Chapter 9, Problem 1WUE

Physics Review A soap bubble hovers motionlessly in the air. If the soap bubble’s mass, including the air inside it, is 2.00 × 10⁻⁴ kg determine the magnitude of the upward force acting on it. (See Section 4.5.)

To determine

The upward force acting on the soap bubble.

Answer to Problem 1WUE

Solution: The upward force on the soap bubble is $1.96\times {10}^{-3}\text{N}$.

Explanation of Solution

Given info: The mass of the soap bubble is $2.00\times {10}^{-4}\text{kg}$.

The upward force on a submerged body is the buoyant force which is equal to the weight of the fluid displaced by the body.

The weight of the air displaced by the soap bubble is given by,

$W=mg$

• W is the weight
• $m$ is the mass of the air displaced
• $g$ is the free fall acceleration

Hence the upward force on the soap bubble is given by,

$F_{up}=mg$

Substitute $9.8\text{m}\cdot {\text{s}}^{\text{-2}}$ for $g$, $2.00\times {10}^{-4}\text{kg}$ for $m$ to determine the buoyant force on the soap bubble,

$\begin{array}{c}{F}_{up}=\left(2.00\times {10}^{-4}\text{kg}\right)\left(9.8\text{m}\cdot {\text{s}}^{\text{-2}}\right)\\ =1.96\times {10}^{-3}\text{N}\end{array}$

Conclusion:

The upward force on the soap bubble is $1.96\times {10}^{-3}\text{N}$