Please help with this one!! i Couldnt solve from part 3 to 6 A helium balloon ri
ID: 1484033 • Letter: P
Question
Please help with this one!! i Couldnt solve from part 3 to 6
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 = 4.9 m. The total mass of the empty balloon and basket is mb = 121 kg and the total volume is Vb = 0.073 m3. Assume the average person that gets into the balloon has a mass mp = 73 kg and volume Vp = 0.077 m3.
1)
What is the volume of helium in the balloon when fully inflated? 492.8
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. answer : 2057.25
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.
4)What is the magnitude of the force of gravity on each person?
5)
What is the magnitude of the buoyant force on each person?
6)
How many FULL people can the balloon lift up? (Your answer must be an integer.)
Explanation / Answer
1) Volume = (4pi R^3 ) /3 = 4 x pi x 4.9^3 /3 = 492.81 m^3
2) Total mass = mass of helium + mass of empty ballon and basket
= (492.81 x 0.18) + ( 121) = 209.71 kg
weight force = mg = 209.71 x 9.81 = 2057.21 N
3)total volume = 492.81 + 0.073 = 492.88 m^3
buoyant force = volume x density of air x g
= 492.88 x 1.28 x 9.81 = 6189.03 N
4) weight force = 73 x 9.81 = 716.13 N
5) buoyant force = volume of air displaced x desnity of air x g
= 0.077 x 1.28 x 9.81 = 0.97 N
6) weight force act downwards and buoyant force upwards.
Weight force = buoyant force
2057.21 + 716.13n = 6189.03 + 0.97n
n = 5.76 person
5 person