Pad 7:52 PM smart physics.com 1 2 3 4 5 67 A helium balloon ride lifts up passen

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Pad 7:52 PM smart physics.com 1 2 3 4 5 67 A helium balloon ride lifts up passengers in a basket. Assume the density of a is 28 kg/ms and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled is R 4.6 m. The total mass of the empty balloon and basket is mb 25 kg and the total volume is V 0.055 m3. Assume the average person that gets into the balloon has a mass mp 72 kg and volume V 0.079 m 1) What is the volume of helium in the balloon when fully inflated? Sub You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question 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 Sub 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 fo on the en e system (but with no people nclude the volume of the balloon, basket, and helium N Sub You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question 4) What the magnitude of the force of gravity on each person N Sub 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 Sub 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 up? (Your answer must be an intege people Submit You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question y Qu 7) Below is some space to write notes on this problem Submit Standard Exercise U Tube Standard Exercis Balloon Standard Exercise Tipler6 13. P.023 Standard Exercise Tipler6 13. P.028 Standard Exercise Tipler6 13. P.041 Standard Exercise Tipler6 13.P. 042 Standard Exercise Tipler6 13. P.045 47% D

Explanation / Answer

here,

Density of Helium, dh = 0.18 kg/m^3
Density of air, da = 1.28 kg/m^3
Radius of Ballon, r = 4.6 m
mass of person, mp = 72kg
Volume of Person, Vp = 0.079 m^3
Volume of basket, Vbas = 0.055 m^3

Part 1 :
ballon is like sphere, so Volume will be

Vb = 4/3*pi*r^3
Vb = (4/3) * 3.14 * 4.6^ 3
Vb = 407.513 m^3

Part B:
Mass balloon = 125 kg
Mass Helium = Dh * Vb
Mh = 0.18 * 407.513
Mh = 73.352 kg

The total mass will be
m = 125 + 73.352
m = 198.352 kg

Force due to gravity will be :
F = mass * acceleration due to gravity
F = m * g
F = 198.352 * 9.81
F = 1945.833 N

Part C :

Mass of displaced volume of air, md = da * Volume
md = 1.28 * 407.513
md = 521.617 kg

The buoyant mass = the volume of air displaced * density
Bouynat mass = Vbas * Da
Bouynat mass = 0.055 * 1.28
Bouyant mass = 0.07 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 = 521.617 - 198.352 + 0.07 = 323.335 kg

The Bouyant force will be
Fb = 323.335 * 9.81
Fb = 3171.916 N

Part 4 :

Force due to gravity (no buoyancy) on each person
Fg = 72 * 9.81
Fg = 706.32 N

Part 5 :

Force with Bouyancy for Each person
F = Fg - rho*vp*g
F = 706.32 - 1.28*0.079 * 9.81
F = 705.328 N

Part 6 :

The number of people who could be lifted by the system
N = 3171.916/705.328
N = 4.497 people. or 4 people

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