A cargo barge is loaded in a saltwater harbor for a trip up a freshwater river.If the rectangular barge is 3.00m by 20.0m and sits 0.900m deep in the harbor, how deep will it sit in the river?
answer in meters
It must displace more fresh water than it did saltwater to float. The depth below the water line will increase by a factor
(seawater density)/(fresh water density)
That ratio is about 1.025.
Reference: http://en.wikipedia.org/wiki/Seawater
To determine how deep the barge will sit in the river, we need to understand the concept of buoyancy.
Buoyancy is the upward force exerted by a fluid on an object submerged or floating in it. The magnitude of this force is equal to the weight of the displaced fluid.
In this case, as the barge moves from the saltwater harbor to the freshwater river, the density of the surrounding fluid changes. Saltwater is denser than freshwater, which means the barge will displace a lesser volume of freshwater than it did in the saltwater.
To calculate how deep the barge will sit in the river, we can use the principle of buoyancy. The weight of the barge will remain constant, but the volume of water displaced will change.
Let's go through the steps:
Step 1: Calculate the volume of water displaced in the saltwater harbor.
Volume of water displaced = length x width x depth
= 20.0m x 3.00m x 0.900m
Step 2: Calculate the density of saltwater.
Density of saltwater = 1030 kg/m^3
Step 3: Calculate the weight of water displaced in the saltwater harbor.
Weight of water displaced = Volume of water displaced x Density of saltwater
Step 4: Calculate the density of freshwater.
Density of freshwater = 1000 kg/m^3
Step 5: Calculate the volume of water displaced in the freshwater river.
Weight of water displaced = Weight of water displaced in the saltwater harbor
Volume of water displaced in the freshwater river = Weight of water displaced / Density of freshwater
Step 6: Calculate the depth the barge will sit in the river.
Depth in the river = Volume of water displaced in the freshwater river / (length x width)
After following these steps, you'll have the answer in meters, which will give you the depth at which the barge will sit in the river.