# Modern Physics I: Find time from energy

• maherelharake
Thanks for you help.In summary, the conversation discusses finding the time it would take for a particle with a rest energy of 2400 MeV and an energy of 15 GeB to travel from Earth to a star four light-years away. The individual suggests using the rest energy and total energy to find the kinetic energy, then using the velocity to determine the time. Another suggestion is to keep everything in terms of c, since the distance is also in terms of c. The individual also shares their calculations, resulting in a time of 4.05 light years for the answer.
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.

## 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?

maherelharake said:

## 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.

## 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.

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.

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.

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.

## 1. What is the equation for finding time from energy in Modern Physics I?

The equation for finding time from energy is t = E / P, where t is time in seconds, E is energy in joules, and P is power in watts.

## 2. Can this equation be used for all types of energy?

No, this equation is specifically for finding time from mechanical energy, which includes kinetic and potential energy. It cannot be used for other forms of energy such as thermal, electromagnetic, or nuclear energy.

## 3. How is this equation derived?

This equation is derived from the fundamental principle of energy conservation, which states that energy cannot be created or destroyed, only transferred or transformed. By rearranging the equation for power (P = E / t), we can solve for time.

## 4. What are the units for time and energy in this equation?

The units for time in this equation are seconds (s), and the units for energy are joules (J). Other commonly used units for energy, such as kilojoules (kJ) or electronvolts (eV), can also be used in this equation as long as they are consistent with the unit for time.

## 5. Can this equation be used for both initial and final energy values?

Yes, this equation can be used for both initial and final energy values as long as the units are consistent. It can also be used to find the time for a specific change in energy, such as from an initial value of 100 J to a final value of 50 J.

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