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: Center of mass of baseball bat problem

  1. Dec 15, 2008 #1
    1. The problem statement, all variables and given/known data

    A baseball bat of length L has a peculiar linear density given by [tex]\lambda[/tex] = [tex]\lambda[/tex]0 * (1+X2/L2)

    Find the x coordinate of the center of mass in terms of L

    2. Relevant equations

    Mxcm= mr

    3. The attempt at a solution

    So I use integration

    The integrand I have is x*[tex]\lambda[/tex] dx and substitue whatever on the right side of the [tex]\lambda[/tex] equation in. Then I just took normal integral.

    However I got wrong answer. The right answer does not contain [tex]\lambda[/tex]0 but mine does

    Can you guys help me ??
  2. jcsd
  3. Dec 15, 2008 #2
    You need to also do an integration to find the total mass, M. This will have a factor lambda_o that will cancel the one you have on the right side.
  4. Dec 15, 2008 #3
    How do I integrate to find mass M ??

    Do I plug in lamda formula*L for M or do I have to integrate lamda*L ??
  5. Dec 15, 2008 #4
    M = int(lambda * dx) will do the job where you take the integral over the length 0 to L.
  6. Dec 15, 2008 #5
    I got (L^2/2 +L^3/4)/(1+L^2/3)

    But it's still not the answer in the book.

    Did I do something wrong ??
  7. Dec 15, 2008 #6


    User Avatar
    Homework Helper

    You've almost got it looks like to me.
    But the numerator should have been multiplied by x

    yielding as an integrand x + x3/L2

    that gives

    x2/2 + x4/4 | from 0 to L or ... 3L2/4

    The total Mass looks integrated a little off.

    Shouldn't that be (L + L/3) = 4L/3 ?

    Then dividing denominator into numerator

    (3/4L2)/(4/3*L) = 9L/16
    Last edited: Dec 15, 2008
  8. Dec 16, 2008 #7
    How can you get 3L^2/4 and 4L/3

    I thought the integral of the total mass will yield L+ L^3/3 ???
  9. Dec 16, 2008 #8


    User Avatar
    Homework Helper

    The integrand for the volume of the mass is 1 +X2/L2 |evaluated between 0 and L

    That yields the result X + X3/3L2 The 0 terms are of no account leaving L + L3/3L2 = L + L/3 = 4L/3

    The integrand for the incremental moments is as I outlined previously.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook