Can Buoyancy and Floating Principles

To determine the maximum amount of lead shots a can can carry without sinking in water, we must apply the fundamental principle of buoyancy, often referred to as Archimedes' principle. This principle states that for an object to float, the upward buoyant force exerted by the fluid must be equal to the total weight of the object and its contents. When an object is at the point of just sinking, it is fully submerged, and the weight of the water it displaces is exactly equal to its total weight.

Buoyancy Concepts Explained

• Volume: The amount of space an object occupies. The total volume of the can is given as 1200 cm³.
• Mass: A measure of the amount of matter in an object. The mass of the empty can is 200 g.
• Density: Defined as mass per unit volume. The density of water is 1 g/cm³, and the density of lead shots is 11.4 g/cm³.
• Buoyant Force: The upward force exerted by a fluid that opposes the weight of an immersed object. For an object to float, this force must balance the total downward weight.
• Water Displacement: When an object is submerged in a fluid, it displaces a volume of that fluid equal to the volume of the submerged part of the object. For a fully submerged object that is just about to sink, the volume of displaced water is equal to the object's total volume.

Floating Weight Calculation for the Can

When the can is on the verge of sinking, it is fully immersed in the water. At this point, the volume of water displaced by the can is equal to the can's total volume. The mass of this displaced water represents the maximum total mass the can, along with its contents, can have to remain afloat.

Step 1: Calculate the maximum volume of water the can can displace.
The can's total volume determines the maximum volume of water it can displace when fully submerged.

Volume of water displaced \( = \text{Total volume of the can} = 1200 \, \text{cm}^3 \)

Step 2: Determine the mass of the displaced water.
Using the given density of water, we can find the mass of the water that the can displaces.

Mass of water displaced \( = \text{Volume of water displaced} \times \text{Density of water} \)
Mass of water displaced \( = 1200 \, \text{cm}^3 \times 1 \, \text{g/cm}^3 \)
Mass of water displaced \( = 1200 \, \text{g} \)

This calculated mass (1200 g) is the maximum total mass (can + lead shots) that the system can have while still floating or being perfectly balanced at the surface of the water.

Lead Shots Mass Determination

The total mass that the can can support is made up of its own mass and the mass of the lead shots it carries. Knowing the maximum total mass and the mass of the empty can, we can find the mass of the lead shots.

Step 3: Calculate the mass of the lead shots.
Subtract the mass of the empty can from the maximum total mass to find the mass of the lead shots.

Mass of lead shots \( = \text{Maximum total mass} - \text{Mass of the can} \)
Mass of lead shots \( = 1200 \, \text{g} - 200 \, \text{g} \)
Mass of lead shots \( = 1000 \, \text{g} \)

Therefore, the can can carry 1000 grams of lead shots without sinking in water.