How to Solve a Tension-Pulley Problem with Acceleration and Force

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The discussion focuses on solving a tension-pulley problem involving a 9.4 kg bucket of water being raised with an upward acceleration of 2.8 m/s². The force exerted by the rope on the bucket is calculated by first determining the weight of the bucket (Fw1) as 92.12 N and then using the equation T - Fw1 = m1(a) to find the tension (T) in the rope, resulting in a total of 118.44 N. Participants emphasize the importance of showing units in calculations for clarity and accuracy. The conversation highlights the significance of understanding gravitational acceleration (ag) in these types of physics problems. Overall, the thread provides valuable insights into the correct approach for solving tension-related physics problems.
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I need advice on where to stick the ag

A (m1=9.4 kg) bucket of water is raised from a well by a rope. (ag=9.8 m/s²) If the upward acceleration of the bucket is (a=2.8 m/s²), find the force exerted by the rope on the bucket.

Finding Fw1
Fw1=m1(ag)
Fw1=(9.4 kg)(9.8 m/s²)
Fw1=92.12 N

Finding Tension
T-Fw1=m1(a)
T-92.12 N =(9.4 kg)(2.8 m/s²)
T=26.32+92.12
T=118.44 N

Am I doing good so far?
 
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Real good. You have asked about what to do with the 'ag' (acceleration of gravity, usually just referred to as 'g'). Still wondering?
 
Yes, but one should show units, e.g. (9.4 kg) for mass of bucket, (9.8 m/s2) for acceleration due to gravity and 2.8 m/s2 for acceleration of the bucket being pulled by the rope.

And for force, 1 N = 1 kg-m/s2.
 
Thank you both, so much for your help. PhantomJay, thank you for your consideration, you helped me understand it now. Astronuc, I really appreciate your help in labeling my units.
 
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