Results 1 to 2 of 2

Math Help - Calculate the work against gravity..?

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    98

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by tbenne3 View Post
    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 m to a height h is w=mgh.

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

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

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

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

    Now the work can be seen to be:

    \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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral to calculate work
    Posted in the Calculus Forum
    Replies: 10
    Last Post: December 22nd 2011, 06:44 PM
  2. Replies: 4
    Last Post: May 3rd 2011, 05:42 AM
  3. Replies: 6
    Last Post: April 30th 2010, 03:15 PM
  4. Calculate the work to pump water out of tank
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 18th 2010, 09:40 AM
  5. Gravity-Work Question
    Posted in the Geometry Forum
    Replies: 5
    Last Post: May 29th 2009, 02:24 PM

Search Tags


/mathhelpforum @mathhelpforum