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# Student Exploration Determining Density via Water Displacement (answers)

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Author: Jack Bauer
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How much water is displaced by object A?

Water has a density of 1 gram per cubic centimeter (1 g/cm3). Based on its density, what is the mass of the displaced water?

Use Archimedes’ principle to determine the mass of object A:

Measure: Click Reset. Notice that object F has the same volume as object A. Drag object F into the water.

Does object F float or sink?.

How much water is displaced by object F?

What is the volume of object F?

What is the volume of object A?

Calculate: The density of an object is equal to its mass divided by its volume: D = m ÷ V. The unit of density is grams per cubic centimeter (g/cc or g/cm3).

What is the density of object A?

Analyze: Click Reset and drop object A back into the water. About what percentage of object A is under the water? How is this percentage related to the density of object A?

(Activity continued on next page)

Activity (continued from previous page)

Gather data: Click Reset. Find how much water is displaced by objects B, C, D, and E. Record your measurements below. Include units.

Calculate: Use your data to find the mass, volume, and density of the two floating objects, C and E. Recall that the mass of a floating object is equal to the mass of displaced water, and the volume of a sinking object is equal to the volume of displaced water. Assume objects B and E have the same volume, as do objects C and D.

Object C: Mass: Volume: Density:

Object E: Mass: Volume: Density:

Analyze: Drag objects C and E into the water. Estimate the percentage of these objects that are submerged below the waterline. List these estimates below:

Object C: Object E:

How do these estimates relate to the densities you calculated above?

Think and discuss: Why can’t you use this Gizmo to measure the densities of objects B, D, and F? If possible, discuss your answer with your classmates and teacher.

Challenge: What can you say about the densities of objects B, D, and F? Is there a way to compare the relative densities of these three objects? Explain.

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