An empty rubber balloon has a mass of 0.0120 kg. The balloon is filled with helium at 01C2 1 atm pressure3 and a density of 0.179 kg4m5. The filled balloon has a radius of 0.500 m.

Apuntes

• Subtopic: Given Data An empty rubber balloon has a mass of 0.0120 kg. It is filled with helium at 0°C, 1 atm pressure, and a helium density of 0.179 kg/m³. The filled balloon has a radius of 0.500 m. • Subtopic: Part a — Buoyant Force To find the buoyant force acting on the balloon, we use Archimedes' principle: \[ F_b = \rho_{air} \times V \times g \] where: - \( \rho_{air} \) is the density of air, - \( V \) is the volume of the balloon, - \( g \) is the acceleration due to gravity (approximately 9.81 m/s²). Assuming the density of air from the hint (see Figure 1.2), which is approximately 1.225 kg/m³ at sea level and 0°C. The volume of the spherical balloon: \[ V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.5)^3 \] Calculating: \[ V = \frac{4}{3} \pi \times 0.125 = \frac{4}{3} \times 3.1416 \times 0.125 \approx 0.5236 \text{ m}^3 \] Now, the buoyant force: \[ F_b = 1.225 \, \text{kg/m}^3 \times 0.5236 \, \text{m}^3 \times 9.81 \, \text{m/s}^2 \] \[ F_b \approx 1.225 \times 0.5236 \times 9.81 \approx 6.29 \text{ N} \] **Answer for part a:** The magnitude of the buoyant force is approximately **6.29 N**. • Subtopic: Part b — Net Force on the Balloon The net force i...