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

[Nemi]

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?

 

[PhanthomJay]

Real good. You have asked about what to do with the 'ag' (acceleration of gravity, usually just referred to as 'g'). Still wondering?

 

[Astronuc]

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.

 

[Nemi]

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.