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Chapter 15: Problem 8

A mountain stream, frothy with entrained air bubbles, presents a serious hazard to hikers who fall into it, for they may sink in the stream where they would float in calm water. Why?

Short Answer

Expert verified
Hikers are more likely to sink in frothy streams because the entrained air bubbles decrease the density of the water, leading to a lower buoyant force. If this force is insufficient to counteract the weight of the hiker, they would sink.

Step by step solution

01

Understand the basics

Firstly, understanding buoyancy is key. To put it simply, an object sinks or floats based on the concept of buoyancy, which is the force exerted on an object that is wholly or partly immersed in a fluid. According to Archimedes' principle, the force of buoyancy that acts on a body immersed in fluid is equal to the weight of the fluid that the body displaces.
02

Air bubbles in stream

In a mountain stream filled with entrained air bubbles, the density of the water is less than in calm water. The presence of air bubbles means that less water is being displaced by the hiker, and thus, the buoyant force is reduced.
03

Role of buoyancy in sinking or floating

For an individual to float, the force of buoyancy must be equal to or greater than the person's weight. However, because the buoyant force is reduced in the frothy stream with entrained air bubbles, it might not be enough to counteract the weight of the hiker, thus causing them to sink.
04

Conclusion

In conclusion, the hiker would be more likely to sink in a frothy mountain stream with entrained air bubbles because the density of the water is lower than in calm water. The reduction of water density leads to a decrease in the amount of water displaced by the hiker, leading to a lower buoyant force. If this force is not enough to counteract the hiker's weight, the hiker would sink.

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