For centuries, we accpeted Newton's 2nd Law as the standard model for motion. Then Einstien came along and siggested a modification in cases of high velocity. The Lorenz factor: γ(v)=(1/square-root of 1−(v^2/c^2)) a) The constant (c) is the speed of light, which is 3 * 10^8 m/s. What is the lim as v approaches 400 γ(v)? You will have to track many decimal places to see a difference from 1. A bullet travels 400 m/s; this limit indicates that time dilation is extremely small (and basically negigible) at that speed. b) In the movie Interstellar, time dialation occurs as 1 hour on the water planet corresponds to 7 years on earth. What is the factor γ in this case (what is the ratio of 7 years to 1 hour)? c) If we rearrange the equation for γ and solve for v, we get: v = c square-root of (γ^2 - 1/γ^2) What velocity v is necesary to get the γ you found in part (b)? d) What is the lim as v approaches c γ(v) ? Write a sentence explaining what this means in terms of time dilation.
1. For centuries, we accpeted Newton's 2nd Law as the standard model for motion. Then Einstien came along and siggested a modification in cases of high velocity. The Lorenz factor:
γ(v)=(1/square-root of 1−(v^2/c^2))
a) The constant (c) is the
b) In the movie Interstellar, time dialation occurs as 1 hour on the water planet corresponds to 7 years on earth. What is the factor γ in this case (what is the ratio of 7 years to 1 hour)?
c) If we rearrange the equation for γ and solve for v, we get:
v = c square-root of (γ^2 - 1/γ^2)
What velocity v is necesary to get the γ you found in part (b)?
d) What is the lim as v approaches c γ(v) ? Write a sentence explaining what this means in terms of time dilation.
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