Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space.One is traveling at 0.650c and the other at 0.850c.The satellites collide and somehow manage to stick together.What is the rest mass of the combined object after the collision?
A)100 kg
B)200 kg
C)277 kg
D)378 kg
E)312 kg

Question

Quizplus · Accepted Answer

The rest mass of the combined object after the collision can be found by using the principle of conservation of momentum and the relativistic formula for momentum, $p = \gamma m v$, where $m$ is the rest mass, $v$ is the velocity, and $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$ is the Lorentz factor. The total energy (rest mass energy plus kinetic energy) of the system before the collision is equal to the total energy of the system after the collision. The rest mass of the combined object is greater than the sum of the rest masses of the individual satellites due to the conversion of kinetic energy into mass, according to Einstein's equation $E = mc^2$. The correct calculation involves finding the total energy of both satellites before the collision and equating it to the rest mass energy of the combined object. The answer is not immediately intuitive and requires calculation, but the correct answer is 312 kg, reflecting the increase in mass due to the kinetic energy of the satellites being converted into mass upon collision.

Two Satellites with Equal Rest Masses of 100 Kg Are