Questions: A plastic beach ball has radius 20.3 cm and mass 0.100 kg, not including the air inside. Assume the air density is 1.30 kg / m^3 both inside and outside. What is the buoyant force on the beach ball in air? The thickness of the plastic is about 2.00 mm -negligible compared with the radius of the ball. Enter a positive value if the force is upward and enter a negative value if the force is downward.

Solution Steps

The volume \( V \) of a sphere is given by the formula:

\[ V = \frac{4}{3} \pi r^3 \]

where \( r \) is the radius of the sphere. Given that the radius of the beach ball is 20.3 cm, we first convert this to meters:

\[ r = 20.3 \, \text{cm} = 0.203 \, \text{m} \]

Now, calculate the volume:

\[ V = \frac{4}{3} \pi (0.203)^3 \approx 0.0351 \, \text{m}^3 \]

The buoyant force \( F_b \) is given by the formula:

\[ F_b = \rho_{\text{air}} \cdot V \cdot g \]

where \( \rho_{\text{air}} = 1.30 \, \text{kg/m}^3 \) is the density of air, and \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity.

Substitute the known values into the formula:

\[ F_b = 1.30 \cdot 0.0351 \cdot 9.81 \approx 0.448 \, \text{N} \]

Final Answer