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Hibbeler 13-25

  1. Feb 28, 2014 #1
    1. The problem statement, all variables and given/known data

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    2. Relevant equations

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    3. The attempt at a solution

    2ac + 3 = 0 => ac = 1.5m/s^2 upwards

    For FBD of C, Newton's 2nd law

    2T - 200g = 200*1.5 => T = 1131N

    For FBD of the beam,

    Take moments about A, and assume beam is rigid (CCW positive):

    2.5T - 3T - 300*6*9.81*3 + Rb*6 = 0

    RB = 8.92kN upwards

    Ra + Rb + T - T - 300*9.81*6 = 0 => RA = 8.73kN

    Is this correct? I don't see why the solution is posting the velocity when asking for a reaction
     

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  3. Feb 28, 2014 #2

    BvU

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    Maybe your copy should have been two-sided and the solutions manual continues on the next page?

    I draw your attention to the guidelines

    However, as I appreciate you at least show some of your work, I will go through part 3.

    Looks identical to what's in the middle picture, so I suppose that IS your work... Anyway, it's OK. Even though I can't find what c is. a is the acceleration, I guess, but even that isn't mentioned under 1.) problem statement, all variables and given/known data .

    Bravo.

    At his point I am missing something. I see 2 T from the pulley in the crate FBD, but I see only one T pulling down on the beam. My mistake or yours ?

    And there is something extra I can't explain: who is trying to pull the motor up with force T ? A little bird ? I sure hope the motor is well bolted on the beam, then!
     
  4. Feb 28, 2014 #3

    BvU

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    Just for the fun of it, and to hone your physics intuition: If the crate is off-center to the left, would you expect Ra < Rb ?
     
  5. Feb 28, 2014 #4

    BvU

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    And another one: the crate requires a bit more than 2 kN. The beam requires ..... If you find Ra+Rb > 17 kN, do you hear alarm bells ring ?
     
  6. Feb 28, 2014 #5
    It's not the motor that's being pulled up, if you take a free body of the motor, a normal force is exerted by the beam onto it, plus a tension force is pulling it down. So T is the normal force, otherwise it would fall through the beam. I accidentally used 300kg/m as the self-weight of the beam (it's actually 30kg/m in the problem), you have to include this, which will also contribute to the reaction, it's not only the crate.

    Yes, Ra should be greater than Rb by intuition, trying to figure out why this is not the case.
     
  7. Feb 28, 2014 #6

    BvU

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    Agree, but we were drawing a free body diagram of the beam!

    Physics intuition again: if you were standing on the beam pulling in Keira Knightley using a rope, would the force ON the beam be (you and her)*g up or down ?
     
  8. Feb 28, 2014 #7
    Yes, you are correct, my mistake, don't know what I was thinking. By Newton's 3rd law, the normal force on the beam should be pointing down.
     
  9. Feb 28, 2014 #8

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    I knew Keira might inspire some good physics!
     
  10. Feb 28, 2014 #9
    haha yes, couldn't find an answer to check against though. For people who have done this problem, I get Ra = 2108.15N and Rb = 1919.65N, hope you get the same answer
     
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