What Is the Acceleration of a Block in a Pulley System?

AI Thread Summary
The discussion revolves around calculating the acceleration and tension in a pulley system involving a 24 kg block and a 5.3 kg block. The initial attempt at solving the problem resulted in an incorrect acceleration value of 3.005 m/s. Participants emphasize the need for a clear diagram to better understand the system's configuration. They suggest modifying the equations to account for the different accelerations of the two blocks and highlight the necessity of establishing a relationship between their accelerations. Accurate setup and additional equations are essential for finding the correct solutions.
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Homework Statement



A 24 kg block with a pulley attached slides along a firctionless surface. It is connected by a massless string to a 5.3 kg block via the arrangement shown. a) Find the acceleration of the 24 kg block. b) Find the tension in the connecting string.

Homework Equations



F = ma

The Attempt at a Solution



For the 24 kg, I thought that 24a = 2T. Then 5.3g - T = 5.3a.
Then set the two equal to each other, so I got a = 3.005 m/s. However, that answer is incorrect. Part b, I would just plug in the part a answer, but my part a answer is incorrect. Please help with setup, etc. Thank you!
 
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Hello physicsnerd11,

Welcome to Physics Forums!
physicsnerd11 said:

Homework Statement



A 24 kg block with a pulley attached slides along a firctionless surface. It is connected by a massless string to a 5.3 kg block via the arrangement shown. a) Find the acceleration of the 24 kg block. b) Find the tension in the connecting string.

Homework Equations



F = ma

The Attempt at a Solution



For the 24 kg, I thought that 24a = 2T. Then 5.3g - T = 5.3a.
Then set the two equal to each other, so I got a = 3.005 m/s. However, that answer is incorrect. Part b, I would just plug in the part a answer, but my part a answer is incorrect. Please help with setup, etc. Thank you!
It's difficult to give you help without a figure, diagram, or description of the system. I can only guess what the specific arrangement is.

But I'm guessing there is some sort of pulley system involved. If so, it means that the two blocks have different velocities, and different accelerations.

So change your equations to something like

24a1 = 2T
5.3g - T = 5.3a2

giving you 2 equations and 3 unknowns. You'll need a third equation to solve this. Given the simple nature of the pulley system, what is relationship between one block's acceleration compared to the other's? :wink:
 

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