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Can you figure out this Physics problem?
The pressure increases by 10000 N/m squared for every meter of depth beneath the surface of the ocean. At what depth does the volume of a pyrex glass cube, .001m on an edge at the surface of the ocean surface, decreases by 1x10 to the negative tenth meters cubed? Assume the Bulk modulus to be 2.6x10 to the tenth N/m squared for pyrex glass.
1 Answer
- 1 decade agoFavorite Answer
The bulk modulus is
B= -V * Δp / ΔV
where V is the original volume, ΔV is the change in volume, and Δp is the change in pressure
(ΔV is negative when Δp is positive, so B is positive)
Δp = -B*ΔV/V
You're told Δp is z*(10000 N/m) where z is the depth in meters below the surface, or
Δp = z*10^4
V = (0.001m)^3 = 1*10^(-9) cubic meters
ΔV = -1*10^(-10)
So,
z*10^4 = 2.6*10^10 * 1*10^(-10) / 1*10^(-9)
z = 2.6 * (10^10 * 10^(-10)) / (10^(-9)* 10^4)
z = 260,000 m
