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Horizontal Velocity given only vertical displacement and the mass of the two objects.

  1. Nov 21, 2009 #1
    1. The problem statement, all variables and given/known data
    As part of a forensic experiment, a 50g bullet is fired horizontally into a 2.0kg wooden pendulum. The pendulum with the bullet embedded in it rises 15cm vertically from its initial position and stops.

    a) Calculate the velocity of the block and bullet just after the collision.
    b) What is the velocity of the bullet just before impact?

    2. Relevant equations
    p = m*v
    W = F*d = ET
    Change in Eg = m*g*change in h
    Ek = 1/2*m*v2
    Change in p = F*change in t
    3. The attempt at a solution
    mbullet = 0.05kg
    mpendulum = 2kg

    In this case i think change in Eg = W in the up direction

    m*g*change in h = Wup
    (2kg + 0.05kg)(9.8N/kg)(0.15m) = Wup
    3.0135N*m = Wup

    Wup = Forceup * displacementup
    (3.0135N*m) / (0.15m) = Forceup
    20.09N = Forceup

    Change in p = F*change in t
    Change in t = Vav/change in d

    Therefore

    pup = 20.09N * ((V2 - V1) * 0.5)/0.15m

    and here is where i'm lost.. This is part of an 8 question assignment sheet, i've finished the previous 7 but this one really has me stumped.
    Would appreciate any help given asap since this is due monday.
     
  2. jcsd
  3. Nov 21, 2009 #2

    kuruman

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    Re: Horizontal Velocity given only vertical displacement and the mass of the two obje

    Forceup is meaningless. You need to conserve mechanical energy in part (a). The potential energy at maximum height is equal to the kinetic energy at the bottom. Say that with an equation and solve for the bullet plus wood system.
     
  4. Nov 22, 2009 #3
    Re: Horizontal Velocity given only vertical displacement and the mass of the two obje

    Tad confused here, as we don't have the height of the pendulum how am i supposed to solve for velocity at the bottom..

    Ek = 1/2mv^2
    Eg = mgh

    We dont have h...

    Edit: Do you mean that the change in gravitational potential energy at the new position of 15cm above is equivalent to the kinetic energy?
    So like

    Ek = Eg
    1/2mv^2 = mgh
    1/2(2.05kg)v^2 = (2.05kg)(9.8N/Kg)(0.15)
    v = 1.714m/s
    ?
     
    Last edited: Nov 22, 2009
  5. Nov 22, 2009 #4

    kuruman

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    Re: Horizontal Velocity given only vertical displacement and the mass of the two obje

    Yes, change in gravitational potential energy. There is no other form of potential energy.
     
  6. Nov 22, 2009 #5
    Re: Horizontal Velocity given only vertical displacement and the mass of the two obje

    Alright, thanks so much for your help!

    Would part b be similar aswell?
     
  7. Nov 22, 2009 #6

    kuruman

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    Re: Horizontal Velocity given only vertical displacement and the mass of the two obje

    No. Treat the problem as an inelastic collision and conserve momentum before and after the collision.
     
  8. Nov 22, 2009 #7
    Re: Horizontal Velocity given only vertical displacement and the mass of the two obje

    Worked perfectly, again thank you so much for your help. How do i set this question to solved?
     
  9. Nov 22, 2009 #8

    kuruman

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    Re: Horizontal Velocity given only vertical displacement and the mass of the two obje

    I am not sure what you mean.
     
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