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Math Help - Friction question.

  1. #1
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    Friction question.

    In a game. A coin of mass 5 grams is struck and slides across a wooden board.
    If the co-efficient of friction of 0.4 and the coin is struck with a speed of 1.5m/s.
    How far will it slide until it comes to rest?

    I got this far... And now i'm stuck...(image attached)

    Limiting friction = 0.05g * 0.4 = 0196N.
    D - 0.196N = 0.05a

    Well i have that u = 1.5m/s and v = 0...however i need acceleration in order to use any of the equations to find the distance..and I'm not sure how to do it...

    Thank-you
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  2. #2
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    The only force acting on the coin after pushing it is the force due to friction, so:
    F_{net} = F_{fr}
    \Rightarrow m\vec{a} = \mu \: mg (Since F_{fr} = \mu F_{n} = \mu F_{g} where F_{n} is the normal force balanced by the force due to gravity F_{g})

    Now that you've found acceleration, apply the kinematics equation:
    \vec{v_{f}} = \vec{v_{i}} + \vec{a}t

    where v_{f} is your final velocity (which is 0 if it's coming to rest) and v_{i} is your initial velocity.
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    Quote Originally Posted by o_O View Post

    Now that you've found acceleration, apply the kinematics equation:
    \vec{v_{f}} = \vec{v_{i}} + \vec{a}t
    I'm getting something thats /100 the answer. (answers 28.7 but im getting 0.287)
    a = \frac{-0.196}{0.05}

    a = -3.92

    First i did
    v = 0. u = 1.5m/s
    v^2 - u^2 = 2as<br />
-2.25 = 2 * -3.92 * s<br />
    s = 0.287

    So i tried with v = u + at
    0 = 1.5 = 3.92t<br />
t = 0.38<br />

    When i sub t, v and u into
    s = 0.5(v + u)t

    I also get s = 0.287.. :S

    Thanks
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  4. #4
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    Quote Originally Posted by AshleyT View Post
    I'm getting something thats /100 the answer. (answers 28.7 but im getting 0.287)
    a = \frac{-0.196}{0.05}

    a = -3.92

    First i did
    v = 0. u = 1.5m/s
    v^2 - u^2 = 2as<br />
-2.25 = 2 * -3.92 * s<br />
    s = 0.287

    So i tried with v = u + at
    0 = 1.5 = 3.92t<br />
t = 0.38<br />

    When i sub t, v and u into
    s = 0.5(v + u)t

    I also get s = 0.287.. :S

    Thanks
    Do you pay attention to units .....?

    Your answer is in metres. No doubt the books answer is in centimetres.
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