Struggling with a Physics Problem: Calculating Meson Velocities

In summary, the question posed is about determining the greatest and least possible speeds of two pi mesons that result from the decay of a high-speed K0 meson. The momentum of the pi mesons in the rest frame of the decaying meson must be calculated, and it is unclear if this needs to be transformed back into the labframe. It is also uncertain if the different speeds are due to measurement from the labframe or if they are actually different. The pi mesons must be going in opposite directions, and their lowest speed will be when they are perpendicular to the direction of motion of the decaying meson. When their directions of motion are parallel to the decaying meson's motion, one pi must compensate for the other
  • #1
blag
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I've just started an introductory modern physics course, and it's making me ache a bit. I'm unsure about this problem:


A high-speed K0 meson is traveling at a speed of 0.9c when it decays into a pi+ and a pi- meson. What are the greatest and least speeds that the mesons may have?

So, if I calculate the momentum of the two pi mesons in the rest frame of the decaying meson... well... I've gotten that far. I'm not sure if I need to transform the momentum somehow back into the labframe. I know I can transform the velocity, but that doesn't seem useful.



And then I have some inkling that the different velocities depend on the direction of the resulting mesons, but I'm not sure what laws to use to obtain them. It's also not clear to me whether the different speeds are only to be different because they're being measured from the labframe or because they're actually different.

I'd appreciate any advice/help that could be given.
 
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  • #2
I think I understand that the particles must be going in opposite directions, and that their lowest speed will be when both directions are perpendicular to the direction of motion of the decaying meson. When the directions of motion are parallel to the decaying particle's motion, one pi has to compensate for the other pi's motion against the original direction, and thus it must be going faster.

I'm uncertain about the above, but even if it is so, I'm not sure how to apply the relativistic transforms to the problem.

thanks
 
  • #3


I understand that learning new concepts and solving problems can be challenging, especially in a subject like modern physics. It is completely normal to feel unsure and have questions when tackling a problem like calculating meson velocities.

Firstly, it is important to understand the concept of relativity and how it affects the measurement of velocities. In this problem, the velocity of the K0 meson is given in terms of the speed of light (c), which is the maximum speed that anything can travel in the universe. This means that the velocity of the K0 meson is already close to the speed of light, and any further increase in velocity is not possible.

Now, to calculate the greatest and least speeds of the pi+ and pi- mesons, we need to consider the conservation of momentum. In the rest frame of the decaying meson, the total momentum before and after the decay must be equal. This means that the momentum of the two pi mesons must be equal to the momentum of the K0 meson before it decayed.

To transform the momentum back into the labframe, we can use the Lorentz transformation equations. These equations allow us to calculate the velocities of the pi+ and pi- mesons in the labframe, taking into account the relative motion between the two frames.

The direction of the resulting mesons does indeed affect their velocities, as the velocity of an object is a vector quantity and includes both magnitude and direction. The laws that govern the relationship between velocity and direction are the laws of vector addition and subtraction.

In conclusion, to solve this problem, you will need to use the concepts of relativity, conservation of momentum, and Lorentz transformations. It is also important to pay attention to the direction of the resulting mesons and use the laws of vector addition and subtraction. Don't be discouraged if it takes some time to fully understand these concepts and how to apply them. Keep practicing and seeking help when needed, and you will eventually master this problem and others like it.
 

1. How can I calculate the velocity of a meson?

To calculate the velocity of a meson, you need to know its mass, energy, and momentum. Using the equation v = p/m, where v is velocity, p is momentum, and m is mass, you can solve for the velocity of the meson.

2. What is the difference between calculating meson velocities and other particle velocities?

The main difference is that mesons are unstable particles, meaning they have a short lifetime before decaying into other particles. This can make it more challenging to accurately measure their momentum and energy, which are necessary for calculating their velocity.

3. What units should I use when calculating meson velocities?

It is important to use consistent units when calculating meson velocities. The most commonly used units are meters for distance, kilograms for mass, and seconds for time. However, other units such as GeV/c (gigaelectronvolts per speed of light) are also commonly used in particle physics.

4. Are there any shortcuts or tricks for calculating meson velocities?

Unfortunately, there are no shortcuts or tricks for calculating meson velocities. It requires a thorough understanding of physics principles and accurate measurements of the meson's mass, energy, and momentum. However, using unit conversions and simplifying equations can make the calculation process easier.

5. How do experimental errors affect the accuracy of calculated meson velocities?

Experimental errors, such as uncertainties in measurements or equipment, can affect the accuracy of calculated meson velocities. It is important to minimize these errors as much as possible and use multiple measurements to improve accuracy. Additionally, using statistical analysis techniques can help quantify and account for these errors.

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