Question

6. A new employee at an Intergalactic Traffic Check Point gets excited and alerts her boss that one of the approaching space freighters (the Century Eagle) might be smuggling something. The employee measures the mass of the freighter to be 150.0 metric tonnes and notes in the log that it is travelling at 0.650c. The freighter documented that this run they have a total mass of 105 metric tonnes. Is the employee right to alert her boss?

Answer 1

Relativisti Mass of object is given by:

m = m0*

= Lorentz factor = 1/sqrt (1 - (v/c)^2)

m0 = Mass of freighter at rest = ? metric tons

m = Relativistic mass as measured by employee = 150.0 metric tons

v = speed of freighter = 0.650*c

So,

m0 = m/

m0 = m*sqrt (1 - (v/c)^2)

m0 = 150*sqrt (1 - (0.650*c/c)^2)

m0 = 150*sqrt (1 - (0.650)^2)

m0 = 113.99 = 114.0 metric tons

So that means mass of freighter at rest was 114.0 metric tons, which is higher than the mass documented by freighter.

So yes employee is right that freighter is smuggling something, and he should alert the boss.

Let me know if you've any query.