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

In summary, the total kinetic energy of two protons approaching each other head on in reference frame S' is 290 MeV, calculated using the relativistic formula for kinetic energy. As seen in reference frame S, which is moving with one of the protons, the total kinetic energy is 270 MeV, which is slightly lower due to the effects of relativity.
  • #1
PsychonautQQ
784
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 ;-(?
 
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  • #2
PsychonautQQ said:
using 1/2 mv^2

You'll need to use the relativistic formula for kinetic energy.
 
  • #3
However we will not provide it. lol
 

1. What is the theory of relativity and how does it affect energy?

The theory of relativity, proposed by Albert Einstein, states that the laws of physics are the same for all observers in uniform motion. This theory has two parts: the special theory of relativity, which deals with objects moving at constant speeds, and the general theory of relativity, which includes gravity. The theory of relativity affects energy by showing that energy and mass are equivalent and can be converted into one another, as expressed by the famous equation E=mc².

2. What is the difference between relativistic and classical energy?

Classical energy is based on Newton's laws of motion and does not take into account the effects of high speeds or gravity. Relativistic energy, on the other hand, considers the effects of special relativity and general relativity, which can significantly impact the energy of an object at high speeds or in the presence of strong gravitational fields. In classical energy, the kinetic energy of an object is calculated as ½mv², while relativistic energy uses the equation E=γmc², where γ is the Lorentz factor.

3. How does time dilation affect the energy of a moving object?

According to the theory of relativity, time is relative and can be affected by the speed of an object. As an object approaches the speed of light, time slows down for that object. This is known as time dilation. As a result, the energy of a moving object appears greater to an observer outside of the object due to the increased time dilation and the resulting increase in relativistic energy.

4. What is the mass-energy equivalence principle?

The mass-energy equivalence principle, also known as Einstein's famous equation E=mc², states that mass and energy are two forms of the same thing and are interchangeable. This means that a small amount of mass can be converted into a large amount of energy, as seen in nuclear reactions. It also means that energy can be converted into mass, as demonstrated by particle accelerators.

5. How does the concept of relativistic energy impact the study of astrophysics?

The concept of relativistic energy has had a significant impact on the study of astrophysics. It is used to explain the tremendous amount of energy released in supernovae explosions, the behavior of particles in the extreme environments of black holes, and the formation of the universe. Relativistic energy is also used in the development of theories such as the Big Bang and the inflationary model of the universe.

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