All GRE Subject Test: Physics Resources
Example Question #1 : Length Contraction
A meter stick, at an angle of 30 degrees with the x-axis, is traveling at 0.6c in the direction of the positive y-axis. To a stationary observer, how long does the meter stick appear to be?
Length contraction only occurs in the direction of motion. This means that the x component of the length, which is cos(30), does not change; length contraction only occurs the the y component, which is sin(30).
First, we find the Lorentz factor:
Next, we apply the time dilation equation to the length in the y direction:
Finally, we find the total length by combining the length-contracted y component and the unchanged x component:
Example Question #2 : Length Contraction
A rocket of length 5 meters passes an observer on earth. The observer measures the passing rocket to be 3 meters long. What is the velocity of the rocket in the reference frame of the Earth-based observer?
Length contraction is given by
Where in this case,
The Lorentz factor is given by:
Combining these two equations, we get:
Solving for v: