# Application to Physics

## Homework Statement

A cylindrical barrel, standing upright on its circular end, contains muddy water. The top of barrel, which has diameter 1 meter, is open. Height of barrel is 1.8 meter and it is filled to a depth of 1.5 meter. Density of water at a depth of h meters below surface is given by $$\delta$$(h)=1+kh kg/m3, where k is a positive constant. Find total work done to pump muddy water to top rim of barrel. Answer is .366(k+1.077)g$$\pi$$ joules

## Homework Equations

force of gravity on slice=density*g*volume

## The Attempt at a Solution

volume of slice$$\approx$$$$\pi$$(1/2)2$$\Delta$$h m3
1+kh(g)($$\pi$$/4)$$\Delta$$h nt
work done on slice$$\approx$$force*distance=1+kh(g)($$\pi$$/4)(1.8-h)$$\Delta$$h joules
total work=$$\int$$01.5$$\pi$$/4g(1+kh)(1.8-h)dh joules=$$\pi$$/4g(1.8h-h2/2+1.8kh2/2-kh3/3)

Mark44
Mentor
Here are some tips on LaTeX.

Use one pair of tags for a whole line, rather than piecemeal.
Inside LaTeX tags, use _n for subscripts and ^n for exponents. If the subscript or exponent is more than a single character, surround them with braces - {}
Integrals look like this (without the leading spaces in the brackets):
[ tex]\int_{a}^{b} f(h) dh [ /tex]