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Acceleration of a system due to gravity

  1. Jan 18, 2015 #1
    The problem was present in a physics 1 exam, and I'm reasonably sure I know the answer, yet my friend contradicts me in my conclusion.

    1. The problem statement, all variables and given/known data
    Find magnitude of acceleration of system ABC. Masses of A, B and C are all equal and each has mass 2.00 kg. Let gravitational acceleration g = 9.81 m/s2. See figure below.
    Problem.png
    Disregard friction - castor, air, and surface.

    2. Relevant equations
    Newtons 2nd law of motion:
    F = m a (1)

    3. The attempt at a solution
    The force on the whole system is gravity's effect on B and C (weight of B and platform C). Through (1):

    F = (2)(2.00 kg)(9.81 m/s2) = 39.24 N

    Acceleration on the whole system is then, under the above force: (Through (1) again):

    a = (39.24 N)/[(3)(2.00 kg)] = 6.54 m/s2.

    Obviously, the acceleration of A is directed horizontally, while B and C are accelerating downwards. Still, the acceleration of each objects will be the same, yet in their respective directions. It is this value which I am after.

    Also, can someone less ignorant than I tell me if I am right in this:
    Without other external forces (other than gravity), the system will never accelerate faster than 9.81 m/s2 and the less the mass of A (and the larger the mass of B and C, equivalently), the closer the systems acceleration will be to 9.81 m/s2.

    Thank you in advance and I apologize for the triviality of the problem :s
     
  2. jcsd
  3. Jan 18, 2015 #2

    Bystander

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    Your analysis is complete and correct for the information you're wanting about the system. Any other questions?
     
  4. Jan 18, 2015 #3

    Doc Al

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    Your analysis is correct.
     
  5. Jan 18, 2015 #4
    Thanks for the (very) quick replies!

    If you don't mind, continuing on the theme of triviality; Could I make something accelerate faster than gravity using wheels and cables, like so (A):
    Idea.png
    Again, disregarding frictions. How should I think when finding acceleration and tensions in these kinds of "problems?"
     
  6. Jan 18, 2015 #5

    Bystander

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    If "A" is the larger mass, the unlabeled mass can be accelerated at greater than g; you've got the double (one and a halfle?) advantage with the pulley set-up. Think of an asymmetric see-saw, or catapult, with a large mass on the short end and a small mass on the long. Trebuchet. Might be a variety of other gravity driven "siege engines."
     
  7. Jan 18, 2015 #6
    Okay, so comparing my previous image to the one below:
    Idea_2.png
    Here, gravity's pull on A (again, like you did, assuming that A's mass is greater than that of the unlabeled), displacing A the distance s, will do the same to the unlabeled weight. In the previous image, displacing A by s, would displace the weight by 2 times s (?). I assume it is harder to displace A in the previous image, then, seeing as the work done by gravity is double there?
     
  8. Jan 18, 2015 #7

    Bystander

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    Is the same. "mgh" is "mgh" regardless of how the pulley, ropes, are rigged. The length of rope you've got to move past a particular point to lift/lower "A" a distance "h" can be changed, and the force you have to apply to pull the rope can be many times greater or less depending on how much mechanical advantage you "rig" into the block(s) and tackle.
     
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