The document describes a relativistic momentum paradox scenario involving two equal masses connected by a massless string and constrained to move parallel at a speed v. When the constraints are removed, the masses collide and stick together into a single blob with greater mass than the sum of the initial masses due to their collision speed. However, the document reasons that the x-direction momentum must remain constant, so the speed of the combined blob must be less than v, slowing down the overall apparatus.

1. Week 77 (3/1/04)
Relativistic momentum paradox
Two equal masses are connected by a massless string with tension T. (By “massless”,
we mean that it has no mass in its unstretched, zero-length state.) The masses
are constrained to move with speed v along parallel lines, as shown below. The
constraints are then removed, and the masses are drawn together. They collide and
make one blob which continues to move to the right. Is the following reasoning
correct? If your answer is “no”, then state what is invalid about whichever of the
four sentences is/are invalid.
“The forces on the masses point in the y-direction. Therefore, there is no change
in momentum in the x-direction. But the mass of the resulting blob is greater than
the sum of the initial masses (because they collided with some relative speed).
Therefore, the speed of the resulting blob must be less than v (to keep px constant),
so the whole apparatus slows down in the x-direction.”
v
v
T