Imagine that you place a cork measuring 1.30 cm * 5.50 cm * 3.00 cm in water and that on top of the cork you place a small cube of lead measuring 1.15 cm on each edge. The density of cork is 0.235 g/cm3, and the density of lead is 11.35 g/cm3. Will the combination of cork plus lead float or sink?

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Calculate the volume of the cork using the formula for the volume of a rectangular prism: \( V_{\text{cork}} = \text{length} \times \text{width} \times \text{height} \).

Calculate the mass of the cork using its density and the volume calculated in the previous step: \( m_{\text{cork}} = \text{density}_{\text{cork}} \times V_{\text{cork}} \).

Calculate the volume of the lead cube using the formula for the volume of a cube: \( V_{\text{lead}} = \text{edge}^3 \).

Calculate the mass of the lead using its density and the volume calculated in the previous step: \( m_{\text{lead}} = \text{density}_{\text{lead}} \times V_{\text{lead}} \).

Determine if the combination will float or sink by comparing the total mass of the cork and lead to the buoyant force, which is equal to the weight of the water displaced by the total volume of the cork and lead. If the total mass is less than the weight of the displaced water, the combination will float; otherwise, it will sink.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that determines whether an object will float or sink in a fluid. An object will float if its density is less than that of the fluid it is placed in, while it will sink if its density is greater.

Buoyancy

Buoyancy is the upward force exerted by a fluid on an object submerged in it. This force counteracts the weight of the object and is responsible for whether it floats or sinks. According to Archimedes' principle, an object will float if the buoyant force is equal to or greater than its weight.

Volume and Displacement

Volume is the amount of space an object occupies, and it plays a key role in determining buoyancy. When an object is placed in a fluid, it displaces a volume of fluid equal to its own volume. The weight of the displaced fluid can be compared to the weight of the object to assess whether it will float or sink.

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