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Bullet hits a block, penetration depth and velocity

  1. Jul 13, 2012 #1
    1. The problem statement, all variables and given/known data
    A bullet with mass and speed v hits a wooden block of mass M that is situated at rest on a frictionless surface. It penetrates the block and gets trapped inside it as a result of a constant retardation force [itex]F_{ret}[/itex] that opposes relative motion between the two objects. Find the common speed of the bullet and the block V, and the penetration length l in terms of m, M, v, and [itex]F_{ret}[/itex].

    2. Relevant equations


    mv=(m+M)V (Eq 1)

    [itex]\frac{1}{2}mv^{2}=F_{ret}l+\frac{1}{2}(m+M)V^{2}[/itex] (Eq 2)

    3. The attempt at a solution
    The common speed of m and M is [itex]V=\frac{mv}{m+M}[/itex] (Eq 3) via conservation of momentum.

    [itex]\frac{1}{2}mv^{2}=F_{ret}l+\frac{1}{2}\frac{m^{2}v^{2}}{(m+M)}[/itex] (where I substituted Eq 3 into Eq 2)

    Let's rearrange:
    [itex]F_{ret}l=\frac{1}{2}m\left( 1-\frac{m}{m+M}\right) v^{2}[/itex]

    No let's solve for the penetration depth l:
    [itex]l=\frac{m\left(1-\frac{m}{m+M}\right) v^{2}}{2F_{ret}}[/itex]

    Not sure if it is correct. Thanks for the help!
     
  2. jcsd
  3. Jul 13, 2012 #2

    Simon Bridge

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    What is it that makes you doubt your answer?
     
  4. Jul 15, 2012 #3

    rude man

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    Certainly your momentum and k.e. conservation equations are correct.
     
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