How Do You Calculate the Acceleration of a Pulley System with Air Resistance?

AI Thread Summary
To calculate the acceleration of a pulley system with weights of 11KG and 33KG, consider the forces acting on each mass, including gravity and air resistance of 77N. The force of gravity on the 11KG weight is 107.8N, while the 33KG weight has a gravitational force of 323.4N. The net force can be found by subtracting the air resistance from the total gravitational forces acting on each weight. It is essential to apply Newton's second law (Fnet = ma) to determine the acceleration, taking into account the tension in the rope, which can be labeled as "T." Understanding the interaction of these forces is crucial for accurately calculating the system's acceleration.
Evolution17
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An 11KG weight and 33KG weight are suspended by a rope on a pulley. There is an air-resistance force of 77N working on all objects. Determine the acceleration.



Fg=mg Fnet=ma ma=f1on2+f2on1



The force of gravity on the 11KG weight is 107.8N (11*9.8) and since this weight will be pulled up (lighter) the 77N works with, coming out to be 184.8N. For the second weight, Fg=323.4N and the Ff will work against it since it is moving down (400.4N). Then I have no clue where to take it next, I could subtract the forces and get 216N and then divide it by the mass but that is clearly wrong. Any further help (or demonstration on how to use the 1on2 2on1 formula) would be greatly appreciated.
 
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Evolution17 said:
Any further help (or demonstration on how to use the 1on2 2on1 formula) would be greatly appreciated. [/b]
No idea what you mean by the 1on2 or 2on1 formula.

Instead, why not draw free body diagrams for each mass. What forces act on each? Apply Newton's 2nd law to each mass.
 
Hi Evolution17! :smile:
Evolution17 said:
The force of gravity on the 11KG weight is 107.8N (11*9.8) and since this weight will be pulled up (lighter) the 77N works with, coming out to be 184.8N. For the second weight, Fg=323.4N and the Ff will work against it since it is moving down (400.4N). Then I have no clue where to take it next, I could subtract the forces and get 216N …

You seem to have added the 77N in both cases (so that they cancel). :redface:
 
I thought so too about the 77N cancelling out, stated it just to be safe. And the 1on2 2on1 formula is used to calculate tension, atleast that's what our teacher taught us. There is no tension lesson in our textbook and the videos on youtube are a bit too complicated.

Also, I did do Newtons second law (fnet=ma) that's how I got the force of gravity, I just don't know how to find the acceleration of the blocks. The 33kg will go down and the 11kg will go up they're connected.
 
Evolution17 said:
I thought so too about the 77N cancelling out, stated it just to be safe. And the 1on2 2on1 formula is used to calculate tension, atleast that's what our teacher taught us. There is no tension lesson in our textbook and the videos on youtube are a bit too complicated.
Just call the tension "T". It's one of the unknowns you can solve for.

Also, I did do Newtons second law (fnet=ma) that's how I got the force of gravity, I just don't know how to find the acceleration of the blocks.
You'll solve for the acceleration, of course. Show the equations you have for each mass.

The 33kg will go down and the 11kg will go up they're connected.
Makes sense.
 
Last edited:
(just got up :zzz:)
Evolution17 said:
I thought so too about the 77N cancelling out, stated it just to be safe.

but the two 77N won't cancel

they pull in the same direction (along the rope), they both make the rope move slower, don't they? :smile:
 

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