Solve Hanging Blocks Homework: Find Max Height

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In summary, the conversation discusses the maximum number of blocks that can be stacked on top of each other before the tower topples. The center of mass must be beyond the edge of the first block for the tower to fall. The equation for determining this involves the distance to the center of mass multiplied by the total mass, which is equal to the sum of individual masses multiplied by their distance from a reference point. The pattern for determining the center of mass for each block can be found by working out the arithmetic series of 0.15L increments.
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ItsImpulse
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Homework Statement



How many blocks can you stack on top of each other before the tower falls? Each block has a mass m and a length l. The first block is on the table. The second block is stacked on top of the first but moved by 0.15L to the right. This pattern continues

Homework Equations



Distance to centre of mass multiplied by total mass is the summation of each individual mass multiplied by distance from reference point .

The Attempt at a Solution



For the tower to topple , centre of mass has to be beyond the edge of the first block so I can say that 0.5L(n)(m) = some form of arithmetic series due to the increments of 0.15L but I don't know how to set up the equation
 
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So start working it out. Where is the center of mass for 1 block on top, for 2, for 3 ? Do you see a pattern ?
 

1. How do I determine the maximum height of hanging blocks in my homework?

To determine the maximum height of hanging blocks in your homework, you can use the equation: h = √(2mgh)/(m + M) where h is the maximum height, m is the mass of the hanging block, M is the mass of the block on the ground, and g is the acceleration due to gravity (9.8 m/s²).

2. What is the difference between hanging blocks and regular blocks?

Hanging blocks are suspended from a support, while regular blocks are resting on a solid surface. This difference affects the calculation of the maximum height, as hanging blocks experience a different type of motion compared to regular blocks.

3. Can I use this equation for any type of hanging block?

Yes, this equation can be used for any type of hanging block as long as the mass and acceleration due to gravity are known. However, it is important to note that this equation assumes ideal conditions and may not be completely accurate in real-world scenarios.

4. How can I apply this concept to real-life situations?

The concept of finding the maximum height of hanging blocks can be applied to various situations in engineering, physics, and architecture. For example, it can be used to determine the maximum height a crane can lift a load or the maximum height a swing can reach.

5. Is there a specific unit of measurement for the maximum height?

The maximum height can be measured in any unit of length, such as meters, feet, or centimeters. It is important to ensure that all values used in the equation are in the same unit of measurement for accurate results.

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