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Motion, Energy balance, momentum question

  1. Apr 21, 2015 #1
    1. The problem statement, all variables and given/known data
    A block of mass m= 10kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05.
    When hit by a bullet of mass 50 g moving with speed v, that gets embedded in it, the block moves and comes to stop after moving a distance of 2m on the table.
    If a freely falling object were to acquire speed v/10 after being dropped from height H, then neglecting energy losses and taking g= 10 m/s2, the value of H is close to:
    A. 0.2 km
    B. 0.3 km
    C. 0.4 km
    D 0.5. km

    2. Relevant equations
    Momentum conservation, energy conservation, Newton laws
    3. The attempt at a solution
    $$M_{bullet} v = ( m_{block} + M_{bullet} )v_{block} $$ ( momentum conservation)

    $$ 1/2 (m_{block} + M_{bullet}) v_{block}^2 = μ (m_{block} + M_{bullet}) g s$$ energy conservation
    $$ v_{block}^2 = 2μgs = 2 * 0.05 * 10 * 2 = 2 $$
    $$ v_{block} = √2 m/s $$
    $$ v = ( m_{block} + M_{bullet} )v_{block}/M_{bullet} ≈ 10000 * √2/50 = 200√2 m/s $$
    $$ v/10 = 20√2 $$

    Now, ## mgH = 1/2 m (v/10)^2 ##
    ## ⇒ H = (20√2)^2/2g = 800/20 = 40 m = 0.04 km ##
    What wrong I have done here?
    It is not matching with options.
     
    Last edited: Apr 21, 2015
  2. jcsd
  3. Apr 21, 2015 #2

    ehild

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    What options are there?
    I think you rounded off too early.
     
  4. Apr 21, 2015 #3
    0.4 km
    0.3 km
    0.2 km
    0.5 km
    But why so error in rounding?
    By a factor of 10?
     
  5. Apr 21, 2015 #4

    ehild

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    Gold Member

    It is not rounding error. Your result is correct, the problem maker has error.
     
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