All Problems

Relativistic Mechanics

Problem 1.341

In a triangle the proper length of each side equals aa. Find the perimeter of this triangle in the reference frame moving relative to it with a constant velocity VV along one of its (a) bisectors; (b) sides. Investigate the results obtained at VcV \ll c and Vc,V \rightarrow c, where cc is the velocity of light.

Reveal Answer
1.341. (a) P=a(1+43β2)P=a\left(1+\sqrt{4-3 \beta^{2}}\right) (b) P=a(1β2+4β2)P=a\left(\sqrt{1-\beta^{2}}+\sqrt{4-\beta^{2}}\right) Here β=V/c\beta=V / c