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Chapter 13: Problem 4

You are in a boat filled with large rocks in the middle of a small pond. You begin to drop the rocks into the water. What happens to the water level of the pond? a) It rises. d) It rises momentarily and then b) It falls. falls when the rocks hit bottom. c) It doesn't change. e) There is not enough information to say.

Short Answer

Expert verified
Answer: b) It falls.

Step by step solution

01

Analyze the initial situation

Initially, there is a boat filled with large rocks in the middle of a pond. The boat is floating, meaning that its weight is balanced by the buoyant force of the water.
02

Understand the concept of buoyant force

Buoyant force is the upward force exerted by a fluid (in this case, water) on a submerged object. It depends on the volume of water displaced by the object. According to Archimedes' principle, the magnitude of this force is equal to the weight of the water displaced by the object.
03

Consider the weight of the boat and rocks

When the boat is filled with rocks, its weight and the weight of the rocks are supported by the buoyant force from the water. This means that the volume of water displaced by the boat is equal to the total weight of the boat and rocks divided by the density of water.
04

Evaluate the effect of dropping rocks into the water

When a rock is dropped into the pond, it sinks to the bottom, displacing the water around it and creating a new buoyant force. The volume of water displaced by the rock is equal to the weight of the rock divided by the density of water.
05

Compare the displacements

Now, we need to compare the volume of water displaced by the rock when it is in the boat to the volume of water displaced when the rock is at the bottom of the pond. If these volumes are equal, then the water level will not change. If the volume displaced by the rock in the boat is greater than when the rock is at the bottom, the water level will fall. If the volume displaced in the boat is smaller, the water level will rise.
06

Determine the displacements

When the rock is in the boat, it contributes to the weight of the boat, and the volume of water displaced is equal to the total weight (boat and rocks) divided by the density of water. When the rock is at the bottom, it only displaces an amount of water equal to its own volume, as its weight no longer contributes to the buoyant force on the boat. Because rocks are typically denser than water, they displace a smaller volume of water when they are at the bottom of the pond compared to their contribution to the displacement of the boat when they are on it.
07

Conclude the effect on water level

Since the volume of water displaced by the rock is greater when it is in the boat than when it is at the bottom of the pond, the water level will fall when the rocks are dropped into the water. The correct answer is: b) It falls.

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