What is the volume of a sand pile using double and triple integrals?

The purpose of these forums is to help you learn how to do physics. We can't do physics for you. :smile:So tell us what you don't understand, and we'll try to explain it to you. :smile:In summary, the conversation discusses setting up and finding the volume of a sand pile and a smaller cap cut from a solid ball. For the sand pile, a double integral and a triple integral are suggested as methods to find the volume, while for the smaller cap, cylindrical and spherical coordinates are mentioned as possible approaches. However, it is important to note that we cannot do the physics for the person asking the question and they should specify where they are stuck and what they do not understand in order
  • #1
suhaimi
2
0
1- The base of a sand pile covers the region in the xy - plane that is bounded by the parabola
x(power of 2) + y = 6 and the line y = x. The height of the sand above the point (x,y) is x(power of 2).
a) set up the volume of sand as
i) a double integral
ii) a triple integral

b) then, find the volume by using any methods you have found from a)i or a)ii

2- let D be the smaller cap cut from a solid ball a radius 2 units by a plane 1 unit from the center of the sphere.
a) Set up the volume of D as an iterated triple integral in
i) cylindrical coordinate
ii) spherical coordinate

b) then, find the volume by using one of two triple integrals you have found from a)i or a)ii.
 
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  • #2
Welcome to PF!

Hi suhaimi! Welcome to PF! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
  • #3


I have no Idea to do it. I stuck from beginning. Can you show me how to solve it
 
  • #4


No. We can't.
 

FAQ: What is the volume of a sand pile using double and triple integrals?

What is a sand pile vector?

A sand pile vector is a representation of the forces acting on particles in a sand pile. It shows the direction and magnitude of these forces, which are typically due to gravity and the weight of the particles themselves.

How is sand pile vector physics related to real-world applications?

Sand pile vector physics is used to understand and predict the behavior of granular materials, such as sand, in various scenarios. This has applications in industries such as construction, agriculture, and geology.

What factors affect the stability of a sand pile?

The stability of a sand pile is affected by the angle of repose, particle size and shape, moisture content, and external forces such as vibrations or wind. The sand pile vector can help analyze and predict the effects of these factors on the stability of the pile.

Can sand pile vector physics be applied to other granular materials?

Yes, the principles of sand pile vector physics can be applied to other granular materials, such as rice, sugar, or gravel. However, the specific parameters and equations used may differ depending on the properties of the material.

How is the sand pile vector calculated?

The sand pile vector is calculated by considering the weight and position of each particle in the pile. This information is used to determine the direction and magnitude of the forces acting on each particle, which are then represented graphically as arrows in the sand pile vector.

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