Question

activity a: slice and dice
get the gizmo ready:

• click reset. check that polystyrene is selected.
• a calculator is recommended for this activity.

introduction: the density of a material is the amount of mass per unit of volume. density is calculated by dividing an objects mass by its volume.
question: how does density depend on the amount of material?

1. form hypothesis: how do you think cutting up a material will affect its density?
2. collect data: click slice. choose a piece of polystyrene and drag it onto the material investigation tray. record the mass and volume, then calculate the density by dividing the mass by the volume. replace the piece, and then repeat for the remaining pieces.

piece	mass (g)	volume (cm³)	density (g/cm³)
2
3
4
5 (if available)

1. analyze: what do you notice about the density of the polystyrene pieces?
2. predict: what do you think is the density of the whole block of polystyrene?
3. test: click reset. drag the whole (uncut) block of polystyrene onto the material investigation tray. record its mass and volume and calculate the density

mass: __ volume: density: __

1. apply: an archaeologist finds a golden figurine. how could she determine if the figurine is solid gold without cutting it?

Explanation:

Step1: Form hypothesis

Density is an intensive property. Cutting a material into pieces should not change its density as long as the material is homogeneous. So, the hypothesis could be: Cutting up a material will not affect its density.

Step2: Collect data

This step requires actual interaction with the Gizmo. Suppose we get the following data (example values):

Piece	Mass (g)	Volume (cm³)	Density (g/cm³)
2	4	10	$\frac{4}{10}=0.4$
3	6	15	$\frac{6}{15}=0.4$
4	8	20	$\frac{8}{20}=0.4$
5	10	25	$\frac{10}{25}=0.4$

Step3: Analyze

We notice that the density of each piece of polystyrene is the same. This is because density is an intensive property which does not depend on the amount of the substance.

Step4: Predict

Since density is intensive, we predict that the density of the whole block of polystyrene is the same as the density of the pieces, which in our example is 0.4 g/cm³.

Step5: Test

After dragging the whole (uncut) block of polystyrene onto the tray and recording mass = 30 g, volume = 75 cm³, density = $\frac{30}{75}=0.4$ g/cm³.

Step6: Apply

The archaeologist can measure the mass of the golden figurine using a balance. To find the volume, she can use the water - displacement method. Fill a graduated cylinder partially with water and record the initial volume $V_1$. Then, submerge the figurine in the water and record the new volume $V_2$. The volume of the figurine is $V = V_2 - V_1$. Then calculate the density $
ho=\frac{m}{V}$. Compare this density with the known density of pure gold. If they match, the figurine is likely solid gold.

Answer:

1. Hypothesis: Cutting up a material will not affect its density.
2. (Data will vary based on Gizmo interaction, example data shown above)
3. The density of each piece of polystyrene is the same.
4. Prediction: The density of the whole block is the same as the pieces (e.g., 0.4 g/cm³).
5. Mass: 30 g, Volume: 75 cm³, Density: 0.4 g/cm³ (example values)
6. Measure mass with a balance, find volume using water - displacement method, calculate density and compare with density of pure gold.