What is the total kinetic energy of two protons in different reference frames?

AI Thread Summary
The discussion focuses on calculating the total kinetic energy of two protons moving at 0.5c in different reference frames. In frame S', the calculated kinetic energy is 290 MeV, but the initial attempt yielded 270 MeV using the classical formula 1/2 mv^2, which is incorrect for relativistic speeds. Participants emphasize the necessity of using the relativistic kinetic energy formula instead. The conversation highlights the confusion surrounding the application of classical mechanics in relativistic contexts. Accurate calculations require understanding relativistic effects on mass and energy.
PsychonautQQ
Messages
781
Reaction score
10

Homework Statement


In the reference frame S', two protons, each moving at .5c, approach each other head on. Calculate the total kinetic energy of the two protons in frame S', and calculate the total kinetic energy of the two protons as seen in reference frame S which is moving with one of the protons.






The Attempt at a Solution


So for the first part apparently the answer I'm looking for is 290MeV

v = .5c so γ = 1.1547

using 1/2 mv^2
m = 1.6726E-27
v = .5(3E8)

and then multiplying this times two for two protons and 1.15 from gamma, then converting that to eV by 1J = 6.24E18 eV I get 270MeV.. back of the book says 290 MeV.. what am I doing wrong ;-(?
 
Physics news on Phys.org
PsychonautQQ said:
using 1/2 mv^2

You'll need to use the relativistic formula for kinetic energy.
 
However we will not provide it. lol
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Kinetic Energy of Colliding Protons
2
Replies
54
Views
10K
Kinetic energy in center of mass reference frame
Replies
3
Views
1K
Special Relativity kinetic energy
Replies
4
Views
2K
Relativistic motion and length contraction
Replies
44
Views
2K
Calculate the kinetic energy of two alpha particles
Replies
2
Views
1K
What Was the Initial Speed of the Proton in a Collision?
Replies
2
Views
3K
Calculating Speed of Protons in a Linear Accelerator: 530 MeV Kinetic Energy
Replies
20
Views
4K
Length contraction numerical problem
Replies
1
Views
1K
Total energy of a mass hanging on a spring
Replies
12
Views
3K
Kinetic Energy for particles (alpha decay)
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top