A helium balloon ride lifts up passengers in a basket. Assume the density of air
ID: 1484330 • Letter: A
Question
A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m3 and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled) is R = 5.1 m. The total mass of the empty balloon and basket is mb = 125 kg and the total volume is Vb = 0.064 m3. Assume the average person that gets into the balloon has a mass mp = 71 kg and volume Vp = 0.077 m3.
1)
What is the volume of helium in the balloon when fully inflated?
m3
You currently have 1 submissions for this question. Only 10 submission are allowed.
You can make 9 more submissions for this question.
Your submissions:
556
Computed value:
556
Submitted:
Wednesday, December 9 at 1:14 PM
Feedback:
Correct!
2)
What is the magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium.
N
You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.
3)
What is the magnitude of the buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium.
N
You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.
4)
What is the magnitude of the force of gravity on each person?
N
You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.
5)
What is the magnitude of the buoyant force on each person?
N
You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.
6)
How many FULL people can the balloon lift up? (Your answer must be an integer.)
people
You currently have 0 submissions for this question. Only 10 submission are allowed.
You can make 10 more submissions for this question.
(Survey Question)
7)
Below is some space to write notes on this problem
Explanation / Answer
1) V = 4/3 pi r^3
V = 1.3333 * 3.141592 * 5.1 ^ 3
V = 555.65 m^3
2) Mass balloon = 125 kg
Mass Helium = d_Helium * Volume = 0.18 kg/m^3 * 555.65 = 100.01 kg
Total Mass =225.01 kg
Force = m*g
m =225.01
g = 9.81
F = m*g
F = 225.01 * 9.81
F = 2207.35 N
3) Mass of displaced volume of air. = d * V
d = 1.28 kg/m^3
V =555.65 m^3
Mass = 1.28 * 555.65
Mass = 711.23 kg
The volume of the basket = 0.064 m^3
The buoyant mass = the volume of air displaced * density
The buoyant mass = 0.064 m^3 * 1.28 kg/m^3 = 0.08192 kg
The buoyant mass is the difference between the balloon full of helium that displaces the air and the helium mass and the basket mass.
m =711.23 - 225.01+ 0.08192 = 486.30
The force = 486.30 * 9.81 = 4770.62 N
4) F person (no buoyancy) = 71 * 9.81 = 696.51 N
Buoyancy on each person = 0.08192
With buoyancy = 696.51 - 0.08192 * 1.28 * 9.81 =695.48 N
the actual force is close enough without the buoyancy, but I gave you both.
The number of people who could be lifted by the system = 4770.62/695.48 = 6.85 people. In this case you have to round downward, so you could lift 6 people.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.