# Solving the Guillotine Problem: Theory & Examples

• Sheldinoh
In summary, the conversation discusses a problem statement involving the use of Newton's law and torque to find the acceleration of masses. The equations used are I=.5MR^2, v=rw, and (M1+M2)a = M1(9.8) + M2(-9.8). The solution also involves finding the tension in different segments of a string.
Sheldinoh
1. The problem statement

http://i868.photobucket.com/albums/ab249/sheldonsimon/ScannedImage.jpg"

I=.5MR^2

## The Attempt at a Solution

mgh + .5mv^2 + Iw^2 = mgh + .5mv^2 + Iw^2

v=rw

I don't know if this is right or not.

Last edited by a moderator:
First of all using Newton's law and torque find the acceleration of the masses.

can you explain that a little more. I'm sorry

It would be 6m/s2 right?

Sheldinoh said:
It would be 6m/s2 right?

(M1+M2)a = M1(9.8) + M2(-9.8)

(20+5)a = 20(9.8) - 5(9.8)

a = 6

No. It is not correct.
Let T1 be the tension in the right segment of the string and T2 that of the left segment.
Then T1 - m1*g = m1a----(1)
R*(T2 - T1) = I*α-----(2)
m2*g - T2 = m2*a.----(3)
Substitute the values of I and α, and solve the equations to find a.

Thank you so much. You are a life saver.

## 1. What is the Guillotine Problem?

The Guillotine Problem is a mathematical puzzle that involves finding the minimum number of cuts needed to divide a rectangle into smaller rectangles of equal size.

## 2. Why is it called the Guillotine Problem?

The problem is named after the execution device, the guillotine, because the cuts required to solve the puzzle resemble the blade of a guillotine.

## 3. What is the significance of solving the Guillotine Problem?

The Guillotine Problem has practical applications in real-life scenarios such as cutting fabric into equal pieces or optimizing the use of space in a packing problem. It also has theoretical implications in the field of computational geometry.

## 4. What are some strategies for solving the Guillotine Problem?

There are several known strategies for solving the Guillotine Problem, including the top-down approach, bottom-up approach, and divide and conquer method. These strategies involve breaking down the original rectangle into smaller sub-problems and finding patterns to determine the minimum number of cuts.

## 5. Are there any real-world examples of the Guillotine Problem?

Yes, the Guillotine Problem has been applied in various industries, such as paper cutting, woodworking, and sheet metal fabrication. It is also commonly used in computer graphics for efficient image cropping and texture mapping.

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