1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding acceleration of block

  1. Feb 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Three blocks A,B and C, whose masses are 9 kg, 9 Kg and 18 kg respectively as shown in the figure, are released from rest. The co-efficient of friction between the block A and the horizontal surface is 0.5 and The co-efficient of friction between the block B and the horizontal surface is 0.5. Find the acceleration of the block C just after the release. [Take g=10 m/s^2]. All strings and pulleys are ideal.


    2. Relevant equations



    3. The attempt at a solution
    I can't figure out how the motion of block B will affect the motion of the other two blocks. I am unable to form any equation here.

    Any help is appreciated. Thanks!
     

    Attached Files:

  2. jcsd
  3. Feb 13, 2013 #2

    tms

    User Avatar

    Start by drawing a diagram showing all the forces on all the blocks. Use symbols, not numbers, in order to see what is going on (plugging in numbers early obscures the physics).

    Block C is the key: without it, nothing will happen. When C is added, it will (maybe, depending on its weight and the other forces) pull B to the right.
     
  4. Feb 13, 2013 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member


    Just take the accelerations of the blocks as aA, aB, and aC, and figure out how they are related. The length of the rope is constant.

    ehild
     
  5. Feb 13, 2013 #4
    I have drawn the free body diagrams (see attachment) But still, I am not sure what to do next?
     

    Attached Files:

  6. Feb 13, 2013 #5
    I have seen some examples in the past where this way of solving problems is used but I have never been able to use this way anywhere.
     
  7. Feb 13, 2013 #6

    tms

    User Avatar

    So far, so good. Now you see if you can figure out what some of the forces are in terms of the others, and you use F = ma.
     
  8. Feb 13, 2013 #7
    2T-μmg=maB
    T-μmg=maA
    Mg-T=MaC

    I have four variables and three equations. I am stuck here. :confused:
     
  9. Feb 13, 2013 #8

    ehild

    User Avatar
    Homework Helper
    Gold Member

    How are the accelerations related?
    Think: if A moves to the right by ΔxA and B moves to the right by ΔxB how much the horizontal part of the rope becomes shorter? And the vertical path longer?


    ehild
     
  10. Feb 13, 2013 #9
    Does it become shorter by ΔxA+2ΔxB?
     
  11. Feb 13, 2013 #10

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Yes, for the horizontal part. And what is the downward displacement of C then?

    ehild
     
  12. Feb 13, 2013 #11
    Wouldn't that be again equal to ΔxA+2ΔxB? :confused:
     
  13. Feb 13, 2013 #12

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Yes, it is. And what about accelerations? They are the second time derivatives of displacements.

    ehild
     
  14. Feb 13, 2013 #13
    aC=aA+2aB

    Do I need to solve these four equations?
     
  15. Feb 13, 2013 #14

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Yes. Express all accelerations from the other three and substitute into aC=aA+2aB. You can use the numerical data it is easier.

    ehild
     
  16. Feb 13, 2013 #15
    Equation (i): T-45=9aA
    Equation (ii): 2T-45=9aB
    Equation (iii): 180-T=18aC

    Multiplying (ii) with 2 and adding it with (i):
    5T-135=9aC ...(iv)

    Multiplying (iii) with 5 and adding it with (iv)
    5(180-27)=99aC
    Solving this equation doesn't give me the right answer. :(
     
  17. Feb 13, 2013 #16

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Find all a-s and T. Show the results.

    ehild
     
  18. Feb 13, 2013 #17
    I only need aC and my last equation doesn't give the right answer.
     
  19. Feb 13, 2013 #18

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Find aA. If it is negative, the initial assumption that it moves was
    not valid.

    ehild
     
  20. Feb 13, 2013 #19
    Yep, aA comes out to be negative. :)

    What next? Assume that A moves left?
     
  21. Feb 13, 2013 #20

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Such problems with ropes and friction, are tricky. You need to take into account that a rope can not push, and the friction can prevent some blocks from motion. You need to determine all accelerations and tensions to be sure that neither of them is negative.

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding acceleration of block
Loading...