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?
weight of freshwater displaced=LW*depth*densityfreshwater*g
weight of saltwater displaced=LW*.9*denstiy salt water*g
but the barge is afloat, so its weight is equal to the water displaced, so
the freshwater and saltwater displaced weights are equal.
LW*depth*densityfresh*g=LW*.9m*density salt*g
depth=.9 densitysalt/densityfreshwater
I did .9(1030/1000) and i got .927...is this correct? i think it is
depends on if you believe 1030kg/m^3 is the density of surface sea water. It varies in my experience from 1020 to 1030.
If you are near a river outlet, it is on the low side.
this piece of info was given by the prof.
To determine how deep the cargo barge will sit in the river, we need to consider the principle of buoyancy.
The buoyant force acting on a submerged object depends on the density of the fluid and the volume of the object. In this case, the density of saltwater is higher than that of freshwater, so the barge will displace less water in the river compared to the harbor.
To calculate the new depth of the barge in the river, we can use the concept of density and the equation:
Buoyant force = weight of the fluid displaced
The weight of the fluid displaced can be calculated using the formula:
Weight = density x volume x gravity
Where:
- Density is the density of the fluid (saltwater or freshwater)
- Volume is the volume of the submerged portion of the barge
- Gravity is the acceleration due to gravity (approximately 9.8 m/s^2)
Let's break down the solution step by step:
Step 1: Calculate the volume of the submerged portion of the barge in the harbor.
The volume is given by the formula:
Volume = length x width x depth
Given:
Length of the barge = 3.00 m
Width of the barge = 20.0 m
Depth in the harbor = 0.900 m
Volume = 3.00 m x 20.0 m x 0.900 m
Volume = 54 cubic meters
Step 2: Calculate the weight of the fluid displaced in the harbor.
The weight is given by the formula:
Weight = density x volume x gravity
Let's assume the density of saltwater is 1025 kg/m^3 and the density of freshwater is 1000 kg/m^3.
For saltwater:
Weight_saltwater = 1025 kg/m^3 x 54 m^3 x 9.8 m/s^2
Weight_saltwater = 54012.6 N (rounded to the nearest tenth)
For freshwater:
Weight_freshwater = 1000 kg/m^3 x 54 m^3 x 9.8 m/s^2
Weight_freshwater = 52920 N
Step 3: Calculate the depth of the barge in the river.
Using the principle of buoyancy, the buoyant force in the harbor and in the river should be equal.
Weight_saltwater = Weight_freshwater
Since the weight of the fluid displaced by the barge will be less in the river, the depth will also be less.
Let's assume the new depth in the river is represented by 'x'.
For saltwater:
Weight_saltwater = density_saltwater x volume x gravity
54012.6 N = 1025 kg/m^3 x 20.0 m x 3.00 m x x m x 9.8 m/s^2
54012.6 N = 61,800 x x
x = 54012.6 N / (61,800 N/m^3)
x = 0.874 m (rounded to three decimal places)
Therefore, the cargo barge will sit approximately 0.874 meters deep in the river.