Solving the Guillotine Problem: Theory & Examples

[Sheldinoh]

1. The problem statement

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Homework Equations

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.

 

[rl.bhat]

First of all using Newton's law and torque find the acceleration of the masses.

 

[Sheldinoh]

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

 

[Sheldinoh]

It would be 6m/s2 right?

 

[rl.bhat]

It would be 6m/s2 right?

Show your calculations.

 

[Sheldinoh]

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

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

a = 6

 

[rl.bhat]

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.

 

[Sheldinoh]

Thank you so much. You are a life saver.