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Urgent help with Forces, Components, Acceleration

  1. Oct 10, 2012 #1
    << Original post restored by Moderators after being deleted by riseofphoenix >>

    While you are packing up to drive to school, you forget your laptop on the roof of your car. As you are driving west towards school at v = 45 mi/hr, you suddenly remember the laptop, roll down your window, and put your hand on the laptop exerting a force of 50 N downward and 20 N horizontally toward the rear of the car on the laptop, and hit the brakes. The coefficient of static friction of between the laptop and car roof is 0.4. The mass of the car is 1200 kg and the mass of the laptop is 4 kg.

    (a) Draw the free body diagram of the laptop. Label ALL forces acting on it. Label your coordinate axes defining your directions.

    I know that:
    v = 20.1168 m/s
    F1 (downward) = 50 N
    F2 (horizontal) = 20 N
    μs = 0.4
    fs = 0.4*n
    mass of the laptop = 4 kg

    Is this how the free-body diagram should look like?
    IMAGE: http://i11.photobucket.com/albums/a179/slourg/freebodydiagram_zps7eb1828b.jpg [Broken]

    (b) What is the maximum acceleration (magnitude AND direction) that can be applied to the car so that the laptop does not end up in several pieces on the pavement?

    Forces in the x-direction:
    20
    fs


    ƩFx = ma
    20 + fs = (4)a
    20 + 0.4n = (4)a​

    ** Solve for normal force, n, from ƩFy = 0 **
    20 + 0.4(-10.8) = (4)a
    20 - 43.2 = (4)a
    -23.2 = (4)a
    -23.2/4 = a
    -5.8 m/s2 = a​

    QUESTION: Is that the answer? a = -5.8 m/s2? If not, can you show me how to get the answer?

    Forces in the y-direction:
    n
    50
    -39.2


    ƩFy = 0
    n + 50 + (-39.2) = 0
    n + 50 - 39.2 = 0
    n + 10.8 = 0
    n = -10.8​
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 10, 2012 #2

    SammyS

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    Depending upon the amount of deceleration due to braking, the force of friction may be towards the rear of the vehicle. Under maximum braking, the force of friction will be towards the rear of the vehicle.

    The normal force is in opposition to both the weight and the applied force of 50 newtons.
     
    Last edited by a moderator: May 6, 2017
  4. Oct 10, 2012 #3
    <<Original post restored by moderators after being deleted by riseofphoenix>>

    Wait...what do you mean?? D=

    Is my answer right???

    Omg...please don't take offense to thins but I have no idea where you're getting at... :(
    Everytime I post a thread like this, I always get extremely vague/abstract answers.
    Can you please clarify?

    Are you saying normal force DOESN'T equal -50 + 39.2?
     
    Last edited by a moderator: Oct 10, 2012
  5. Oct 10, 2012 #4

    SammyS

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    No.
    Yes, that's what I'm saying.

    What are the vertical forces acting on the laptop?
     
  6. Oct 10, 2012 #5
    <<Original post restored by moderators after being deleted by riseofphoenix>>

    So what does N equal then?

    n + (-50) + (-39.2) = 0
    n = 89.2??
     
    Last edited by a moderator: Oct 10, 2012
  7. Oct 10, 2012 #6

    SammyS

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    Yes.
     
  8. Oct 10, 2012 #7

    SammyS

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    The main force keeping the laptop from sliding (forward) as the car brakes is the force of friction between the roof & the laptop. To keep the laptop from sliding forward, in what direction must the force of friction act on the laptop?

    That 20 N component merely aids in keeping the laptop from sliding forward.
     
  9. Oct 10, 2012 #8
    <<Original post restored by moderators after being deleted by riseofphoenix>>

    So it should be...

    20 + 0.4(89.2) = (4)a
    20 + 35.68 = (4)a
    55.68 = (4)a
    13.92 m/s2= a

    Is that the answer?
     
    Last edited by a moderator: Oct 10, 2012
  10. Oct 10, 2012 #9

    SammyS

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    The method looks good.

    Let's see ... How could we check the answer?
     
  11. Oct 10, 2012 #10
    <<Original post restored by moderators after being deleted by riseofphoenix>>

    East! since the car is already moving west.
    Right?

    So is the direction East?
     
    Last edited by a moderator: Oct 10, 2012
  12. Oct 10, 2012 #11

    SammyS

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    If the car's moving west, then yes, east. Also, if the car's moving west then the 20 newton component is also east.
     
  13. Oct 10, 2012 #12

    ZapperZ

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    From the PF rules:

    This thread will not be deleted.

    Zz.
     
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