Seawater has a density of about 1024 kg/m^3. In fresh water, the water line on a certain rectangular raft (8.8cm thick) moves 3.2 cm when a load of cargo is placed on it. How much will the same load of cargo move the water line in seawater? What is the pressure in fresh water at a depth of 162.5 m? (Don't forget to include air pressure) What would the depth be for that same pressure in seawater?

To answer the first question, we need to understand the concept of buoyancy. When an object is placed in a fluid, it experiences an upward force called buoyant force. The magnitude of this force is equal to the weight of the fluid displaced by the object.

In the case of the rectangular raft, the load of cargo placed on it causes it to sink slightly, moving the water line. We can use the concept of buoyancy to determine the change in water line in seawater compared to freshwater.

The density of seawater is given as 1024 kg/m^3, and freshwater does not have a specified density, so we'll assume it to be approximately 1000 kg/m^3.

To find the change in water line in seawater, we can use the ratio of densities:

change in water line in seawater = (density of freshwater / density of seawater) * change in water line in freshwater

change in water line in seawater = (1000 kg/m^3 / 1024 kg/m^3) * 3.2 cm

Now, let's calculate:

change in water line in seawater = (0.9765625) * 3.2 cm

change in water line in seawater ≈ 3.126 cm

So, the same load of cargo will move the water line approximately 3.126 cm in seawater.

Moving on to the second question, let's determine the pressure in fresh water at a depth of 162.5 m. We need to consider both the hydrostatic pressure due to the depth and the atmospheric pressure.

The hydrostatic pressure (P) can be calculated using the formula:

P = ρgh

where:
ρ = density of the fluid
g = acceleration due to gravity
h = depth

The atmospheric pressure (Patm) at sea level is approximately 101325 Pa.

To calculate the pressure at a depth of 162.5 m in fresh water, we assume the density of fresh water to be 1000 kg/m^3. The acceleration due to gravity, g, is approximately 9.8 m/s^2.

P = (density of fresh water) * g * h + Patm

P = (1000 kg/m^3) * (9.8 m/s^2) * (162.5 m) + 101325 Pa

Now, let's calculate:

P ≈ 1008750 Pa + 101325 Pa

P ≈ 1110075 Pa

Therefore, the pressure in fresh water at a depth of 162.5 m is approximately 1110075 Pa.

For the last question, let's find the depth in seawater that would result in the same pressure.

We can rearrange the formula for pressure in fresh water and solve for depth:

h = (P - Patm) / (ρg)

Using the pressure we just calculated (P ≈ 1110075 Pa) and the density of seawater (ρ = 1024 kg/m^3), we can find the depth.

h = (1110075 Pa - 101325 Pa) / (1024 kg/m^3 * 9.8 m/s^2)

Now, let's calculate:

h ≈ 108.777 m

Therefore, the depth in seawater that would result in the same pressure is approximately 108.777 m.