Physics, 16.12.2019 21:31 lelliott86

Find the density of seawater at a depth where the pressure is 950 atm if the density at the surface is 1100 kg/m3. seawater has a bulk modulus of 2.3 × 10^9n/m2.
answer in units of kg/m3.

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Answer from: Luchi8115

GIVEN DATA

Pressure = 950 atm.

since 1 atm = 101325 N/m² ; 950 atm = 9.626×10⁷ N/m²

density of surface (ρ) = 1100 kg/m³ ,

Bulk modulus of sea water (K) = 2.3×10⁹ N/m² ,

Determine the density of sea water (ρ)=?

From the concept of compressibility and bulk modulus, compressibility is the reciprocal of elasticity. The bulk modulus is defined as the ratio of compressive stress to the volumetric strain.

Volumetric strain is defined as it is the ratio of change in volume to the original volume.

Therefore, Volumetric strain = -(dV/V)

Negative sign indicates that decrese in pressure with incresed volume.

In the limit δP tends to zero.

K = -V dP/dV

consider V = 1/ρ, and differentiate

K = ρ.dP/dρ

dρ = ρ.dP/K, use this eqution to find the density of seawater

= (1100 kg/m³ × 9.626×10⁷ N/m²) / (2.3×10⁹ N/m²)

= 46.037 kg/m³

Density of sea water at 950 atm. pressure is 46.037 kg/m³.

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Answer from: Quest

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