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ME Statics - Wedge problem

  1. Nov 19, 2014 #1
    1. The problem statement, all variables and given/known data
    The crate shown is held against wedge B by a spring. The spring is 96.0% of its original uncompressed lengthl=2.75m, and the spring constant is given ask=1650N/m. The coefficient of static friction at all contacting surfaces is μs=0.150. The mass of the crate is m=22.0kg . The angle is θ=11.0∘. Neglect the mass of the wedge. Assume the crate only moves in the y direction and that wedge A cannot move.
    8.3_main.jpg
    Determine the magnitude of the smallest horizontal force P that is necessary to begin moving the crate upward.
    2. Relevant equations


    3. The attempt at a solution
    I found the normal from the spring and the weight of the box to be 397N (this is known to be the correct value).

    Since A can't move, we can draw a FBD of block B.

    Untitled.png
    I noticed that I drew the line for the 79 degree angle for f wrong. ignore it. The 79 degrees is supposed to be along the Y-axis. The number is still correct.

    Sum of the forces in X = 0 = -P + Ncos79 + .15Nsin79

    Sum of the forces in Y=0=-397+NSin79 - .15Ncos79

    Using a matrix to solve for P we get P=141 N which is incorrect. I've ran out of ideas here. Every way I do it I seem to get the same answer but it supposedly incorrect.
     
  2. jcsd
  3. Nov 20, 2014 #2

    NascentOxygen

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    Staff: Mentor

    You have substituted your integer answer into the equations and confirmed it's a perfect fit?

    Do you know what the correct answer is supposed to be?

    I make the spring & weight combo to be 397.1N (using g=9.8 m/s²).
     
    Last edited: Nov 20, 2014
  4. Nov 20, 2014 #3
    Yes. It's close enough. The answer doesn't need to be exact. It's 3 sig-figs and within 5 or 10 % and the program will let you know the answer.
     
  5. Nov 20, 2014 #4

    NascentOxygen

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    Staff: Mentor

    My working agrees with your pair of ∑ f equations.
     
  6. Nov 20, 2014 #5
    Very strange... I will ask my professor tomorrow. Thank you, Sir.
     
  7. Nov 15, 2016 #6
    You forgot the force of static friction between the crate and block B, opposing block B moving to the left (it points to the right at the top of the block). When you sum forces in the x this will change your answer slightly for F which actually changes a lot in your answer. Hope this helps anyone else who is looking to this for help!
     
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