How Deep Must You Dive to Match Venus's Surface Pressure?

[lmannoia]

Homework Statement

Water has a density of 1000kg/m^3, so a column of water n meters tall and 1 meter square at its base has a mass of nx1000kg. On either Earth or Venus, which have nearly the same surface gravity, a mass of 1 kg weighs about 9.8 Newtons. Calculate how deep you would have to descend into Earth's oceans for the pressure to equal the atmospheric pressure on Venus's surface, about 9 x 10^6 N/m^2.

Homework Equations

Density = mass/volume
Pressure = force/unit of surface area

The Attempt at a Solution

I'm confused as to how to relate pressure to density or mass. Any hint or push in the right direction would be greatly appreciated. Thanks!

 

[zhermes]

Remember that pressure is force per unit area. So (for instance), what would be the pressure underneath the column of water in the beginning of the problem?

 

[lmannoia]

Would the pressure equal (n meters)(1000kg)(9.8m/s^2)/m^3?

 

[zhermes]

Would the pressure equal (n meters)(1000kg)(9.8m/s^2)/m^3?

You're on the right track, but not quite.

If we're looking for pressure, we should start with force---provided by gravity, thus F = mg. Mass m is then density times volume. Try to keep everything symbolic here (i.e. use $$\rho$$ instead of 1000). So what's the volume of the column? Then plug in for the force. Now, over what area is that force being distributed?---the pressure is then P = F/A