An observer moving at a speed of 0.960 c relative to a rod (Fig. P26.14) measure
ID: 2240874 • Letter: A
Question
An observer moving at a speed of 0.960 c relative to a rod (Fig. P26.14) measures its length to be 2.00 m and sees its length to be oriented at 30.0 o with respect to the direction of motion.
The proper length of the rod= 6.27 m
What is the orientation angle in a reference frame moving with the rod?
An observer moving at a speed of 0.960 c relative to a rod (Fig. P26.14) measures its length to be 2.00 m and sees its length to be oriented at 30.0 o with respect to the direction of motion. The proper length of the rod= 6.27 m What is the orientation angle in a reference frame moving with the rod?Explanation / Answer
Here
Length along the DIRECTION of Motion = 2*Cos(30)
= 1.732 m
L' = L0*sqrt(1 - v^2/c^2)
L0x = 1.732/sqrt(1 - 0.960^2)
= 6.1857 m
Along the Direction perpendiculat to the Motion
Length remains same , L0y = 2*Sin(30)
= 1 m
Therfore
Proper Length = sqrt(L0x^2 + L0y^2)
= sqrt(6.1857^2 + 1^2)
Proper length = 6.27 m
orientation angle = arctan(L0y / L0x)
= arctan(1/6.1857)
= 9.183 degree