Effect of Radiation Pressure on a Moving Object

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Discussion Overview

The discussion centers around the effects of radiation pressure on a moving object, specifically examining scenarios where the object absorbs or emits radiation. Participants explore the implications of these interactions on the object's velocity and momentum in different reference frames, touching on concepts from classical mechanics and relativity.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether a 1 kg mass sliding on a frictionless floor at 10 m/s slows down when exposed to radiation, which is absorbed by the mass.
  • Another participant suggests that if the radiation is absorbed, the mass must increase, leading to a decrease in speed due to conservation of momentum.
  • It is noted that in reference frames where the body is momentarily at rest, the radiation has a backward component due to aberration, which could affect the motion of the mass.
  • A different scenario is proposed where a mass emits radiation instead of absorbing it, raising the question of whether it would speed up or maintain its speed in the rest frame of the floor.
  • Participants discuss that the outcome of the mass's speed when emitting radiation depends on the direction of the emitted radiation, with some arguing that isotropic emission would not result in acceleration.
  • There is a suggestion that if the radiation is emitted vertically in the floor's rest frame, the object would lose mass and gain speed, while others argue that the emission direction must be considered in both frames.
  • Some participants express confusion about how the emission direction is perceived differently in the emitter's frame versus the ground's frame, leading to further exploration of the implications of isotropic versus non-isotropic radiation.
  • One participant emphasizes that a radiating spherical mass in free space would radiate equally in all directions, suggesting that it would not lose momentum in its own reference frame.
  • Another participant clarifies that while the emitter does not accelerate in any frame, it loses momentum in the ground frame as its mass decreases, while the radiation gains momentum.

Areas of Agreement / Disagreement

Participants express multiple competing views on the effects of radiation pressure and the resulting changes in momentum and speed of the mass. The discussion remains unresolved, with no consensus on the outcomes of the scenarios presented.

Contextual Notes

Participants highlight the importance of reference frames in understanding the behavior of the mass under radiation pressure, noting that assumptions about isotropy and the direction of radiation play critical roles in the analysis. There are unresolved mathematical steps and dependencies on definitions that affect the conclusions drawn.

  • #31
On a Dutch forum, there is a discussion about the following problem:

A ##1 \mathrm{kg}## mass slides across a frictionless floor with an initial velocity of ##10\, \mathrm{m/s}##. The top surface of the mass has an area of ##1\, \mathrm{m^2} ##. The floor is perpendicularly irradiated with light of intensity ## 1\, \mathrm{W/m^2} ##. How long does it take for the speed of the mass to decrease to ## 1\, \mathrm{m/s} ##?

opgavestraling2.webp


This can be seen as an interaction between the mass, the floor, and the incoming radiation.
Can I assume that the horizontal momentum of the mass remains constant when viewed from the frame of the floor?

More precisely: does the relativistic horizontal momentum of the mass remain constant from the initial state (1), throughout the interaction, until the final state (2)? That is,

$$
\gamma_1 m_1 v_1 = \gamma(t) m(t) v(t) = \gamma_2 m_2 v_2
$$

Is it valid to calculate the increase in mass via the energy absorbed from the incoming radiation, and then determine the change in velocity by assuming that the relativistic horizontal momentum remains constant?

ps No idea what is wrong with the LaTeX rendering.
[Mentors' note: You needed double hash delimiters not single dollar signs for the inline delimters. We've fixed this post for you, but next time check out our Latex help guide]
 
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  • #32
Didn't we discuss this already?

Yes, the point is that the horizontal momentum is conserved and the mass is the only thing with horizontal momentum. As long as you're allowed to assume there's no reflection and the radiation is perpendicular to the floor in the floor rest frame, anyway. And that it doesn't lose any energy by radiation during whatever period it's absorbing radiation.
 
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