Newton's laws with buckets and strings

[runner2392]

Problem: "One 2.80kg paint bucket is hanging by a massless cord from another 2.80kg paint bucket, also hanging by a massless cord"

a. Calculate the tension in the upper cord when the two buckets are pulled upward with an acceleration of 1.54m/s^2 by the upper cord.

T1 = upper cord's tension
T2 = lower cord's tension

The formula to be used for (a) is T1 = T2 + mg + ma. I am not understanding why it is not T1 = T2 + 2mg + 2ma since the upper cord is carrying the weight of both buckets.

 

[vivekrai]

Because In the second expression you wrote, You have taken into account both the action and reaction pair forces.

Remember, You always take the forces which act on the body and NOT which the body applies on us.

 

[Shootertrex]

I am not understanding why it is not T1 = T2 + 2mg + 2ma since the upper cord is carrying the weight of both buckets.

You would not put both the forces of gravity into the equation along with T2. This is because T2 is already the force of gravity on the lower bucket, so adding it in again will be wrong.

If the buckets are not accelerating, then the equation would be T1=T2 +mg. T1 is the sum of the gravitational force acting on all mass it must to hold up directly (bucket 1) and the force that will oppose the force pulling down on bucket 1 (T2). I hope I explained it well enough for you.