1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: A parabolic force distribution is applied to a beam

  1. Sep 20, 2012 #1
    1. The problem statement, all variables and given/known data

    3. The attempt at a solution
    So I noticed the units of w_0 were in N. In other words to find the moment I would have to integrate 100∫01 x2+1-2x dx. However I ended up with the wrong answer.

    The correct answer requires that I integrate 100∫01 x2+1-2x x dx

    However, if I do it this way I don't see how the units work out... Do you think this is a mistake? I think they wanted w_0 to be a distributed load with units N/m...
  2. jcsd
  3. Sep 20, 2012 #2


    User Avatar
    Science Advisor

    The only math involved here is simple integration so I am moving this to the "physic homework" section.
  4. Sep 20, 2012 #3
    The units of w_0 are in N/m2. If you integrate 100∫01 x2+1-2x dx, you get force.

    I suppose you mean 100∫(01 x2+1-2x)x dx. Yes, you need to integrate this to find the moment.
  5. Sep 20, 2012 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    In problems of this type it is easier to re-define things a bit, so units do not get in the way. Say the distance is x meters (so x is dimensionless!). Then if the "constant" is w0 N, the constant w0 is also dimensionless. This will make everything work out more easily than the original choice where x is distance (so has attached units of meters) and where w0 is an initial constant with dimensions of N/m2.

    Anyway, the point is that you want to match the first moments of the forces, so you want to match force × distance (this is NOT work!) on both sides.

  6. Sep 20, 2012 #5
    Thanks everyone! So is w(x) a distributed force? In other words w(x)*dx gives us a small fraction of the force at a certain x and then we multiply this value by x to get the moment?
  7. Sep 21, 2012 #6
    Yes, w(x) is a distributed loading. As you have pointed out the total force supplied by the loading is the integral of the load function along the length it passes over. This total load is then applied at the centroid of the area underneath the load curve in order to have the same net effect that the distributed load itself had on the beam. From here your problem becomes a simple moment balancing issue.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook