19. •••

(a) To see that length contraction is negligible at everyday speeds, determine the length contraction

(ΔL) of an automobile 5.00 m long when it is traveling at 100 km/h. The diameter of an atomic nucleus is on the order of 10−15 m. How does your answer compare to this?

(b) Suppose that it is possible to measure a length contraction for this car of 0.0100 mm or larger. What minimum car speed would be required to detect this effect? [Hint for (a): Express the length contraction in terms of x = v/c and recall that if x  1, then 1−x2 ≈1−(x2 /2).]