# Thread: Calculate the work against gravity..?

1. ## Calculate the work against gravity..?

Calculate the work against gravity required to build a tower of height 35 ft in the shape of a right circular cone with base of radius 7 ft out of brick. Assume that brick has density .

___________ ft-lbs.

2. Originally Posted by tbenne3
Calculate the work against gravity required to build a tower of height 35 ft in the shape of a right circular cone with base of radius 7 ft out of brick. Assume that brick has density .

___________ ft-lbs.
The work required to raise a mass $\displaystyle m$ to a height $\displaystyle h$ is $\displaystyle w=mgh$.

The radius of the cone at a height $\displaystyle 0\le h\le 35$ feet is:

$\displaystyle r=-\frac{h}{5}+7$

The volume of a slice of the cone perpendicular to the axis at a height $\displaystyle h$ and of thickness $\displaystyle \Delta h$ is:

$\displaystyle V_{\Delta h}(h)=\pi r^2 \Delta h=\pi (7-(h/5))^2 \Delta h$

Now the work can be seen to be:

$\displaystyle \int_{h=0}^{35} \pi r^2 \rho\, g\, h \; dh=\int_{h=0}^{35}\pi (7-(h/5))^2 \rho\, g\, h \; dh$

CB

,

,

### a man mass 70kg ascent of light of 36step each 20 cm height .What is the work against gravity

Click on a term to search for related topics.