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Two Blocks connected by a rope

  1. Nov 7, 2014 #1
    1. The problem statement, all variables and given/known data
    The problem is from a worksheet and is a picture so I will try to describe the picture. A 3kg block and a 7kg block are connected by a rope and the 7kg block is falling from a table and the 3kg block is on the table. We are supposed to find the acceleration of the 3kg block in the x direction assuming it is a frictionless area.

    2. Relevant equations
    f=ma

    3. The attempt at a solution
    My teacher told me it is 7m/s^2 and he explained why and I am trying to understand why his explanation is true.

    First I will tell you what went through my head as I tried to solve this problem initially before I asked the teacher. I knew that the 7kg block was connected to the 3kg block by a rope and the 7kg block was falling and therefore pulling the rope which in turn would move the 3kg block. I knew that the mass was 7kg and that the acceleration due to gravity was causing it to fall at 9.8m/s^2 ( I will use 10m/s^2 for simplicity) so I calculated the force acting on the block to be 70N downward. From this I figured that if the block was falling with 70N of force then it must be pulling the rope with 70N which would be pulling the 3kg block at 70N. By this logic I calculated the acceleration with f=ma 70N=(3kg)(a) and calculated it to be (70/3) m/s^2. This is what I initially thought.

    I will paraphrase what my teacher said: He explained that there is 70N of force, but it is acting on both objects and therefore we have to apply both the mass of the 3kg and the 7kg in the calculation, thus: 70N=10kg(a) and a would equal 7m/s^2. I am sure he is right I am not arguing that I am just having trouble accepting his explanation as true when I picture the situation as I stated above as 70N of force pulling a 3kg block. I need some help in order to picture what is happening differently so I can understand why this is true, because naturally I see the situation happening differently.

    Any help is greatly appreciated.
     
  2. jcsd
  3. Nov 7, 2014 #2
    I tried to include an image:
     

    Attached Files:

  4. Nov 7, 2014 #3

    mfb

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    If that would be true, the 7kg-block would be in force equilibrium and would not accelerate at all. That's not what happens.
    Oh, and it would allow extremely large accelerations just by replacing the 3kg-object by something very light (or even nearly massless), in contradiction to actual falling objects.
     
  5. Nov 7, 2014 #4
    Ok i like your example and I can see why my reasoning is not correct... Unfortunately Im having trouble still about viewing both blocks as 1 system
     
  6. Nov 7, 2014 #5
    I am also a little confused about what you mean about the force equilibrium part i dont see why that is true
     
  7. Nov 7, 2014 #6

    mfb

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    If you have 70 N downwards from gravity and 70 N upwards from tension, the total force on the block is 70N - 70 N = 0. Use F=m*a to calculate the acceleration of the block with zero force.

    The tension in the rope will be less than 70N.
     
  8. Nov 7, 2014 #7
    I think I understand, thanks. Overall that would mean no matter how heavy the falling block is and how light the block on the table is the acceleration in the x direction could never be more than the acceleration due to gravity correct?
     
  9. Nov 7, 2014 #8

    mfb

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    Correct.


    (It is possible to make things fall faster than 10m/s^2 just with gravity, but that needs different setups)
     
  10. Nov 7, 2014 #9
    see
    I can explain this in my words and with what i know. Actually here we are supposed to consider both the blocks and thread as 1 particular system. And this system always has a common acceleration. Let me give you an example 'when a train moves at a time acceleration of all bogies is same'. Hence here we have to consider the mass of both objects on which force of 70N due to gravitational force is applied. i hope you got it.
     
  11. Nov 8, 2014 #10
    Thank you, the hard part about this problem for me was treating it as one system because I did not see it like that at first
     
  12. Nov 8, 2014 #11

    PhanthomJay

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    I don't fault you at all for not understanding the forces and accelerations by looking at the system. Although the answer and explanation is correct, you should get used to drawing free body diagrams for each block. The hanging block has its own weight downward and the unknown tension in the rope acting up. Apply newtons 2nd law to get an equation with T and a unknown. Do the same for the other block to get a second equation. Then solve the two equations for the 2 unknowns T and a.
     
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