17.2 Modern Physics: Relativity of Length

In this online activity we learned how relativity distorts the length of objects as they approach the speed of light. We will be using length contraction equation L=L_0/sqrt[1-(v^2/c^2)]. As in the previous activity questions will be followed with a screenshot and the appropriate answers.

Question #1: Imagine riding on the left end of the light clock. A pulse of light departs the left end, travels to the right end, reflects, and returns to the left end of the light clock. Does your measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth?

Answer: The round trip time depends on whether the clock is stationary or moving.

Question#2: Will the round-trip time interval for the light pulse as measured on the earth be longer, shorter, or the same as the time interval measured on the light clock?

Answer: The round-trip time will be measured to be shorter than the time measured relative to the earth.

Question #3: You have probably noticed that the length of the moving light clock is smaller than the length of the stationary light clock. Could the round-trip time interval as measured on the earth be equal to the product of the Lorentz factor and the proper time interval if the moving light clock were the same size as the stationary light clock?

Answer: Yes, if the loreanzt factor is known and the time required  for a moving clock to travel a given distance we can use the formula stated at the beginning of the activity to calculate the time required to reach the same distance relative to the stationary frame.

Question #4: A light clock is 1000 m long when measured at rest. How long would earth-bound observer's measure the clock to be if it had a Lorentz factor of 1.3 relative to the earth?

 Answer: The Lorentz factor is 1.3, and the length is 1000m at rest, so we use the formula given at the beginning of this activity to calculate the contracted length. We obtain 1000/1.3  = 769 meters.