A right-angled construction frame ABC,when measured at rest,has dimensions as follows: AB = 28.00 m,AC = 10.00 m,and BC = 26.15 m.The frame is given a velocity of 0.80 c,relative to the space platform,in a direction parallel to AC.The dimensions of the moving frame are measured simultaneously by observers on the platform.In the figure,the length AB measured by these observers is closest to:
A)26.8 m
B)27.4 m
C)26.2 m
D)25.7 m
E)28.0 m

Question

A right-angled construction frame ABC,when measured at rest,has dimensions as follows: AB = 28.00 m,AC = 10.00 m,and BC = 26.15 m.The frame is given a velocity of 0.80 c,relative to the space platform,in a direction parallel to AC.The dimensions of the moving frame are measured simultaneously by observers on the platform.In the figure,the length AB measured by these observers is closest to:
A)26.8 m 
B)27.4 m 
C)26.2 m 
D)25.7 m 
E)28.0 m

Quizplus · Accepted Answer

According to the Lorentz transformation, the length contraction factor is given by:
$\sqrt{1-\frac{v^2}{c^2}}$
Plugging in the values, we get the length contraction factor to be:
$\sqrt{1-\frac{0.8^2}{1^2}}$
= $0.6$
Therefore, the length AB measured by observers on the platform is given by:
AB' = AB x length contraction factor
= 28 x 0.6
= 16.8 m
Therefore, the closest answer choice is A) 26.8 m.

A Right-Angled Construction Frame ABC,when Measured at Rest,has Dimensions as Follows