Relativistic speed of a particle

Click For Summary
To find the speed of a particle whose total energy is twice its rest energy, the equation E² = p²c² + m²c⁴ is utilized. The attempt led to the conclusion that momentum p equals SQRT(3)mc, but this approach mistakenly equated momentum with mv, which is incorrect in relativistic physics. In relativity, momentum is defined as p = gamma*mv, where gamma is the Lorentz factor. The correct method involves applying the relativistic energy-momentum relationship to derive the particle's speed. Understanding the distinction between classical and relativistic momentum is crucial for solving such problems.
harpf
Messages
12
Reaction score
0

Homework Statement


Find the speed of a particle whose total energy is twice its rest energy.

Homework Equations


E2 = p2c2 +m2c4

The Attempt at a Solution


4m2c4 = p2c2 +m2c4
3m2c4 = p2c2
SQRT(3)mc2 = pc
SQRT(3)mc = p
SQRT(3)mc = mv
SQRT(3)c = v
I know I can use E = gamma*mc2 to get the answer, but what have I done wrong in my approach? Thank you.
 
Physics news on Phys.org
harpf said:
SQRT(3)mc = p
SQRT(3)mc = mv
Your mistake was thinking that momentum equals mv. That's not true in relativity. In relativity, p = gamma*mv.
 
Thank you. I appreciate the help.
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
View full post »

Similar threads

Ultra-Relativistic Particle Decaying to Identical Particles
  • · Replies 1 ·
Replies
1
Views
1K
Photon collides with stationary electron
  • · Replies 6 ·
Replies
6
Views
5K
Escape Velocity of a Neutron Star: Relativistic Calculation
  • · Replies 1 ·
Replies
1
Views
2K
Calculating the Planck Length
  • · Replies 3 ·
Replies
3
Views
661
Energy to accelerate an 1kg object to 0.9965c?
  • · Replies 8 ·
Replies
8
Views
3K
Relativistic Mass Exam Question
  • · Replies 1 ·
Replies
1
Views
2K
How can I derive the relativistic de Broglie equation?
  • · Replies 23 ·
Replies
23
Views
4K
Correction to non relativistic KE
  • · Replies 19 ·
Replies
19
Views
3K
Relativistic Particle Speed Approximation using Total Energy
  • · Replies 1 ·
Replies
1
Views
1K
High School What is m in Kinetic Energy? Relativistic mass or Rest mass?
  • · Replies 55 ·
2
Replies
55
Views
6K