't subscribe to the absolute speed limit thing. I need a formula that ignores the speed of light and gives me the acceleration and speed of a mass-less object.
If you choose to ignore the laws of physics, then you can do anything you want (just ask superman!)...except speculate about it on this forum. On this forum, we deal only in reality. Thread locked.
 

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