0

(This is a quick one)

Suppose Im standing still (in my perspective) and a hoverboard is flying at $0.8c$ w.r.t me.

I see that the ball (red) is moving at $0.8c$. I measured earlier that the ball is $15$ kg, before it went on the hoverboard. So, its 'rest mass' is $15$ kg for me. But, when its on the hoverboard, its mass will be the 'relativistic mass' $m = γm$ (rest mass), which will be $25$ kg.

So, if I get on the hoverboard, and measure the mass of the ball, will I measure it to be $25$ kg, or $15$ kg?

i.e Is the 'rest mass' (or 'mass measured when object is rest in my frame') same in both cases or not?

enter image description here

Qmechanic
  • 220,844
Rohit Shekhawat
  • 1,306

1 Answers1

2

Rest mass of a body is the mass measured when the body is at rest w.r.t. you. It is always the same. Just make sure that the object's whose rest mass you want to measure is at rest w.r.t. you. The actual mass of the object will be greater than the rest mass if the object is in motion w.r.t. you.

It is impossible to measure the actual mass of a body in motion w.r.t us. We calculate the actual mass of a body in motion using the relativistic mass expression given by theory of relativity.

So, if you board the hoverboard, you will measure the mass of the red sphere to be $15.00$ kg only as the sphere is at rest w.r.t. you in that case (you will measure the rest mass only). At the same time, for an observer on the ground, its actual mass is $25.00$ kg, as that observer measures the speed of the sphere to be $0.8c$.