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Homework Help: Football tackle force

  1. Nov 28, 2007 #1
    1. The problem statement, all variables and given/known data
    A 110 kg football linebacker moving at 2 m/s tackles head-on a 70 kg halfback running 4 m/s. If they have an inelastic collision, and neglecting the effects due to digging in of cleats:
    a)If the collision takes .5 sec, what is the force imparted on the halfback?
    b) what is the force imparted on the linebacker?

    2. Relevant equations

    3. The attempt at a solution

    110(2) + 70(-4) = 110v + 70v
    v= 1/3 m/s in halfback's direction

    when i solve, I get a negative force. Is this possible?
    For both a and b, i get -513.34 N, is this correct?

    a)F=(70)(.333 - 4)/.5
    F=-513.4 N

    b)F=(110)(-.333 - 2)/.5
    F=-513.4 N
    Last edited: Nov 28, 2007
  2. jcsd
  3. Nov 29, 2007 #2
    I'm not going to calculate the numbers, but using variables:

    [tex]m_1 v_1 + m_2 v_2 = (m_1 + m_2)v[/tex]

    Solve for [tex]v[/tex]:

    [tex]\frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}=v[/tex]

    Using v, you can get change in momentum:

    [tex]\Delta p_1=m_1(v_1 - v)[/tex]
    [tex]\Delta p_2=m_2(v_2 - v)[/tex]

    Then you can calulate the force in each case.

    [tex]F_1=\frac{m_1(v_1 - v)}{t}[/tex]
    [tex]F_2=\frac{m_2(v_2 - v)}{t}[/tex]

    Yes, you can get a negative value for force. Force is a vector, as is velocity.

    So initially, assume the halfback is running in the positive x direction, his velocity is positive. The linebacker will be running in the negative x direction with a negative velocity.
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