What is the tension in each piece of rope in an accelerating balloon system?

[endverse]

Homework Statement

If the balloon in the diagram drawn below is accelerating upwards at 0.40 m/s (squared), calculate the tension in each piece of rope. Assume that the rope has no mass.

The diagram:

Homework Equations

F = ma

The Attempt at a Solution

For the bottom piece of rope
Fnet = Fa - Fg
Fnet = ma - mg
Fnet = (9.00)(0.40) - (9.00)(9.8)

where Fnet is the tension in the piece of rope, Fa is the force accelerating the balloon upwards, and m is the mass of the object held up by the rope

 

[endverse]

no help?? I have this problem set due tomorrow.. any answer would be so appreciated

 

[kerimek]

. The force of gravity, Fg, is subtracted since it is acting in the opposite direction of the acceleration.

Fnet = 3.6 N

For the top piece of rope
Fnet = Fa - Fg
Fnet = ma - mg
Fnet = (4.00)(0.40) - (4.00)(9.8)

Fnet = -1.6 N

This means that the tension in the bottom piece of rope is 3.6 N and the tension in the top piece of rope is -1.6 N, which indicates that the top rope is actually experiencing a downward force. This may seem counterintuitive, but it is due to the fact that the balloon is accelerating upwards, causing a net force in the downward direction on the top rope. It is important to note that the negative sign indicates the direction of the force, not its magnitude. Both pieces of rope are experiencing tension, but in different directions due to the acceleration of the balloon.