- #1
agnimusayoti
- 240
- 23
- Homework Statement
- Suppose an observer O measures a particle of mass m moving in the x direction to have speed v, energy E, and momentum p. Observer O', moving at speed u in the x direction; measures v', E', and p' for the same object. (a) Use the Lorentz velocity transformation to find E' and p' in terms of m, u, and v. (b) Reduce (E')^2 - (p'c)^2 to its simplest form.
- Relevant Equations
- Lorentz velocity transformation:
$$v'=(v-u)/(1-(uv/c^2))$$
Relationship between energy-momentum:
$$E^2=(pc)^2 +(mc^2)^2$$
I try to use relativistic energy equation:
$$E'=\gamma mc^2$$
But, I use
$$\gamma=\frac{1}{\sqrt{(1-(\frac{v'}{c})^2}}$$
then I use Lorentz velocity transformation.
$$v'=\frac{v-u}{1-\frac{uv}{c^2}}$$
At the end, I end up with messy equation for E' but still have light speed c in the terms. How should I do to get E' just in terms of m, u, and v?
$$E'=\gamma mc^2$$
But, I use
$$\gamma=\frac{1}{\sqrt{(1-(\frac{v'}{c})^2}}$$
then I use Lorentz velocity transformation.
$$v'=\frac{v-u}{1-\frac{uv}{c^2}}$$
At the end, I end up with messy equation for E' but still have light speed c in the terms. How should I do to get E' just in terms of m, u, and v?