Question

If the airplane of Passage Problem 37.71 has a rest mass of 20,000kg , what is its relativistic mass when the plane is moving at 180m/s ?

a) 8,000kg

b) 12,000kg

c) 16,000kg

d) 25,000kg

e) 33,000kg

Short answer

Option-d is correct

Step-by-step solution

NOT GIVEN

This exercise is similar to Passage Problem 37.71 , but now we are asked to find the relativistic mass of the airplane, which is moving at u = 180m/srelative to the stationary observer. The relationship between the (given) rest mass m of the plane and its (unknown) relativistic mass $m_{rev}$ is $m_{rev}=\frac{m}{\sqrt{1-{\displaystyle \frac{u^2}{c^2}}}}$. Again, we use the speed of light in the alternate universe, which is c = 300m/s .

Realizing that m = 20,000kg and u = 180 m/s , the relativistic mass of the plane is

$m_{rev}=\frac{m}{\sqrt{1-{\displaystyle \frac{u^2}{c^2}}}}=\frac{20000}{\sqrt{1-{\displaystyle \frac{{180}^2}{{300}^2}}}}=25,000kg$

which is the answer of choice (d).

In the alternative universe, the plane would weigh 5,000kg more when it is moving than when it is at rest. Again, this is a substantial change that can't be overlooked every time it happens in this universe!