TBR physics chapter 2 example 2.3a (limiting cases)

[poop420]

The question is about 2 masses. M1 and M2 held together by a pully. and ask which equation would give the acceleration.
The 2 equations that i narrowed it down to where
A) a = (m1 - m2)g/(m1+m2)
B) a = (m1+m2)g/(m1-m2)
They said to set the limited case to 0 acceleration in which m1=m2. And it says only equation A would fulfill this . But I dont see this happening . Why is B wrong as well ??

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[Sed8&Intub8]

So lets see. For example, if they are hanging off a pulley and they are both large weights what do you think will happen?
Lets say one is m1=46kg and m2=45kg, you wouldn't expect them to accelerate very fast would you? Plug those numbers into A and B and see what happens?

A will make them go slow (as excepted), B will make them fly away

 

[DrknoSDN]

It is basically saying that if you had 2 equal masses on the opposite end of a pulley you should assume they would not be moving (acceleration of zero). What equation describes that scenario?

For A, if you have M1 and M2 as the same... You get (0 g) /(M1+M2) = 0
Zero over anything is zero so A is true. If the masses are equal you would expect zero acceleration because equal masses hanging should not accelerate if they were stationary to start.

B is false because there is no way to have acceleration be zero. It's not possible because you would have both positive mass (mass cannot be zero or negative) giving you the equation:
acceleration = (positive + positive) * g / (Positive) = Positive for all real values.
B can never have zero acceleration so that is false because we know it is possible for two masses hanging on each side of a pulley to not be accelerating.

 

[poop420]

So lets see. For example, if they are hanging off a pulley and they are both large weights what do you think will happen?
Lets say one is m1=46kg and m2=45kg, you wouldn't expect them to accelerate very fast would you? Plug those numbers into A and B and see what happens?

A will make them go slow (as excepted), B will make them fly away

I get that method of getting the right answer but what about when m1=m2 like the book used.. so lets say m1=1 and m2=2 . Then B would be a= (1+1/1-1) x g which would be a= (2/0) x g and if you divide by a 0 then the entire number is a 0 so a = 0 But the book says this cannot happen. I apologize if this sounds dumb

 

[Sed8&Intub8]

I get that method of getting the right answer but what about when m1=m2 like the book used.. so lets say m1=1 and m2=2 . Then B would be a= (1+1/1-1) x g which would be a= (2/0) x g and if you divide by a 0 then the entire number is a 0 so a = 0 But the book says this cannot happen. I apologize if this sounds dumb

You can't divide by zero

 

[poop420]

You can't divide by zero

Thats it!! thank you!!!! Sorry that was stupid !!