**Problem : **
What is the energy of a particle with mass 3.2×10^{-27} kilograms and velocity 0.9*c*?

**Problem : **
A particle has a momentum with magnitude 1.2×10^{5} kgm/s and energy 4.42×10^{-11}
Joules. What is its mass?

**Problem : **
Two protons approach each other from opposite direction, traveling with equal and opposite speeds 0.6*c*.
The collide to form a single particle that is at rest. What is the mass of this particle? (The proton mass is
1.67×10^{-27} kilograms).

M = |

For the two protons this comes out as 4.175×10

**Problem : **
A particle of mass *m* and speed *v* approaches an identical particle at rest. The particles stick together
to form larger particle with mass M. What is the speed of the larger particle after the collision?

= |

Doing a little bit of algebra we find:

(1 - V^{2}/c^{2}) = V^{2}(1 - v^{2}/c^{2})âá’V = |

**Problem : **
Two particles with equal mass *m* approach each other with speed *u*. They collide to form a single
particle with mass *M*, which is at rest. Show the energy is conserved in the frame of the *M* particle.

M = |

The expression for energy conservation in the rest frame of the large particle is:

+ = |

Hence the energy is the same after the collision as before in this frame.

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