Relativistic Collision Effects on Speed, Mass

In summary, the question is about the effects of a collision between two balls of putty moving near the speed of light. The scenario involves a slight perpendicular displacement instead of a head-on collision, resulting in a rotating system. The final speed remains the same, but the final mass is smaller due to less energy going into mass conversion. If the rotation is stopped, the mass becomes smaller. This is in line with the equations of relativity. The system's mass is determined by the initial energies of the colliding bodies, regardless of whether they rotate or not. The final answer is confirmed by analyzing the collision from the center of mass frame.
  • #1
gsimo1234
7
0
To a moderator: this is a theoretical, concept-based question.

Say two balls of putty, moving relativistically near the speed of light, collide (although i understand this is not possible theoretically and realistically). They collide at a slight perpendicular displacement, instead of head-on, so that in the final state the stuck together system is rotating. Compared to the non-rotating head-on collision, how will this effect the final speed, and how will this effect the Mf' (final mass)? Imagine that you stop the lump from spinning, will its mass be great. less, or equal to Mf'?

Here is what I got out of this situation; Vf remains the same, since rotation does not affect the conservation of momentum. However, less "energy" goes into the mass conversion, so there is less mass. If we stop it from spinning, we do work on the system, adding this rotational energy into the system and the mass willl then be greater to the final mass.

I'm not sure if I'm understanding the theory correct.

P.S. Please don't say "it will vaporize" or "this is not possible"; Let's ASSUME that they stick together relativistically and also rotate, without vaporizing.
 
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  • #2
If two colliding bodies attach to each other, the system mass is determined with their initial energies solely. It does not matter whether they rotate or not. In the frontal collision it is their atoms/molecules that will rotate/vibrate more.

If you stop the rotation, the mass will become smaller because you take away some energy from the system.
 
  • #3
by looking at the equations of relativity, your answer actually does make sense; rotate or not, it will have the same final speed and thus same final mass! Thank you so much!

Can anyone confirm this?
 
  • #4
Yes, you can always analyze the collision from the center of mass frame. In that frame if the final mass is spinning then it will have more energy and therefore more mass than an otherwise identical non-spinning mass. This energy and mass will come from the original mass energy of the system.
 

1. What is the theory of relativity?

The theory of relativity is a fundamental principle of physics that explains the relationship between space and time. It was first proposed by Albert Einstein in the early 20th century and has since been tested and confirmed through numerous experiments.

2. How does the theory of relativity impact collisions at high speeds?

According to the theory of relativity, the mass of an object increases as its speed approaches the speed of light. This means that at high speeds, the mass of an object involved in a collision will be greater than its rest mass, resulting in different effects on the collision compared to non-relativistic speeds.

3. What is the equation for calculating relativistic mass?

The equation for calculating relativistic mass is m = m0 / √(1 - v^2/c^2), where m0 is the rest mass of the object, v is the velocity, and c is the speed of light. This equation takes into account the increase in mass at high speeds due to the theory of relativity.

4. How does the increase in mass at high speeds affect the speed of objects involved in a collision?

The increase in mass at high speeds results in a decrease in the velocity of the objects involved in a collision. This is because the total momentum of the system must remain constant, and an increase in mass leads to a decrease in velocity.

5. Are there any real-world applications of relativistic collision effects?

Yes, there are many real-world applications of relativistic collision effects. One example is in particle accelerators, where particles are accelerated to near the speed of light and collide with each other, producing new particles. The theory of relativity is also crucial in understanding the behavior of objects in space, such as satellites and spacecraft, which travel at high speeds and are affected by relativistic effects.

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