Cubical block on a cylinder challenging problem

In summary, the challenge of the cubical block on a cylinder problem is to determine the maximum possible height that a cubical block can be stacked on top of a cylinder without falling over. The solution to this problem is affected by the dimensions and weights of the cubical block and cylinder, as well as the surface friction between the two objects. This problem can be solved using the principles of physics, specifically the equations of static equilibrium and torque. It has real-world applications in the design of structures and objects that need to be stacked or balanced on top of cylindrical objects, and there are multiple solutions to this problem.
  • #1
david456103
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Homework Statement


A cubical block of side L rests on a fixed cylindrical drum of radius R. Find the largest value of L for which the block is stable.

This is problem 6.35 from the Kleppner+Kolenkow Introduction to Mechanics book. I honestly have no clue where to even start on this problem. Anyone care to give me a hint?
 
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  • #2
Say you displace the block by an angle θ. Where's the support point? Where's the center of mass in relation to the support point?
 

FAQ: Cubical block on a cylinder challenging problem

What is the challenge of the cubical block on a cylinder problem?

The challenge of this problem is to determine the maximum possible height that a cubical block can be stacked on top of a cylinder without falling over.

What are the factors that affect the solution to this problem?

The solution to this problem is affected by the dimensions and weights of the cubical block and cylinder, as well as the surface friction between the two objects.

How can this problem be solved mathematically?

This problem can be solved using the principles of physics, specifically the equations of static equilibrium and torque. By balancing the forces and moments acting on the block and cylinder, the maximum height can be calculated.

Are there any real-world applications of this problem?

Yes, this problem has real-world applications in the design of structures and objects that need to be stacked or balanced on top of cylindrical objects, such as storage containers or building columns.

Is there only one solution to this problem?

No, there are multiple solutions to this problem as the maximum height will vary depending on the dimensions and weights of the block and cylinder. The solution can also be affected by external factors such as wind or vibrations.

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