Results 1 to 2 of 2

Math Help - work by pumping

  1. #1
    Member
    Joined
    Jul 2009
    Posts
    127

    work by pumping

    A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x^6 from x=1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.

    ok the part thats screwing me up is The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x^6 from x=1 to x=1 im not sure what to do with that.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by dat1611 View Post
    A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x^6 from x=1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.

    ok the part thats screwing me up is The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x^6 from x=1 to x=1 im not sure what to do with that.
    volume of a horizontal cross-section is 2 \cdot 2x \cdot dy

    since y = x^6 , x = y^{\frac{1}{6}}

    volume of a horizontal cross-section is 4y^{\frac{1}{6}} \cdot dy

    weight of a horizontal cross-section is 62 \cdot 4y^{\frac{1}{6}} \cdot dy

    distance each horizontal cross-section needs to be lifted is (1-y)

    work = \int_0^1 62 \cdot 4y^{\frac{1}{6}}(1-y) \, dy<br />
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 22nd 2010, 10:15 AM
  2. pumping out a liquid - work
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 11th 2010, 05:41 PM
  3. work pumping water into hemispherical tank
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 8th 2010, 07:17 PM
  4. work by pumping
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 19th 2009, 02:09 PM
  5. work done in pumping something
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 19th 2007, 09:41 AM

Search Tags


/mathhelpforum @mathhelpforum