Checking answer to stacking problem

  • Thread starter timetraveller123
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In summary, the conversation discusses a problem involving stacking bricks on a smooth horizontal surface with an offset at each block. The question is how many bricks can be stacked before the pile topples over, and the solution involves calculating the center of mass and setting it equal to half the length of the block. The final answer is 6 bricks.
  • #1
timetraveller123
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Homework Statement


A uniform brick of length L is laid on a smooth horizontal surface. Other equal bricks are now piled on as shown, so that the sides form a continuous plane, but the ends are offset at each block from the previous brick by a distance 0.15L. How many bricks can be stacked in this manner before the pile topples over?

Homework Equations


centre of mass = (m1x1 + m2x2) / (m1 + m2)

The Attempt at a Solution


i did the solution and got total number of blocks when toppling occurs is 7 is it correct i did it stating that toppling occurs when center of mass is at least l/2 away from the center is it correct?
one more the question states smooth floor is it important?
 
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  • #2
vishnu 73 said:
total number of blocks when toppling occurs is 7
Yes.
vishnu 73 said:
when center of mass is at least l/2 away from the center
The centre of mass of which set of bricks, and L/2 from the mass centre of what?
 
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  • #3
i started calculating the centre of mass from on top of the stack so if at any point the centre of mass a block and the blocks above it lies outside of it it topples is the logic correct
 
  • #4
vishnu 73 said:
... i did it stating that toppling occurs when center of mass is at least l/2 away from the center is it correct?
The idea is correct, but I don't see how you got 7 bricks. Can you show me?
 
  • #5
vishnu 73 said:
i started calculating the centre of mass from on top of the stack so if at any point the centre of mass a block and the blocks above it lies outside of it it topples is the logic correct
That's still a bit garbled. I assume you mean that if the centre of mass of the bricks above a given brick lies beyond that given brick then they will topple.
So when it topples, where is the tipping point?
 
  • #6
so i assumed n blocks were stacked
so the centre of mass of top two blocks measured from the centre of bottom block is
(0 * m + 0.15L *m)/2m
then using this the centre of mass top two blocks and the third block from top once again measured from centre of third block is

( 0.15L *m)/2m + 0.15L)*2m/3m here 3m is the mass of all three blocks and the third block itself is not contributing to the numerator

so for n blocks the centre of mass from the centre of nth block is (the equation is expanded out and cancelling m and l)

(0.15 + 0.15(2) ...0.15*n)/(n+1) ≥ 0.5 here 0.5 is representive of half the length of the block as centre of mass was measured from centre of block half the length means that it is tipping over

solving for n gives 6.67 or 7 blocks when it topples
is it logical or have i made i mistake
 
  • #7
haruspex said:
So when it topples, where is the tipping point?
You did not explicitly answer the question that @haruspex asked, but the answer is implicit in the inequality that you set up. Anyway, it seems you understand the basics of the problem although your solution is a bit unorthodox.
vishnu 73 said:
solving for n gives 6.67 or 7 blocks when it topples
The problem is asking, "How many bricks can be stacked in this manner before the pile topples over?"
 
  • #8
oh 6 then?
 
  • #9
vishnu 73 said:
oh 6 then?
Right.
 
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  • #10
thanks
 

FAQ: Checking answer to stacking problem

What is the purpose of the stacking problem?

The purpose of the stacking problem is to assess an individual's ability to think critically and solve complex problems. It involves arranging a set of items in a specific order based on given criteria.

How do you check the answer to a stacking problem?

To check the answer to a stacking problem, you can follow these steps:

  • Review the given criteria and make sure the items are stacked in the correct order.
  • Check for any errors or mistakes in the stacking arrangement.
  • Compare the final arrangement to the correct answer.
  • If the stacking problem involves physical objects, you can physically stack them according to your answer to see if it matches the correct arrangement.

What are some common mistakes people make when solving a stacking problem?

Some common mistakes people make when solving a stacking problem include:

  • Misinterpreting the given criteria and stacking the items in the wrong order.
  • Forgetting to include all the items in the stacking arrangement.
  • Not paying attention to specific details, such as the orientation of the items or the number of items in each stack.
  • Making careless errors, such as stacking an item upside down or in the wrong position.

How can I improve my skills in solving stacking problems?

To improve your skills in solving stacking problems, you can try the following strategies:

  • Practice regularly with different types of stacking problems.
  • Pay attention to details and carefully read the given criteria before attempting to solve the problem.
  • Break down the problem into smaller, more manageable steps.
  • Use trial and error to test different arrangements and find the correct solution.
  • Seek help from others or discuss the problem with a study group to gain new perspectives.

Are there any real-world applications of stacking problems?

Yes, stacking problems have real-world applications in various fields, including:

  • Manufacturing and production, where items need to be stacked in a specific order for efficient processing and transport.
  • Logistics and supply chain management, where items need to be stacked in a specific way to optimize space and ensure safe transportation.
  • Inventory management, where items need to be stacked in a specific order to facilitate easy access and retrieval.
  • Architecture and design, where the arrangement of stacked objects can affect the stability and aesthetics of a structure.

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