Question

An airplane 40.0 m in length in its rest system is moving at a uniform velocity with respect to earth at a speed of 630 m/sec. (a) by what fraction of its rest length will it appear to be shortened to an observer on earth? (b) how long would it take by earth clocks for the ai rplane's clock to fall behind by one microsecond? (assume that special relativity only applies).

Answer 1

The required values are |ΔL| / Lo = 2.21 x 10^-12 and Δto = 5.25 d

Explanation:

• Length of airplane = 40 m
• Speed = 630 m/s

Solution:

(a) |ΔL| / Lo = 1 -  √  1 - B^2

|ΔL| / Lo = 1 - ( 1 - 1/2 B^2)

|ΔL| / Lo = 1/2  ( 630 / 3 x 10^8 )

|ΔL| / Lo = 2.21 x 10^-12

(b) Δto = τ / y -1

Δto = τ / (1 - B^2 )^-1/2  - 1

Δto = τ / (1 + 1 /2 B^2 -1 )

Δto = 2 τ  / B^2

Δto = 2 ( 1 x 10^-6 s ) ( 1 d / 86400 )/ ( 630 ) ( 2.998 x 10^8 )

Δto = 5.25 d

The required values are |ΔL| / Lo = 2.21 x 10^-12 and Δto = 5.25 d