Balloon FreeBodyDiagram Question

[faylihn]

This is my gr. 11 physics problem that I can't get. I would be very grateful if someone could help me. A hot air balloon has a force of gravity of 3000N but has an upward force of 3800N due to the hot air. Person A is on the ground and pulling the balloon with a force of 540N [Left 40degree Down]. Person B is pulling with a force of 700N straight down. Person B's rope is 30m long. How long will it take to pull the balloon down. The problem is #52 from p148 of Irving Physics and the answer is 7.5 seconds but I have no idea how they got it there. Thanks for any help you might give!

 

[Andrew Mason]

This is my gr. 11 physics problem that I can't get. I would be very grateful if someone could help me. A hot air balloon has a force of gravity of 3000N but has an upward force of 3800N due to the hot air. Person A is on the ground and pulling the balloon with a force of 540N [Left 40degree Down]. Person B is pulling with a force of 700N straight down. Person B's rope is 30m long. How long will it take to pull the balloon down. The problem is #52 from p148 of Irving Physics and the answer is 7.5 seconds but I have no idea how they got it there. Thanks for any help you might give!

Work out the net force:

Downward forces - upward forces = mass of balloon x acceleration

You have to work out the downward forces (ie. downward component of A's force).

I think you will find that the net force is downward. Once you figure out the acceleration, you have to work out how long it takes for the balloon to descend to the ground. Do you know how to do that? B's rope gives you its height above the ground.

AM

 

[Brian Earley]

Does the balloon begin at rest? I solved it and got 8.6 seconds.

 

[whozum]

Define your angle for Person A. I don't think the 40 degrees is oriented right.

3800 up - 3000 down - 700 down - 540sin40 down.

That means net force is 247N towards earth.
Find the mass of the balloon if you know the force of gravity and the acceleration of gravity. Divide the net force above by this mass and use the resulting acceleration in a position equation solved for time.

I got 8.6seconds also...

 

[Andrew Mason]

Define your angle for Person A. I don't think the 40 degrees is oriented right.

3800 up - 3000 down - 700 down - 540sin40 down.

That means net force is 247N towards earth.
Find the mass of the balloon if you know the force of gravity and the acceleration of gravity. Divide the net force above by this mass and use the resulting acceleration in a position equation solved for time.

I got 8.6seconds also...

7.5 seconds is the answer if you take the angle of B's rope as 40 degrees from the vertical (which is not what I would have said from the question) and use 10 m/sec^2 for g. Either that or a few metres of B's rope is lying on the ground.

AM