How Do You Calculate Kinetic Energy in Relativistic Collisions?

In summary, a particle mass ##m## with kinetic energy ##k## collides with a stationary particle of mass ##2m##, creating a composite mass of ##\sqrt{17}m##. The value of ##k## can be found using mass-energy conservation and momentum conservation, and is determined to be ##2mc^2##.
  • #1
1bigman
12
0

Homework Statement



We have a particle mass ##m## with kinetic energy ##k## colliding with a stationary particle of mass ##2m##. The collision creates a composite mass of ##\sqrt{17}m##. Find the value of ##k##

Homework Equations

The Attempt at a Solution



I have tried using mass-energy conservation and also momentum conservation, but I can't seem to get the required result of ##k=2mc^2##
 
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  • #2
Please show your work. Simply generically describing what you tried unsuccessfully isn't helpful at all.
 
  • #3
vela said:
Please show your work. Simply generically describing what you tried unsuccessfully isn't helpful at all.

My apologies. Fairly new round here... I've figured it out now, but many thanks anyways
 

What is a relativistic collision?

A relativistic collision is a type of collision that involves objects moving at a significant fraction of the speed of light. This means that the laws of special relativity must be taken into account when calculating the effects of the collision.

What are the key principles of special relativity that apply to relativistic collisions?

The two key principles of special relativity that apply to relativistic collisions are time dilation and length contraction. Time dilation states that time appears to pass slower for objects moving at high speeds, while length contraction states that objects appear to shorten in the direction of motion.

How do relativistic collisions differ from classical collisions?

Relativistic collisions differ from classical collisions in several ways. In classical collisions, the objects involved are typically moving at much lower speeds, and the effects of special relativity can be ignored. Additionally, in relativistic collisions, the total energy and momentum of the system must be conserved, while this is not necessarily the case in classical collisions.

What are some real-world applications of relativistic collisions?

Relativistic collisions have many real-world applications, including in particle accelerators and nuclear reactors. They are also important for understanding the behavior of high-speed particles in space, such as cosmic rays and particles in the solar wind.

How are relativistic collisions studied and analyzed?

Relativistic collisions are studied and analyzed using mathematical models and equations based on the principles of special relativity. These models take into account the velocities and masses of the objects involved, as well as the conservation of energy and momentum. They are also studied through experiments, such as those conducted in particle accelerators.

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