Why Does Multiplying Pressure by \(10^5\) Help in Calculating Depth?

[iRaid]

Homework Statement

PART B

Homework Equations

$$P = \rho gh$$

The Attempt at a Solution

Well I tried doing 412 = (1025)(9.8)h.. Divide by 10045 (9.8 x 1025). And ended up getting .041..
I found out that I need to use 412 x 10⁵ for the pressure which I have no idea why.

Any help?

Also, the answer is 4100m

 

[berkeman]

Homework Statement

PART B

Homework Equations

$$P = \rho gh$$

The Attempt at a Solution

Well I tried doing 412 = (1025)(9.8)h.. Divide by 10045 (9.8 x 1025). And ended up getting .041..
I found out that I need to use 412 x 10⁵ for the pressure which I have no idea why.

Any help?

Also, the answer is 4100m

You are mixing your units. "Atmospheres" is not an mks unit. You should write units in your equations as you go, to make sure that they are consistent (LSH units = RHS units, and the units of any quantities you are adding are the same).

 

[rock.freak667]

In your equation P=ρgh, P is measured in Pascals (Pa)

 

[iRaid]

Oh right thanks

 

[rwisz]

.

Sure, I can help with this problem! First, let's take a look at the formula P = ρgh. This is known as the hydrostatic pressure formula, where P represents pressure, ρ represents density, g represents acceleration due to gravity, and h represents height. In order to solve for h, we need to isolate it on one side of the equation.

To do this, we can divide both sides by ρg, giving us the equation h = P/ρg. Now, let's substitute in the given values. We know that P = 412 x 105 Pa and ρ = 1025 kg/m^3. We also know that g = 9.8 m/s^2. Plugging these values into the equation, we get:

h = (412 x 105 Pa) / (1025 kg/m^3 x 9.8 m/s^2)

Simplifying, we get:

h = 4100 m

So, the answer of 4100m is correct. It seems like you were on the right track with your attempt, but you may have made a calculation error. Remember to always double check your work and use proper units in your calculations.

I hope this helps! Good luck on your finals tomorrow. Remember to stay calm and focused, and you'll do great!