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Math Help - Friction??

  1. #1
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    Friction??

    Heres a problem I cant get I've managed to solve equations like this without involving the equation for friction, but this is slightly more taxing, for me...

    a ball of mass
    m, position x(t) and velocity v(t) = dx/dt, where t is time. The equation of
    motion of the ball is

    m
    dv/dt = μmg ,

    where the only force on the ball is the friction,
    μ > 0 is the constant coefficient of friction and g the acceleration
    due to gravity.
    Ball starts with initial speed
    V0, at position x = 0 and t = 0.

    (a)Solve equation of motion and determine
    v(t).
    (b)Solve d
    x/dt = v(t), using the result from part (a), and determine x(t).
    Find time
    T at which ball stops.

    If someone could get me started I'd appreciate it, what do I need to do to deal with the friction part?

    I already know

    dv/dt = -k/m*v => int dv/v = -k/mdt

    v(t) = exp(-k/mt+C) = C'exp(-k/mt)

    but this doesn't account for friction...



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  2. #2
    Member
    Joined
    May 2006
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    Quote Originally Posted by mrjohnson View Post
    Heres a problem I cant get I've managed to solve equations like this without involving the equation for friction, but this is slightly more taxing, for me...



    a ball of mass m, position x(t) and velocity v(t) = dx/dt, where t is time. The equation of
    motion of the ball is



    m
    dv/dt = μmg ,

    where the only force on the ball is the friction,



    μ > 0 is the constant coefficient of friction and g the acceleration
    due to gravity.
    Ball starts with initial speed V0, at position x = 0 and t = 0.

    (a)Solve equation of motion and determine v(t).
    (b)Solve dx/dt = v(t), using the result from part (a), and determine x(t).
    Find time T at which ball stops.

    If someone could get me started I'd appreciate it, what do I need to do to deal with the friction part?

    I already know

    dv/dt = -k/m*v => int dv/v = -k/mdt

    v(t) = exp(-k/mt+C) = C'exp(-k/mt)

    but this doesn't account for friction...






    It is already accounted for in the equation of motion:

    m \frac{dv}{dt}=-\mu m g

    This is the equation of motion of a body of mass m moving on a horizontal
    surface with no other force than friction (with the additional assumption that
    the initial velocity is positive)

    ZB


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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mrjohnson View Post
    m
    dv/dt = μmg ,
    where the only force on the ball is the friction,
    μ > 0 is the constant coefficient of friction and g the acceleration
    due to gravity.
    Ball starts with initial speed
    V0, at position x = 0 and t = 0.

    (a)Solve equation of motion and determine
    v(t).
    (b)Solve d
    x/dt = v(t), using the result from part (a), and determine x(t).
    Find time
    T at which ball stops.

    I already know

    dv/dt = -k/m*v => int dv/v = -k/mdt
    Why are you using this equation of motion when one has already been given to you??

    m \frac{dv}{dt} = - \mu mg

    \frac{dv}{dt} = - \mu g

    v = \int (- \mu g) ~dt

    Just integrate.

    -Dan
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