Atwood's Machine: Solving for Force & Acceleration

[KevinFan]

Homework Statement

http://[url%3Dhttps://postimg.org/image/pov8gzkr5/][ATTACH=full]200173[/ATTACH]

[ATTACH=full]200174[/ATTACH]
The question is shown above in the image.
[h2]Homework Equations[/h2]
F=ma

[h2]The Attempt at a Solution[/h2]
I personally think the answer should be option B. The movable pulley requires 1/2 of the force compare with the fixed pulley, therefore the a1 is 2 times a2. Can anyone confirm my logics please?

 

[ehild]

Homework Statement

http://[url%3Dhttps://postimg.org/image/pov8gzkr5/][ATTACH=full]200175[/ATTACH]

[ATTACH=full]200176[/ATTACH]
The question is shown above in the image.
[h2]Homework Equations[/h2]
F=ma

[h2]The Attempt at a Solution[/h2]
I personally think the answer should be option B. The movable pulley requires 1/2 of the force compare with the fixed pulley, therefore the a1 is 2 times a2. Can anyone confirm my logics please?[/QUOTE]
No. The ratio is determined by fact that the length of the whole rope is constant.

 

[KevinFan]

No. The ratio is determined by fact that the length of the whole rope is constant.

Could you elaborate a bit?

 

[ehild]

Imagine that m1 raises by 1 cm. How much does the piece of rope keeping the left pulley get shorter? The length of the whole rope does not change. So the right piece gets longer. What is the diplacement of m2?

 

[KevinFan]

Imagine that m1 raises by 1 cm. How much does the piece of rope keeping the left pulley get shorter? The length of the whole rope does not change. So the right piece gets longer. What is the diplacement of m2?

I think the displacement of m2 would be 1cm as well

 

[ehild]

Why? The right piece of string should be longer by the same as the left piece gets shorter. But the left piece consists of two pieces, and both of them gets shorter by 1 cm.

 

[KevinFan]

Why? The right piece of string should be longer by the same as the left piece gets shorter. But the left piece consists of two pieces, and both of them gets shorter by 1 cm.

View attachment 110436

oh... so the displacement of m2 should be 2 cm and a1=1cm/t^2, a2=2cm/t^2. abs(a1)=abs(1/2(a2))
Option C is the correct answer

 

[ehild]

Yes

 

[KevinFan]

Yes

Thank you very much for your explanation