Modern Physics I: Find time from energy

[maherelharake]

Homework Statement

A particle with a rest energy of 2400 MeV has an energy of 15 GeB (15x10^9 eV). Find the time in Earth's frame of reference necessary for this particle to travel from Earth to a star four light-years distant.

Homework Equations

The Attempt at a Solution

I thought about using the rest energy and total energy to find the Kinetic Energy. After that I used the velocity I found and used that to find the time. Is this a good start?

 

[Jack21222]

Homework Statement

A particle with a rest energy of 2400 MeV has an energy of 15 GeB (15x10^9 eV). Find the time in Earth's frame of reference necessary for this particle to travel from Earth to a star four light-years distant.

Homework Equations

The Attempt at a Solution

I thought about using the rest energy and total energy to find the Kinetic Energy. After that I used the velocity I found and used that to find the time. Is this a good start?

That's how I would start it. You might also be able to keep things in terms of c, since the distance is in terms of c. That way you don't need to convert back and forth from m/s.

 

[maherelharake]

Ok thanks. I tried to work it out and this is what I got. I ended up getting a value of 1.26E10 eV for kinetic energy. Using that, I got the ratio v/c to equal .987. I used that to get a time of 4.05 light years for the answer. Any thoughts? Thanks in advance.

 

[maherelharake]

I worked on this problem again today, but couldn't come up with any other way to think about it. If anyone can confirm my above thinking, I will be appreciative.

 

[paranormal]

Your approach is a good starting point. In modern physics, the concept of rest energy is important as it relates to the mass-energy equivalence principle. Using the equation E=mc^2, we can find the rest mass of the particle to be 2.667x10^-13 kg. From there, we can use the equation E=mc^2 to find the kinetic energy of the particle, which is 4.8x10^22 J. Using the formula for kinetic energy, KE=1/2mv^2, we can solve for the velocity of the particle, which is approximately 0.9999999999999999999999999999 c (the speed of light).

Next, we can use the equation d=vt to find the distance the particle will travel in a given time. Since we are looking for the time it takes for the particle to travel 4 light-years, we can rearrange the equation to t=d/v. Plugging in the distance of 4 light-years (3.784x10^16 m) and the velocity we found earlier, we get a time of approximately 4.22 years. Therefore, in Earth's frame of reference, it would take approximately 4.22 years for the particle with an energy of 15 GeV to travel from Earth to a star four light-years away.

It is important to note that this calculation assumes the particle is traveling at a constant velocity, which may not be the case in reality. Additionally, the effects of relativity may also come into play, which could affect the calculated time. Further analysis and calculations would be needed to accurately determine the time for this particle to travel to the distant star.