Relativistic energy and time dilation

[Marin]

hi there!

I`m stuck on the following two questions and I hope you could help me :)

I´m given the kinetic energy of a particle. How am I supposed to calculate its velocity? there´s no mass of rest, no total energy, just the kinetic energy.



2. While trying to calculate the time dilation in the inertial frame of a satellite, it´s velocity appears too small to experience relativistic effects. The satellite´s orbit´s radius around the Earth is 20.10^6m, which gives a velocity of v=1454,4 m/s (with respect to Earth´s angular velocity). Now plugging it into the Lorentz factor "gamma" it appears to be really insignificant! Am I doing something wrong there?


thanks a lot in advance!

 

[gabbagabbahey]

For your first question, I would assume that you are told what type of particle it is. If so, you can look up its rest mass and use that to calculate its velocity.For your 2nd question, I didn't bother plugging in the numbers, but your answer seems reasonable. The time dilation of a satellite is very small. If your calculator doesn't have enough significant digits to give you a more accurate answer than $\gamma=1$ , you can use a taylor approximation for gamma to get: $$\gamma=\left( 1-\frac{v^2}{c^2}\right)^{-1/2} \approx 1+\frac{v^2}{2c^2}$$ to give you a better answer.

 

[Marin]

thanks, gabbagabbahey!

but I still find it incorrect not to give such essential constants in the assignments. I thought I was doing it wrong :)