What is the Speed of a Proton at Triumf?

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To determine the speed of a proton with a kinetic energy of 500 MeV, special relativity must be applied due to the high energy involved. The mass of the proton is given as 938.27 MeV/c², and the correct speed is calculated to be 0.758c, where c is the speed of light. The initial attempt using the classical kinetic energy formula K = (1/2)mv² resulted in an incorrect value of 1.0323c. The relevant equation to use is KE = (gamma - 1)mc², where gamma accounts for relativistic effects. Understanding that "Triumf" refers to a particle accelerator is also essential for context.
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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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You will need to use special relativity to tackle this problem. Triumf is just a particle accelerator.
 
The formula KE = (gamma -1)mc^2 may be helpful for your endeavors.
where gamma = (1-v^2/v^2)^(-1/2)
 

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