Question

A small piece of cork weighs 0.2 N in air. When held submerged underwater, the cork exhibits an upward force of 0.757 N. What is the density of the cork?

Answer 1

To calculate the density of the cork, we first find its volume from the buoyant force and then divide the weight of the cork in air by this volume, resulting in a density of 0.264 kg/m³.

Step-by-step explanation:

To determine the density of the cork, we must understand that the upward force exerted on the cork when submerged underwater is the buoyant force. This force is equal to the weight of the water displaced by the cork. Since the weight of the cork in air is 0.2 N and the buoyant force is 0.757 N, the weight of the water displaced by the cork is 0.757 N. The weight of the water displaced provides the volume of the cork because the density of water is 1,000 kg/m³ (or equivalently, the weight of 1 m³ of water is 9.81 kN). We can calculate the volume of the cork using the equation:

V = buoyant force / (density of water × gravitational acceleration)

V = 0.757 N / (1,000 kg/m³ × 9.81 m/s²)

V = 0.757 N / 9,810 N/m³

V = 0.0000772 m³

Now we can find the cork's density by dividing its weight by its volume:

density of cork = weight of cork in air / volume of cork

density of cork = 0.2 N / 0.0000772 m³

density of cork = 2.59 N/m³

Since the weight in Newtons can be converted to mass by dividing by gravitational acceleration (N = kg·m/s²), we can convert the cork's density to kg/m³:

density of cork = 2.59 kg⋅m/s² / 9.81 m/s²

density of cork = 0.264 kg/m³

The density of the cork is therefore 0.264 kg/m³.