Chapter 20, Problem 45A

a. Would a balloon rise in an atmosphere where the pressure was somehow the same at all altitudes?

b. Would a balloon rise in the complete absence of atmospheric pressure (for example, at the surface of the moon)?

To determine

To identify: Whether a balloon will rise or not for the given condition.

Answer to Problem 45A

No, the balloon will not rise.

Explanation of Solution

Introduction:

When a body is placed in a fluid then it displaces some amount of fluid. The displaced weight start applying some upward force (or buoyancy force) and its magnitude is equal to weight of displaced fluid. Therefore, when the body has a weight lesser than buoyancy force then body is pushed upward. This is the reason for floating of one object over other.

The weight of body is directly proportional to density. So, if two gases of different densities are mixed, then the gas which has low density will float over the other gas.

The balloon is filled with helium which has lower density than other gases that are present in atmosphere like oxygen, nitrogen. For floating of balloon only there is comparison of densities of gasses outside and inside the balloon not pressure. Thus, pressure does not have any effect.

To determine

To identify: Whether a balloon will rise or not for the given condition.

Answer to Problem 45A

No, a balloon will not rise.

Explanation of Solution

Introduction:

When a body is placed in a fluid then it displaces some amount of fluid. The displaced weight start applying some upward force (or buoyancy force) and its magnitude is equal to weight of displaced fluid. Therefore, when the body has a weight lesser than buoyancy force then body is pushed upward. This is the reason for floating of one object over other.

The weight of body is directly proportional to density. So, if two gases of different densities are mixed, then the gas which has low density will float over the other gas.

When there is no pressure then there is completely vacuum. For floating of balloon only there is comparison between densities of gasses outside and inside the balloon not pressure. The density of air present in balloon will always greater than the outside of balloon.

Thus, balloon will not rise in the absence of atmospheric pressure.