A simple physics formula is density equals mass divided by volume. In problem 2 above, the density was δ(x,y,z) = e^((x^2+y^2+z^2)^3/2).The volume of the object could be calculated from the equations for volumes of spheres and cones with some simple subtraction. Why do we need to do a triple integral to find the mass of the solid? Why can’t we just use the physics formula M = ρ ·V ? Explain when we need a triple integral to calculate mass, and when we can get away with the simple physics formula. Most importantly, explain how the triple integral of p*dV uses the same physics formula and explain what the idea of an integral means.
A simple physics formula is density equals mass divided by volume. In problem 2 above, the density was δ(x,y,z) = e^((x^2+y^2+z^2)^3/2).The volume of the object could be calculated from the equations for volumes of spheres and cones with some simple subtraction. Why do we need to do a triple integral to find the mass of the solid? Why can’t we just use the physics formula M = ρ ·V ? Explain when we need a triple integral to calculate mass, and when we can get away with the simple physics formula. Most importantly, explain how the triple integral of p*dV uses the same physics formula and explain what the idea of an integral means.
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
Problem 59P: At one point in space, the direction of the electric field vector Is given In the Cartesian system...
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A simple physics formula is density equals mass divided by volume. In problem 2 above, the density was δ(x,y,z) = e^((x^2+y^2+z^2)^3/2).The volume of the object could be calculated from the equations for volumes of spheres and cones with some simple subtraction. Why do we need to do a triple integral to find the mass of the solid? Why can’t we just use the physics formula M = ρ ·V ? Explain when we need a triple integral to calculate mass, and when we can get away with the simple physics formula. Most importantly, explain how the triple integral of p*dV uses the same physics formula and explain what the idea of an integral means.
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