During heavy rain, a section of a mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.40km x 0.40km and that mud has a density of 1900kg/m3 (cubic meters). What is the mass of the mud sitting above 4.0m2 (squared meters)area of the valley floor?
1) get initial volume (2500x800x2)
2) divide that volume by the surface area (400x400)
3) you have depth from equation 2
4) (4x4xdepthx1900)
Visualize it as this. You first find the cube. Then they want a cube inside that cube, the base being a 2x2 which is 4 meters squared.
If Depth is 25 then 25x4x1900 = 1.9x10^5kg
To find the mass of the mud sitting above a given area of the valley floor, we need to calculate the volume of the mud and then multiply it by its density.
Step 1: Calculate the volume of the mud:
Volume of the mud = length × width × depth
Given:
Length = 2.5 km = 2500 m
Width = 0.80 km = 800 m
Depth = 2.0 m
Volume of the mud = 2500 m × 800 m × 2.0 m
Step 2: Convert the volume to cubic meters:
Since the given density is in kg/m^3, we need to convert the volume to cubic meters.
Volume of the mud = (2500 m × 800 m × 2.0 m) / (1000 m/1 km)^3
Step 3: Calculate the mass of the mud:
Mass of the mud = Volume of the mud × Density of mud
Given:
Density of mud = 1900 kg/m^3
Mass of the mud = Volume of the mud × Density of mud
Finally, multiply the calculated mass of the mud by the area of the valley floor to get the mass of mud sitting above 4.0 m^2 area of the valley floor.
To find the mass of the mud sitting above a certain area of the valley floor, we need to calculate the volume of the mud above that area and then multiply it by the density of the mud.
First, let's find the volume of the mud that slipped into the valley.
Given:
Width of the section of the mountainside (horizontal distance) = 2.5 km = 2500 m
Height of the section of the mountainside (vertical distance along the slope) = 0.80 km = 800 m
Depth of the mud slide = 2.0 m
The volume can be calculated by multiplying the length, width, and height of the section of the mountainside:
Volume of mud slide = Length × Width × Depth
Volume of mud slide = 2500 m × 800 m × 2.0 m
Next, we need to find the area of the valley floor above which we want to calculate the mass of the mud.
Given:
Length of the valley floor area = Width of the valley floor area = 0.40 km = 400 m
The area can be calculated by multiplying the length and width of the valley floor:
Area of valley floor = Length × Width
Area of valley floor = 400 m × 400 m
Now, let's calculate the volume of mud above the 4.0 m² area on the valley floor.
The volume of mud above a certain area can be found by multiplying the area of that section by the average depth of the mud.
Volume of mud above 4.0 m² = (Area of 4.0 m² ÷ Area of valley floor) × Volume of mud slide
Volume of mud above 4.0 m² = (4.0 m² ÷ (400 m × 400 m)) × (2500 m × 800 m × 2.0 m)
Finally, to find the mass of the mud, we multiply the volume by the density of the mud.
Mass of mud above 4.0 m² = Volume of mud above 4.0 m² × Density of mud
Mass of mud above 4.0 m² = (4.0 m² ÷ (400 m × 400 m)) × (2500 m × 800 m × 2.0 m) × 1900 kg/m³
Now, you can plug in the values and calculate the mass of the mud above the 4.0 m² area of the valley floor.