Active Physics lab - Relativity

Purpose:
To further analyze Einstein's 2nd postulate, which leads to relativity; which states that no object travels faster than speed of light.

Material:
A working laptop with internet connection and java.
Website: http://wps.aw.com/aw_young_physics_11/13/3510/898597.cw/index.html
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Questions were to be answered from section 17.1 and 17.2


17.1
Question 1: Distance traveled by the light pulse
How does the distance traveled by the light pulse on the moving light clock compare to the distance traveled by the light pulse on the stationary light clock?

Distance traveled by light on moving clock is "slower" than stationary clock.
In fact, it is off by γ factor, which was set to be 1.45. (Light on moving travels 1.45 times slower to an outside observer)


Question 2: Time interval required for light pulse travel, as measured on the earth
Given that the speed of the light pulse is independent of the speed of the light clock, how does the time interval for the light pulse to travel to the top mirror and back on the moving light clock compare to on the stationary light clock?

γ was set to be 1.41. The time on stationary was 6.67 and moving 9.40. 9.40s and 6.67s were related by a factor of 1.41, which was the value of constant.

 Question 3: Time interval required for light pulse travel, as measured on the light clock
Imagine yourself riding on the light clock. In your frame of reference, does the light pulse travel a larger distance when the clock is moving, and hence require a larger time interval to complete a single round trip?

No, the time in moving time reference does not differ from the time of rest frame. Although according to stationary observer, light travels slower.

Question 4: The effect of velocity on time dilation
Will the difference in light pulse travel time between the earth's timers and the light clock's timers increase, decrease, or stay the same as the velocity of the light clock is decreased?

The difference in light travel time is slower (decreased) as velocity is decreased. (As v -> 0, γ -> 1).

Question 5: The time dilation formula
Using the time dilation formula, predict how long it will take for the light pulse to travel back and forth between mirrors, as measured by an earth-bound observer, when the light clock has a Lorentz factor (γ) of 1.2.

Δt = γΔt_proper

1.2 = γ

1.2 = 1/(1-v^2/c^2)^0.5

solving for v yields

v = c/1.2 * (1.2^2 - 1)^0.5

v = 165,831,239.52 m/s

Question 6: The time dilation formula, one more time
If the time interval between departure and return of the light pulse is measured to be 7.45 µs by an earth-bound observer, what is the Lorentz factor of the light clock as it moves relative to the earth?

Solving for γ, 

γ = Δt / (Δt + 7.45μs)

17.2

Question 1: Round-trip time interval, as measured on the light clock
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?

Yes. The length "contracts" as the object travels relatively "fast." The faster the object moves (the closer its constant velocity to the speed of light, the shorter the distance / length is).

Question 2: Round-trip time interval, as measured on the earth
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?

Depends on whose frame of reference is measuring it. In the frame of the traveling clock, the time will be the same as the stationary one measured by a stationary observer. If the time of traveling clock is measured by a stationary observer, then: 1. length/ distance will appear shorter/ less, and 2, time it takes for the light to travel will be longer.

Question 3: Why does the moving light clock shrink?
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?

γ was set to be 1.41. Time was 6.61, while time proper was 9.50. They were off by γ factor, or 1.41 (refer back to time dilation). Since distance/ length is velocity * time, since time is longer in a moving object and it must always equal to velocity v (constant), then distance must decrease proportionally (by factor of γ).

Yes, the time interval as measured by earth (rest frame) is equal to lorentz factor γ times proper time interval (moving), hence Δt = γ(Δt_p)

Question 4: The length contraction formula
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?

L_p = 1000m

γ = 1.3

L = (L_p)/γ

L = 769.23 m