How High Does a Balloon Rise With 97000 J Work Against Gravity and Wind?

[Atomos]

a 500kg hot-air balloon takes off from rest at the surface of the earth. the nonconservative wind and lift forces take the balloon up, doing 97000 J of work on the balloon in the process. At what height above the surface of the Earth does the balloon have a speed of 8.00 m/s?

I stared at this question for atleast an hour and I was convinced that there is no solution. Then I tried just deducting the kinetic energy at 8.00 m/s from 97000 and using that as the gravitation protential, and I get the answer that is in the back of the book. I do not agree with this. Where does the question indicate that all of this work is done at once allowing the balloon to have 97000J of mechanical energy during the entire trip? Is not it reasonable to assume that the lift forces are constantly doing work on the balloon and therefore the balloon did not have that 97000J all along?

 

[Chi Meson]

The mechanical energy gained by the balloon comes from the buoyant force and wind. The 97000 J is the total work from buoyant force (Wb) and wind (Ww) [negative work of air resistance is ignored, I assume].

The work not mentioned is the negative work done by gravity (mgh). The work-energy theorem says that the net work done on an object is equal to the change in kinetic energy. Therefore Wb+Ww+(-mgh)=delta K. Which is what you got.

 

[Curious3141]

a 500kg hot-air balloon takes off from rest at the surface of the earth. the nonconservative wind and lift forces take the balloon up, doing 97000 J of work on the balloon in the process. At what height above the surface of the Earth does the balloon have a speed of 8.00 m/s?

I stared at this question for atleast an hour and I was convinced that there is no solution. Then I tried just deducting the kinetic energy at 8.00 m/s from 97000 and using that as the gravitation protential, and I get the answer that is in the back of the book. I do not agree with this. Where does the question indicate that all of this work is done at once allowing the balloon to have 97000J of mechanical energy during the entire trip? Is not it reasonable to assume that the lift forces are constantly doing work on the balloon and therefore the balloon did not have that 97000J all along?

The question would've been better phrased like so : "Find the height of the balloon when it attains a speed of 8 m/s, assuming that, by this point, a total of 97,000 J of work had been done on the balloon by the buoyant force."

 

[Ukitake Jyuushirou]

juz wondering, is the ans 17 meter?

 

[Ukitake Jyuushirou]

this qn is from a ****ell and Johnson Physics textbook ver 6 rite? i rem doing a qn like this yesterday ... lol