Here’s a little physics riddle. It’s really meant as a moment of self-reflection for physics teachers (I invite you to compare what answers you’d give within Relativity Theory).
We’re in the context of Newtonian mechanics.
There are three small bodies. In the inertial coordinate system (t, x, y, z), we know the following about the three bodies (at a given instant of time):
- The first has mass 3 kg
- The second has velocity (1, 0, 0) m/s
- The third has momentum (2, 0, 0) kg⋅m/s
Now consider a new coordinate system (t’, x’, y’, z’) related to the first by the following transformation (a Galileian boost):
t’ = t, x’ = x - u⋅t, y’ = y, z’ = z with u = 1 m/s
Questions:
- What is the mass of the first body in the new coordinate system?
- What is the velocity of the second body in the new coordinate system?
- What is the momentum of the third body in the new coordinate system?
Can you give definite answers to these three questions, and motivate your answers with simple physical principles? Note that by “definite answer” I don’t necessarily mean an answer with a definite numerical value.
The new coordinate system is moving one meter per second in the x-direction. This is small enough compared to the speed of light that we can ignore relativity. So the mass is the same and the velocity and momentum just get shifted by one meter per second, no?
Yes we’re considering Newtonian mechanics in any case. What I’m especially curious about is what physical principles people use to motivate their answers.
Regarding the third body, consider the case where its mass is, say, 2 kg, and the case where it’s 1 kg instead (the momentum being the same).