Chapter 20, Problem 16A

a. How much buoyant force acts on a 1-N balloon suspended at rest in air?

b. What happens if the buoyant force decreases?

c. What happens if the buoyant force increases?

To determine

The buoyant force acts on a balloon.

Answer to Problem 16A

The buoyant force acts on a balloon is $1\text{ N}$ .

Explanation of Solution

Given:

The weight of the balloon is $1\text{ N}$ .

Formula used.

The expression for buoyant force is,

  $F_{\text{Buoyant}}=\rho gV$

Here, $\rho$ is the density, $g$ is the acceleration due to gravity, and $V$ is the volume.

Calculation:

Consider the balloon is at rest. Hence, the net force acting on the balloon is zero.

Since the balloon is at rest, the buoyant force is equal to the weight of the air displaced.

The buoyant force is,

  $\begin{array}{l}{F}_{\text{Buoyant}}=\text{Weight of air displaced}\\ F_{\text{Buoyant}}=1\text{ N}\end{array}$

Conclusion:

Thus, the buoyant force is $1\text{ N}$ .

To determine

To explain: The effect on balloon if buoyant force decreases.

Answer to Problem 16A

The balloon moves down when the buoyant force decreases.

Explanation of Solution

Introduction:

The expression for buoyant force as follows:

  $F_{\text{Buoyant}}=\rho gV$

Here, $\rho$ is the density, $g$ is the acceleration due to gravity, and $V$ is the volume.

An object which is less dense in comparison to the surrounding air will rise upward.

A gas filled balloon moves down in the air as its density is less than the air surrounding the balloon. Buoyant force increases, then the balloon moves up.

When the buoyant force decreases, then the balloon moves down.

Conclusion:

Thus, the balloon moves down when the buoyant force decreases.

To determine

To explain: The effect on balloon if the buoyant force increases.

Answer to Problem 16A

The balloon moves up when the buoyant force increases.

Explanation of Solution

Introduction:

The buoyant force is

  $F_{\text{Buoyant}}=\rho gV$

Here, $V$ is the volume, $g$ is the acceleration due to gravity and $\rho$ is the density

An object which is less dense in comparison to the surrounding air will rise upward.

A gas filled balloon rises in the air as its density is less than the air surrounding the balloon.

When the buoyant force increases, then the balloon moves up.

Conclusion:

Thus, the balloon moves up when the buoyant force increases.