A helium balloon ride lifts up passengers in a basket. Assume the density of air

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 = 5.3 m. The total mass of the empty balloon and basket is mb = 128 kg and the total volume is Vb = 0.074 m3. Assume the average person that gets into the balloon has a mass mp = 70 kg and volume Vp = 0.076 m3.

1) the volume of helium in the balloon when fully inflated?

623.614519 m3

2) the magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium.

2356.85851 N

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

4)What is the magnitude of the force of gravity on each person?

N

5)What is the magnitude of the buoyant force on each person?

N

6)How many FULL people can the balloon lift up? (Your answer must be an integer.)

people

Only 3,4,5,6

Explanation / Answer

Problem One: volume
================
V = 4/3 pi r^3
V = 1.3333 * 3.141592 * 5.3 ^ 3
V = 623.61 m^3

Problem Two: Force
===============
Mass balloon = 128 kg
Mass Helium = d_Helium * Volume = 0.18 kg/m^3 * 623.61 =112.25 kg
Total Mass = 240.25kg

Force = m*g
m = 240.25
g = 9.81
F = m*g
F = 2356.86 N

Problem Three: Buoyant Force
======================
((623.61+0.074)*1.28)*9.81 =7831.48 N

Problem Four
==========
F =mg = 70 x 9.81 = 686.7 N

Problem Five :

Fb_m = 0.076 x 1.28 x 9.81 = 0.95 N

Six :

7831.48 - 2356.86  = n( 686.7 - 0.95)

n = 7.98

so 7 person

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.