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Pushing Block Question

  1. Oct 22, 2004 #1
    Blocks of mass 5,10,15kg are lined up from left to right in that order on a frictionless surface so each is touching the next one. A rightward-pointing force of magnitude 17N is applied to the left-most block. What is the magnitude of the force that the middle block exerts on the rightmost one?
    answer: 8.5N

    What is the magnitude of the force that the left most block exerts on the middle one?
    answer: 14.2N

    Suppose now that the left-right order of the blocks is reversed. Now find the magnitude ofthe force that the leftmost block exerts on the middle one?
    answer: 8.5N

    I already know the answer, but i do not understand the the concept behind solving this. can someone explain to me what kind of equations i need to use and why the question 1 and question 3 have the same answer. THanks :)
     
  2. jcsd
  3. Oct 22, 2004 #2

    HallsofIvy

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    That problem is actually much simpler than it looks. All of the masses must move together so, first, think of the masses as a single 5+10+15 = 30 kg mass. Since F= ma, 17N= 30a so a= 17/30 m/s2.

    The right most block has mass 15 kg. Again, F= ma. Since it is moving at a= 17/30,
    we must have F= 15(17/30)= 17/2 = 8.5 N. The only way any force is applied to that block is by the middle on pushing it.

    The middle block has mass 10 kg. Since it is also moving at a= 17/30, we must have F= 10(17/30)= 17/3 N. But the middle block is push on the right block with for 17/2 N so the right block is pushing on the middle block with force -17/2 N (Newton's third law). Taking F to be the force the left block applies to the middle block, we have total force= F- 17/2= 17/3 so F= 17/2+ 17/3= 51/6+ 34/6= 85/6= 14 1/6 N which is actually slight less than "14.2". You think of this as "the left block pushes the middle block with force 85/6 N. 17/3 of that accelerates it and the other 17/2 is passed on to the right block".

    Now the order is switched: the masses of the blocks are 15 kg, 10 kg, 5 kg.
    Still, the total mass is 30 kg so the common acceleration of all blocks is 17/30 m/s2. There is 17 N force applied to the right block. Since it has mass 15 kg, it requires only 15(17/30)= 17/2 N to accelerate it. The rest of the 17 N, 17- 17/2= 17/2 N is "passed on" to the next block. The force the left block exerts on the middle block is 17/2= 8.5 N.
     
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