# Hot air balloon buoyancy problem

• Jpyhsics
Jpyhsics
Homework Statement
A hot-air balloon is initially floating (stationary) a few metres above the ground. The radius of the spherical balloon is 6.25 m, and the density of surrounding air is 1.29 kg m-3. "Ballast" is weight of negligible volume that can be dropped to make the balloon rise. How much weight would you have to drop overboard to make the balloon rise 105 m in 15.0 s? You may assume that the density of surrounding air remains constant.
Relevant Equations
Archimedes principle: Fb=rho*gV
Vsphere= 4/3*pi*r^3
Initially the hot air balloon is stationary so...
FB=Fg
ρgV=mg
m=1319.2...kg
FB=Fg=12941N

In the air...
a=2d/t^2=0.933...m/s^2
Fnet=FB-Fg
(1319-x)(0.93...)=12941-(1319-x)g
x=114.6 kg

but apparently this is wrong?...

Homework Helper
Problem Statement: A hot-air balloon is initially floating (stationary) a few metres above the ground. The radius of the spherical balloon is 6.25 m, and the density of surrounding air is 1.29 kg m-3. "Ballast" is weight of negligible volume that can be dropped to make the balloon rise. How much weight would you have to drop overboard to make the balloon rise 105 m in 15.0 s? You may assume that the density of surrounding air remains constant.
Relevant Equations: Archimedes principle: Fb=rho*gV
Vsphere= 4/3*pi*r^3

Initially the hot air balloon is stationary so...
FB=Fg
ρgV=mg
m=1319.2...kg
FB=Fg=12941N

In the air...
a=2d/t^2=0.933...m/s^2
Fnet=FB-Fg
(1319-x)(0.93...)=12941-(1319-x)g
x=114.6 kg

but apparently this is wrong?...
Why do you think it is wrong?

lomidrevo
I didn't calculate using the given values, but equations you have used seems to be correct.
Hint: your solution would be more readable if you work only with symbolic names for the quantities throughout your calculation, and put in the given values in the end.

Homework Helper
Gold Member
2022 Award
but apparently this is wrong?...
Do you know what the answer is claimed to be?

Jpyhsics
Why do you think it is wrong?
I was marked wrong by the system.

Jpyhsics
Do you know what the answer is claimed to be?

Homework Helper
I was marked wrong by the system.
Try to enter the result with three digits .

Jpyhsics
Try to enter the result with three digits .
So I figured out that they were asking for weight and not mass, but thanks everyone.

Jpyhsics
The answer was supposed to be 1124 N.

Homework Helper
So I figured out that they were asking for weight and not mass, but thanks everyone.
Yes, it was weight... It is easy to overlook.