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Car Coming to a Stop w/ Kinetic Energy and Friction

  1. Nov 14, 2014 #1
    1. The problem statement, all variables and given/known data
    An 1100-kg car traveling at 24 m/s coasts through some wet mud in which the net horizontal resistive force exerted on the car from all causes (mostly the force exerted by the mud) is 1.7 x 10^4 N. Determine the car’s speed as it leaves the 18-m-long patch of mud.

    [itex]m = 1,100 kg[/itex]
    [itex]v_i = 24 m/s[/itex]
    [itex]\vec F = -1.7x10^4 N[/itex]
    [itex]\vec s = 18 m[/itex]

    2. Relevant equations
    [itex]KE_i = \frac {1}{2} mv_i^2[/itex]
    [itex]\Delta KE = \vec F \vec s[/itex]
    [itex]\Delta KE = KE_f - KE_i \Rightarrow KE_f = \Delta KE + KE_i \Rightarrow \frac {1}{2} mv_f^2 = \Delta KE + KE_i[/itex]
    [itex]\Rightarrow v_f = \sqrt {\frac {2(\Delta KE + KE_i)}{m}}[/itex]

    3. The attempt at a solution
    [itex]KE_i = \frac {1}{2} (1,100 kg)(24 m/s)^2 = 316,800 J[/itex]
    [itex]\Delta KE = (-1.7x10^4 N)(18 m) = -306,000 J[/itex]
    [itex]\Rightarrow v_f = \sqrt {\frac {2((-306,000 J) + (316,800))}{(1,100 kg)}} = 4.4312 m/s \sim 4.4 m/s[/itex]

  2. jcsd
  3. Nov 14, 2014 #2


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    Staff: Mentor

    That looks right.

    And it means the title of this thread is a bit misleading.
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