Consider two particles, each of rest mass $m_0 = 10 \,\textrm{kg}$, which in the laboratory frame of reference each have speed $\frac{12}{13}c$. They are headed toward each other, collide, and stick together. Because of momentum conservation, the resulting blob is at rest in the laboratory. What is the rest mass of the blob?

Consider two particles, each of rest mass $m_0 = 100\,\textrm{kg}$. One of these is at rest in the laboratory, and the other is headed toward it (from the right) at speed $\frac{255}{257}c$. The two particles stick together, and the blob moves to the left in the laboratory. What is the relativistic mass of the blob?

Determine the speed of the blob in the previous part.

Find the frame of reference in which the two particles are heading toward each other with equal but opposite velocities (much as in the first part of this problem). What is the velocity of this frame relative to the laboratory frame?