Why is it difficult to push a light object ľike an air mattress under water? How is it that a massive ship can float?

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UpStudy AI · Accepted Answer

Pushing a light object like an air mattress underwater is challenging because of the **buoyant force** exerted by the surrounding water. To understand why this happens and how massive ships are able to float, let's delve into the principles of buoyancy and density.

### **1. Buoyant Force and Archimedes' Principle**

- **Archimedes' Principle** states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
  
  $$
  \text{Buoyant Force} = \text{Weight of Displaced Water}
  $$

- For an **air mattress**, which contains a significant amount of air, the overall density of the mattress (mass per unit volume) is much lower than that of water. This means the mattress displaces a volume of water whose weight is greater than the mattress itself, resulting in a strong upward buoyant force that keeps it afloat.

### **2. Difficulty in Submerging Light Objects**

- **Low Density:** Light objects like air mattresses have trapped air, making their average density less than water. To push them underwater, you must exert a force sufficient to overcome this buoyant force. Since the buoyant force is substantial relative to the object's weight, it requires considerable effort to submerge it.

- **Surface Area and Pressure:** Additionally, large surface areas can make it harder to apply concentrated force needed to partially displace the water around the object, further resisting submersion.

### **3. Why Massive Ships Float**

- **Design and Displacement:** Although ships are massive, they are engineered to displace a large volume of water. The hull of the ship is shaped to move enough water aside so that the weight of the displaced water equals the weight of the ship.

- **Overall Density:** Ships are constructed with materials and designs that ensure their **average density** (total mass divided by total volume, including the hollow parts filled with air) is less than that of water. This allows the buoyant force to support the ship's weight effectively.

- **Distribution of Mass:** The distribution of a ship’s mass also plays a role in stability. A well-designed ship distributes its weight in a way that maintains equilibrium, preventing it from tipping or sinking under normal conditions.

### **4. Practical Implications**

- **Submarines vs. Air Mattresses:** Unlike an air mattress, a submarine can control its buoyancy by adjusting the amount of water and air in its ballast tanks, allowing it to submerge or surface as needed. This manipulation of overall density and displacement demonstrates a more controlled approach to floating compared to passive objects like air mattresses.

### **Conclusion**

The difficulty in pushing a light object like an air mattress underwater arises from the substantial buoyant force due to its low density and large volume of displaced water. In contrast, massive ships float because they are meticulously designed to displace enough water to balance their weight, maintaining an average density that allows them to stay afloat despite their size.
Pushing a light object like an air mattress underwater is hard because it displaces a lot of water, creating a strong upward force that keeps it afloat. Ships float because they are designed to displace enough water to balance their weight, making their overall density less than water.

Why is it difficult to push a light object ľike an air mattress under water? How is it that a massive ship can float?

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