Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Integral Word Problem

  1. Feb 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A 100 lb bag of sand is lifted for 2 seconds at the rate of 4 feet per second . find the work done in lifting the bag if the sand leaks out at the rate of 1.5 lbs per second.

    2. Relevant equations

    3. The attempt at a solution
    Here's my attempt at it:
    work = force x distance
    force = 100-1.5t
    distance = 4t
    work = 400t-6t2
    Now I integrate for t=2 and t=0
    =200t2-2t3 for t=2 and t=0

    Any mistakes?
  2. jcsd
  3. Feb 15, 2012 #2


    User Avatar
    Homework Helper

    This is not correct. Work =force times distance is valid only when the force is constant during the displacement.
    If you integrate work with respect to time, you do not get work.

    Use that power = force times velocity, and integrate the power over time.

  4. Feb 15, 2012 #3
    Ehild, thanks for pointing this out. I had a hunch that integrating work does not give you work, that should be common sense by now for me.

    power = force x velocity
    force = 100-1.5t
    velocity = 4
    power = 400-6t
    Now I integrate for t=2 and t=0
    work = ∫(400-6t)dt
    =400t-3t2 for t=2 and t=0
  5. Feb 15, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    That looks much better.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook