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: Energy Lost when Steel Sphere collides with a soft plate of material

  1. May 11, 2010 #1
    Hi everyone. This isn't a homework question; just something I was thinking about and would like some advice on how I should tackle it.

    1. The problem statement, all variables and given/known data

    How can I approximate the Kinetic Energy Lost of a Steel Sphere when it collides with a soft sheet of material.

    A solid steel sphere of radius R impacts a homogeneous material (e.g clay) of depth D at a velocity v. I want to find the energy imparted to the material when one side of the ball just touches the other side of the material. In other words, I can also find the final velocity of the ball and calculate the energy lost to the material.

    2. Relevant equations

    I first write:

    where x is the depth the ball has penetrated
    and note that l refers to half of the line indicated in the diagram.


    I assume the steel ball and soft material have uniform density and Young's Modulus.

    [tex]F=\frac{E A \Delta L}{L}[/tex]

    3. The attempt at a solution

    I consider the force acted by the material with Young's Modulus E on the sphere as it burrows through facing increasing surface area of the material, given by [tex]\pil^2[/tex], where l depends on x. Then I integrate over the thickness of the material, D.

    Using Hooke's Law, I write


    Which equates the force with respect to x the amount the ball has traveled into the material. Then I integrate it from 0 to D with respect to x, and hence find the work done by the material. Is this a sound approach or did I get something really wrong?

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted