A Helium Balloon and Buoyancy

[TMO]

Homework Statement

A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg¹m^-3 and the density of helium in the balloon is 0.18 kg¹m^-3. The radius of the balloon (when filled) is R = 5 m. The total mass of the empty balloon and basket is m_b = 123 kg and the total volume is V_b = 0.066 m³. Assume the average person that gets into the balloon has a mass m_p = 73 kg and volume V_p = 0.076 m³. 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.

Homework Equations

$$V_{sph} = \frac{4}{3} \cdot \pi \cdot r^3$$
$$F_b = \rho_{fluid} \cdot V \cdot g$$

The Attempt at a Solution

Since the volume of the balloon and basket is given by $$V_b$$ and the volume of the balloon is given by $$\frac{4}{3} \cdot \pi \cdot R^3,$$ it seems natural to conclude that the magnitude of the buoyancy force is $$(1.28 \cdot V_b + 0.18 \cdot \frac{4}{3} \cdot \pi \cdot R^3) \cdot g,$$ but this does not seem to provide the correct answer. Any advice?

Thank you for your time. :)

 

[BruceW]

$$F_b = \rho_{fluid} \cdot V \cdot g$$

This is the correct equation for the buoyant force. But you need to be careful about what density to use.

First think of a simple example, like a solid object immersed in water. Would the buoyant force be calculated using the density of the object, or the water?