Basic measurements and conversion not so basic

[Saterial]

Homework Statement

During heavy rain, a section of a mountainside measuring 3.6 km horizontally, 0.53 km up along the slope, and 1.1 m 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 1.2 km x 1.2 km and that the mass of a cubic meter of mud is 1900 kg. What is the mass of the mud sitting above a 2.2 m2 area of the valley floor?

Homework Equations

v = lwh?

The Attempt at a Solution

To be honest, I can't necessarily figure out where to start. Looking at the question, I have a length, width and height... can I assume that the slope is a perfect vertical(lol) and use that as a length to find volume? This question seems really basic to me, the answer is looking for the mass of the mud sitting above a specific height, however, it states that a cubic meter of mud is 1900 kg.

Can I simply just multiply 1900 kg/m^2 by 2.2 m^2 to obtain 4180 kg ? I can't figure out why the other supplied information would be of any help at all. If I think about this logically, if there is mud stacked on top itself at a higher height, would that not change the mass ? This is where I thought maybe the dimensions of the mountain side were necessary.

Can anyone shed some light on this problem?

Thanks

 

[rickz02]

can I assume that the slope is a perfect vertical(lol) and use that as a length to find volume?

No you can't, this is where you're going to use the dimensions of the mountainside. Also take note that

1.1 m deep slips into a valley in a mud slide.

Can I simply just multiply 1900 kg/m^2 by 2.2 m^2 to obtain 4180 kg?

I believe you simply can't do that, you are given with a volumetric density 1900 kg/m³.

if there is mud stacked on top itself at a higher height, would that not change the mass?

Obviously the mass would. Aside from the fact you are adding mud, the mountainside is also sloping so the mass from a lower layer is lesser than that of the above.

I suggest you draw a diagram so you can easily see the whole problem.

Honestly the question of this problem is quite tricky. It says

What is the mass of the mud sitting above a 2.2 m2 area of the valley floor?

Where exactly is 2.2 m² area of the valley floor, is it near the slope?

 

[rickz02]

can I assume that the slope is a perfect vertical(lol) and use that as a length to find volume?

No you can't, this is where you're going to use the dimensions of the mountainside. Also take note that

1.1 m deep slips into a valley in a mud slide.

Can I simply just multiply 1900 kg/m^2 by 2.2 m^2 to obtain 4180 kg?

I believe you simply can't do that, you are given with a volumetric density 1900 kg/m³.

if there is mud stacked on top itself at a higher height, would that not change the mass?

Obviously the mass would. Aside from the fact you are adding mud, the mountainside is also sloping so the mass from a lower layer is lesser than that of the above.

I suggest you draw a diagram so you can easily see the whole problem.

Honestly the question of this problem is quite tricky. It says

What is the mass of the mud sitting above a 2.2 m2 area of the valley floor?

Where exactly is 2.2 m² area of the valley floor, is it near the slope? I guess it is...

 

[Saterial]

I believe that the 2.2 m^2 is after the mudslide and off the slope, so it becomes level area in the valley.

How can the dimensions of the mountain be used? If the slope does contain a curvature, how can the 0.53 km even be accounted for?

The mud is uniformly distributed over a 1.44 km^2 (or 1440 m^2) area. Would that mean I need to determine the volume of mud in a 2.2 m^2 area and multiply that by 1900 kg? If so, can I assume no curvature in the dimensions and do the following?

V = (3.6 km)(0.53 km)(0.0011 km)
= 2.10 x 10^-3 km^3
= 2100000 m^3

Take that volume and use it as the total volume of the mudslide, determine how much of that volume is enclosed in a 2.2 m^2 area, and multiply it by 1900 kg?

 

[rwisz]

for your question. It is understandable that this problem may seem basic at first glance, but let's break it down step by step to see how we can solve it.

First, let's start by identifying the given information. We have the measurements of the section of mountainside (3.6 km horizontally, 0.53 km up along the slope, and 1.1 m deep), the dimensions of the valley (1.2 km x 1.2 km), and the mass of a cubic meter of mud (1900 kg). We are also given the specific area of the valley floor that we need to find the mass for (2.2 m2).

Next, we need to think about how we can use this information to find the mass of the mud above the given area. Since we are dealing with a three-dimensional object (the mud), we need to calculate its volume in order to find its mass. This is where the dimensions of the mountainside and the valley come into play.

We can use the dimensions of the mountainside to calculate the volume of the mud that has slipped into the valley. The formula for volume (v) is v = lwh, where l is the length, w is the width, and h is the height. In this case, the length and width are given by the dimensions of the mountainside (3.6 km and 0.53 km, respectively), and the height is given by the depth of the mud (1.1 m). So, the volume of the mud is:

v = (3.6 km)(0.53 km)(1.1 m) = 2.04 km3

Now, we need to find the volume of mud that is sitting above the given area (2.2 m2) on the valley floor. To do this, we need to find the height of the mud above this area. We can do this by dividing the volume of the mud by the surface area of the valley:

h = v/A = (2.04 km3)/(1.2 km x 1.2 km) = 1.42 m

So, the height of the mud above the given area is 1.42 m. Now, we can use this height to find the volume of the mud above this area:

v = (1.42 m)(2.2 m2) = 3.12 m3

Finally, we can use the mass