Chapter 8, Problem 10RQ

Does the buoyant force on a floating object depend on the weight of the object or on the weight of the fluid displaced by the object? Or are these two weights the same for the special case of floating? Defend your answer.

To determine

Whether the buoyant force on a floating object is dependent on the weight of the object or on the weight of the fluid displaced by the object and whether these two weights the same for special case of floating.

Answer to Problem 10RQ

The buoyant force on a floating object is dependent on the weight of the fluid displaced by the object and these two weights are not equal.

Explanation of Solution

The upthrust force encountered by an object, when immersed in the fluid is due to the force exerted by the molecules of fluid, is known as buoyant force. This force is equal to the removed fluid's weight. In the situation, when the weight of the body is similar to this upward force, the body will float. Whereas, when the weight of the body immersed is more, then it will sink. So, the buoyant force of a floating object is only dependent on the weight of the fluid displaced.

In the special case of flotation, the buoyant force acting on the body will be equivalent to the weight. This can be seen by an example, where a block of iron with mass will sink in water. This is because the density of iron is more than the density of the water, as the result block will displace more water. On the other hand, when the bowl of iron with mass is immersed in water, it would replace more water. When the buoyant force is equal to the weight of the bowl, then it would not sink. Therefore, the weight of the object and weight of the fluid displaced by the object are not the same for the special case.

Conclusion:

Therefore, the buoyant force on a floating object is dependent on the weight of the fluid displaced by the object and these two weights are not equal.