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Difficulty: MediumProperties of Matter

A machinist measures the mass of an irregular steel fastener to be 84 g84\text{ g}. To determine its volume, the fastener is submerged in a graduated cylinder filled with 50 mL50\text{ mL} of water, causing the water level to rise to 62 mL62\text{ mL}. What is the density of the steel fastener in g/cm3\text{g/cm}^3?

Answer: 7 g/cm³

Answer

The density of the steel fastener is 7 g/cm37\text{ g/cm}^3.
Density is calculated by dividing mass by volume (Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}). The volume of the irregular fastener is found by subtracting the initial water volume from the final water volume (62 mL−50 mL=12 cm362\text{ mL} - 50\text{ mL} = 12\text{ cm}^3). Dividing the mass of 84 g84\text{ g} by the volume of 12 cm312\text{ cm}^3 gives 7 g/cm37\text{ g/cm}^3.

Step-by-Step Solution

1
Determine the volume of the fastener using the water displacement method
Displaced volume = 62 mL−50 mL=12 mL=12 cm362\text{ mL} - 50\text{ mL} = 12\text{ mL} = 12\text{ cm}^3
The volume of an irregular submerged solid equals the volume of fluid it displaces, where 1 mL=1 cm31\text{ mL} = 1\text{ cm}^3.
2
Calculate density by dividing mass by displaced volume
Density=84 g12 cm3=7 g/cm3\text{Density} = \frac{84\text{ g}}{12\text{ cm}^3} = 7\text{ g/cm}^3
Density is defined as mass per unit volume (ρ=mV\rho = \frac{m}{V}).

Key Concept

Density and Water Displacement
Estimated Time:1m 0s
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Topics

Properties of Matter

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