In order to find how many balloons we need to lift an 80 kg person we start by finding how much weight one balloon can lift. To do this we find the net force acting on a single balloon. The balloon is only acted on by the buoyant force (upwards), and the force of gravity (downwards), thus:
F
n
e
t
=
F
B
−
F
g
=
ρ
a
i
r
g
V
−
(
m
+
ρ
H
e
V
)
g
Here we have used the fact that the mass of the balloon is m=1 gram plus the mass of the helium gas, which is the density of helium multiplied by the volume. Rearranging this gives:
F
n
e
t
=
(
ρ
a
i
r
−
ρ
H
e
)
g
V
−
m
g
We can find the density of air as
ρ
a
i
r
=
0.2
ρ
o
x
y
g
e
n
+
0.8
ρ
n
i
t
r
o
g
e
n
where the densities of oxygen and nitrogen are of the diatomic molecules at the temperature and pressures we want. Since only our temperature is different from standard temperature and pressure (STP) we can find the new densities as:
ρ
=
ρ
s
t
p
×
273
T
With T being the temperature we wish to use. This gives a density of diatomic oxygen of 1.31 kg/m
3
and a density of diatomic nitrogen of 1.15 kg/m
3
. Thus our density of air is 1.18 kg/m
3
. We can also find the volume of one spherical balloon as:
V
=
4
π
3
r
3
=
4
π
3
(
0.2
)
3
=
0.0335
m
3
Now we may calculate our force due to one balloon (density of He is 0.163 kg/m
3
).
F
n
e
t
=
0.324
N
Now that we know the lifting force of one balloon, we can take the total force we need to lift (the weight of a 80 kg person), and divide by this lift to find how many balloons we need.
F
g
=
M
g
=
(
80
kg
)
(
9.8
)
=
784
N
The number of balloons we need (x) is then:
x
=
F
g
F
n
e
t
=
784
0.324
=
2420
Thus we would need 2420 of these circus balloons to lift a 80 kg person
How many circus balloons will it take to lift a 80.0 kg person?
The pressure is 1.00 atmospheres. The temperature is 298 K. The air is composed of 20.0% oxygen and 80.0% nitrogen.
Each balloon is a perfect sphere, 40 cm in diameter, filled with helium gas (also at 1.00 atmospheres). The mass of the balloon rubber and string for each balloon is 1.00g
1 answer
1 answer