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Conservation Of Energy With Friction

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data

    Hi, Im having trouble with this problem. I'ld be very grateful if anyone could help me :) I've only done it with the conservation of energy way because Im not too sure how to go about it with the D'alembert principle.

    A Car with a mass of 100kg is pulled along a horizontal surface by a force of 1000N. The car is initially at rest, and is pulled 25 meters. The co-efficient of friction between the car and road is 0.6.

    Determine the acceleration of the car using the principle of conservation of energy and D’alemberts principle.

    Car Mass: 100kg
    Co-efficient of friction is 0.6
    N = (mg) = 100 x 9.81 = 981N
    Frictional Resistance (Fr) = μN = 0.6x981 = 588.6N
    Distance = 25 meters.

    3. The attempt at a solution

    Using Conservation of energy:

    PE + KE + Win = PE + KE + Wout + Losses
    0 + 0 + (F x Distance) = 0 + (1/2 mv^2)+ 0 + (Fr x distance)

    (F x Distance) - (Fr x distance) = 1/2 x mv^2

    (1000N x 25meters) – (588.6 x 25 meters) = 1/2 x 1000v^2

    (1000N x 25meters) – (588.6 x 25 meters) / (1/2 x 1000) = v^2

    47.07 = v^2

    6.86 m/s = V

    Acceleration is 6.86 m/s

    Any help would be much appreciated :)
     
  2. jcsd
  3. May 8, 2013 #2

    Doc Al

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    Staff: Mentor

    V is the final velocity, not the acceleration. You'll have to use some kinematics to get the acceleration from the velocity and the distance. (Or just apply Newton's 2nd law.)
     
  4. May 8, 2013 #3
    hi,

    Thanks for taking the time to respond.

    I've used this equation before but the lecturer never told me it was kinematics :/

    is everything correct now?
    ebjDmnG.jpg

    thanks again.
     
    Last edited: May 8, 2013
  5. May 8, 2013 #4

    Doc Al

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    Staff: Mentor

    The kinematic approach is fine, but I see that you made an error in calculating V2 in your first post. Revisit that.
     
  6. May 8, 2013 #5
    hmm, i did make a mistake

    :/

    Im getting 4.114 as acceleration now which seems correct

    M x a = F
    100 x 4.114 = 411.4N

    Force - resistive force = F
    1000N – 588.6 = 411.4N

    So i think I got there :)

    Would this be correct for the D'alembert principle method?
    VahDnrr.png

    Thanks again :)
     
    Last edited: May 8, 2013
  7. May 8, 2013 #6

    Doc Al

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    Staff: Mentor

    You got it! :approve:
     
  8. May 8, 2013 #7
    excellent :) Thanks again for all your help
     
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