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 = 5.4 m. The total mass of the empty balloon and basket is mb = 121 kg and the total volume is Vb = 0.062 m3. Assume the average person that gets into the balloon has a mass mp = 72 kg and volume Vp = 0.079 m3.

volume of helium in the balloon when fully inflated? :660

magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium. : 2352

buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium. :8287

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

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

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

Answer 1

I think you have no doubt in the answers that you found. So I will answer for the following questions,

For finding the magnitude of force of gravity of each person, we need to find the weight of each person. Weight doesn't care what other set of forces acts on a body. We just need to find the mass and gravitational field.

W1 = mp*g

mass of a person,mp=72 kg

g=9.8 m/s²

w1=705.6 N

We know that the magnitude of buoyant force on each person depends upon air displaced by each person. Remember, this assumes that the balloon is tethered to the ground so it is not accelerating.

So, the buoyant force,B1 = a*Vp

B1=1.28*0.079=0.10112 N

So let us find the total weight of system,W = W0 + n*W1

Next find out the the total static buoyant force on system,B = B0 + n*B1

In order for the balloon to lift, B > W.

So, B0 + n*B1 > W0 + n*W1

We will solve for n, pretending it is an equals sign, and give an answer that is floored to the nearest integer.

B0 + n*B1 = W0 + n*W1

B0 - W0 = n*W1 - n*B1

n*(W1 - B1) = (B0 - W0)

n = (B0 - W0)/(W1 - B1)

n=(8287-2352)/(705.6-0.10112)=8.41

n=8