Tension Problems Given Two Weights

[yandereni]

Homework Statement

One 3.2kg paint bucket(B) is hanging by a massless cord from another 3.2kg paint bucket(A), also hanging by a massless cord.
a.) if the buckets are at rest, what is the tension in each cord?
b.) if the two buckets are pulled upward with an acceleration of 1.6m/s² by the upper cord, calculate the tension in each cord.

this is one of the problems I am confused with actually

Homework Equations

all i can make out is :
1. finding the tension when at rest
box[a] ==> FtensA = (a_grav)(m_A) + Ftens B
box ==> FtensB = (a_grav)(m_B)
2. finding the tension force given the acceleration 1.6m/s²
box[a]==>FtensA = m_Aa_A +FtensB
box==>FtensB = m_Ba_B

The Attempt at a Solution

I tried to solve for the tension when at rest and this is how it turned out:
FtensA = (9.8m/s²)(3.2kg) + FtensB
= 31.6N + 31.6N
= 63.2N
FtensB = (9.8m/s²)(3.2kg)
= 31.6N

Then I tried to solve for the tension given the acceleration
FtensA = (1.6m/s²)(3.2) + FtensB
= 5.12N + 5.12N
= 10.24N
FtensB = (1.6m/s²)(3.2kg)
= 10.24N

I really think that I'm wrong in here because its really confusing...Thanks In Advance! :)

<<Moderator note: Edited for formatting.>>

 

[Cake]

Part A you did correctly(though your calculation is a bit off). But when you take the tension of the cord given the new upward acceleration, remember that the first tension that you calculated doesn't go away. So how do you think you should approach part B with that in mind?

 

[Orodruin]

FtensA = (agrav)(mA) + Ftens B

In this case, (agrav) is the gravitational acceleration which means that mA(agrav) is the gravitational force acting on the bucket A. Since the bucket is at rest, the equation is a force balance for bucket A (all forces must sum to zero).

FtensA = mAaA +FtensB

The gravitational force does not disappear just because you are accelerating the bucket. Also, since the buckets are now being accelerated, the forces should not add to zero, but perhaps one of Newton's laws can tell you what it should sum to?

 

[yandereni]

Oh, now it all makes sense. I forgot the part where the bucket is at rest. Thank you so much! I understand everything now. :)