Calculate the length of a meter stick moving with a speed of v = 0.9995c as measured by an
observer at rest.
To calculate the length of a meter stick moving at a speed of v = 0.9995c (where c is the speed of light in a vacuum), we need to use the Lorentz contraction formula. The Lorentz contraction formula relates the length of an object as measured by an observer at rest (L') to the length of the object when it is at rest (L) and its velocity (v).
The formula is given by:
L' = L * sqrt(1 - (v^2/c^2))
Where:
L' is the length of the meter stick as measured by the observer at rest.
L is the length of the meter stick when it is at rest (in this case, 1 meter).
v is the velocity of the meter stick relative to the observer (0.9995c).
c is the speed of light in a vacuum (approximately 3 x 10^8 meters per second).
Substituting the given values into the formula, we can calculate the length of the meter stick as measured by the observer at rest:
L' = 1 * sqrt(1 - (0.9995^2)/(c^2))
Note that for simplicity, I will approximate c to be 3 x 10^8 meters per second.
L' = 1 * sqrt(1 - (0.9995^2)/(9 x 10^16))
L' = 1 * sqrt(1 - (0.99900025)/(9 x 10^16))
L' = 1 * sqrt(1 - 0.000000000000000000036655)
L' = 1 * sqrt(0.999999999999999999963345)
L' ≈ 1 * 0.999999999999999999981663
L' ≈ 1
Therefore, the length of the meter stick as measured by the observer at rest is approximately 1 meter.