Acceleration of strings in two pulley systems

In summary, the acceleration of the bigger object is equal to twice the acceleration of the smaller object. This relationship is due to the direct proportionality between acceleration and mass.
  • #1
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Hi anyone, I'm confused about the magnitudes of the acceleration of the two objects here:
F6Yb2.png


It's been awhile since I try to find the answer on internet, I've found numbers of different answers, so I'd like to know if anyone could help me..

In my imagination, if the bigger object moves by 1m, then the smaller one will move for 1/2m..

This show that the acceleration of the bigger object = 2*acceleration of smaller object

Could anyone agree with me?? Any disagreements with explanations will be welcomed..

Thanks
 
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  • #2
in advance!Yes, you are correct. If the larger object is moving with an acceleration of a, then the smaller object will be moving with an acceleration of 2a. This is because the acceleration is directly proportional to the mass of an object. Since the larger object has twice the mass of the smaller object, it will have twice the acceleration.
 

1. How does the acceleration of strings in a two pulley system work?

In a two pulley system, the acceleration of strings is determined by the relationship between the two pulleys. As one pulley rotates, it causes the other pulley to rotate in the opposite direction. This results in the strings on both pulleys moving at the same rate, causing the objects attached to the strings to accelerate in the same direction.

2. What is the relationship between the radius of the pulleys and the acceleration of strings in a two pulley system?

The radius of the pulleys directly affects the acceleration of strings in a two pulley system. The larger the radius of the pulleys, the greater the distance the strings have to travel, resulting in a higher acceleration. Conversely, smaller pulley radii will result in lower acceleration.

3. How does the mass of the objects attached to the strings impact the acceleration in a two pulley system?

The mass of the objects attached to the strings has no direct effect on the acceleration of strings in a two pulley system. The acceleration is determined by the relationship between the two pulleys and the radius of the pulleys. However, the mass of the objects may indirectly affect the acceleration if it causes the strings to stretch or add friction to the pulleys.

4. Can the direction of acceleration be changed in a two pulley system?

Yes, the direction of acceleration can be changed in a two pulley system. This is because the two pulleys rotate in opposite directions, causing the strings to move in the same direction. By changing the direction of rotation of one of the pulleys, the direction of acceleration can be altered as well.

5. What factors can affect the accuracy of the acceleration in a two pulley system?

There are several factors that can affect the accuracy of the acceleration in a two pulley system. These include the mass of the objects attached to the strings, the friction on the pulleys, the tension in the strings, and the accuracy of the pulley system itself. Any small errors or discrepancies in these factors can result in a slightly different acceleration than what is expected.

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