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Free Body Diagram of a Truck with a Box

  1. Oct 10, 2014 #1
    1. The problem statement, all variables and given/known data
    A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you stomp on the gas and the truck accelerates. To your horror, the box starts to slide toward the back of the truck. (Assume that the truck is accelerating to the right.)

    Draw clearly labeled free-body diagram for the truck. (The bed of the truck is not frictionless.)
    Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded.

    2. Relevant equations
    Nground: Normal force
    Nb: Reaction to the normal force on the box from the truck
    Froad: Reaction force to tires' backward push
    Fk: The box's friction force on the truck bed
    WT: Weight of the truck

    3. The attempt at a solution
    Nground points up.
    WT and Nb point down.
    Froad points right.
    Fk points left.

    I made the length of Fk shorter than Froad.
    I made the length of Nground = length of WT = length of Nb.

    Now I'm thinking that the length of WT and Nb should be equal but together add up to the length of Nground so that the net force in the y direction is 0.
     
  2. jcsd
  3. Oct 10, 2014 #2

    mfb

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    Can you attach a picture of your sketch? That would help a lot.

    Yes you'll have to add the weight of box and truck for the force between truck and ground - in the same way you cannot simply remove the mass of the driver or any part of the truck from this force.
     
  4. Oct 10, 2014 #3
    My only options are the ones I provided in relevant equations. I assume that WT includes the weight of the box in the truck too so I don't think that's the issue here. Here's the sketch, the two overlapping vectors at the bottom are WT and Nb.
     

    Attached Files:

    Last edited: Oct 10, 2014
  5. Oct 10, 2014 #4
    Here's a little diagram I made too if that helps at all.
     

    Attached Files:

  6. Oct 11, 2014 #5

    haruspex

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    Since you are listing all the forces on the truck, and the normal force between the truck and the box is one of these, you should not include that in WT. So the normal force from the ground should equal their sum.
    But why do you think WT and Nb would be equal? And why have you drawn Fk about equal in length to Froad?
     
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