What is the Speed of a Proton at Triumf?

In summary, to determine the speed of a proton with a kinetic energy of 500 MeV, we need to use special relativity and the formula KE = (gamma -1)mc^2, where gamma = (1-v^2/v^2)^(-1/2). The mass of the proton is 938.27 MeV/c^2 and "triumf" refers to a particle accelerator. The correct answer is 0.758c, where c is the speed of light. The incorrect answer of 1.0323c was obtained by plugging in the given numbers to the equation without considering special relativity.
  • #1
erinec
31
0

Homework Statement


Determine the speed of a proton whose kinetic energy is 500 MeV. The mass of a proton is 938.27 MeV/c2.


Homework Equations


K = (1/2)mv2??



The Attempt at a Solution


The correct answer is supposed to be 0.758c, where c is the speed of light.
Of course, I plugged in the given numbers to the equation and got the wrong answer 1.0323 c. What did I do wrong? What does it mean by "triumf"?

Thanks
 
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  • #2
You will need to use special relativity to tackle this problem. Triumf is just a particle accelerator.
 
  • #3
The formula KE = (gamma -1)mc^2 may be helpful for your endeavors.
where gamma = (1-v^2/v^2)^(-1/2)
 

FAQ: What is the Speed of a Proton at Triumf?

What is the speed of a proton at TRIUMF?

The speed of a proton at TRIUMF (Tri-University Meson Facility) is approximately 99.999999% the speed of light, or 299,792,458 meters per second. This is achieved using powerful particle accelerators.

How is the speed of a proton at TRIUMF measured?

The speed of a proton at TRIUMF is measured using specialized detectors that track the path and time of flight of the proton. By measuring the time it takes for the proton to travel a known distance, its speed can be calculated.

How does the speed of a proton at TRIUMF compare to other particle accelerators?

The speed of a proton at TRIUMF is comparable to other high-energy particle accelerators, such as the Large Hadron Collider (LHC) at CERN. However, TRIUMF is unique in its ability to accelerate both protons and other particles, such as neutrons and muons, to high speeds.

What is the significance of studying the speed of protons at TRIUMF?

Studying the speed of protons at TRIUMF allows scientists to better understand the fundamental particles that make up our universe. It also has practical applications, such as in medical imaging and cancer treatment, where high-energy protons can be used to target and destroy cancer cells.

Can the speed of a proton at TRIUMF be changed?

Yes, the speed of a proton at TRIUMF can be changed by adjusting the intensity and energy of the particle accelerator. This allows scientists to study the effects of different speeds on particles and their interactions, providing valuable insights into the nature of matter.

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