Question

exploring density directions: a student wants to create a density column using some common household materials. first, calculate the density of each substance listed on the back of this paper. second, identify its position in the column based on its density

Explanation:

To solve the problem of creating a density column, we follow these steps:

Step 1: Recall the formula for density

The formula for density is $
ho = \frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume.

Step 2: Gather data for each substance

(Assuming we have substances like honey, corn syrup, dish soap, water, vegetable oil, rubbing alcohol, etc. with their respective masses and volumes. For example, let's take some common values:

• Honey: $m = 142\ \text{g}$, $V = 100\ \text{mL}$
• Corn syrup: $m = 136\ \text{g}$, $V = 100\ \text{mL}$
• Dish soap: $m = 116\ \text{g}$, $V = 100\ \text{mL}$
• Water: $m = 100\ \text{g}$, $V = 100\ \text{mL}$
• Vegetable oil: $m = 92\ \text{g}$, $V = 100\ \text{mL}$
• Rubbing alcohol: $m = 78\ \text{g}$, $V = 100\ \text{mL}$)

Step 3: Calculate density for each substance

• Honey: $

ho = \frac{142\ \text{g}}{100\ \text{mL}} = 1.42\ \text{g/mL}$

• Corn syrup: $

ho = \frac{136\ \text{g}}{100\ \text{mL}} = 1.36\ \text{g/mL}$

• Dish soap: $

ho = \frac{116\ \text{g}}{100\ \text{mL}} = 1.16\ \text{g/mL}$

• Water: $

ho = \frac{100\ \text{g}}{100\ \text{mL}} = 1.00\ \text{g/mL}$

• Vegetable oil: $

ho = \frac{92\ \text{g}}{100\ \text{mL}} = 0.92\ \text{g/mL}$

• Rubbing alcohol: $

ho = \frac{78\ \text{g}}{100\ \text{mL}} = 0.78\ \text{g/mL}$

Step 4: Order substances by density (highest to lowest)

The order from highest density to lowest density is: Honey ($1.42$), Corn Syrup ($1.36$), Dish Soap ($1.16$), Water ($1.00$), Vegetable Oil ($0.92$), Rubbing Alcohol ($0.78$).

Step 5: Assign positions in the density column

• Position 20 (bottom, highest density): Honey
• Position 19: Corn Syrup
• Position 18: Dish Soap
• Position 17: Water
• Position 16: Vegetable Oil
• Position 15: Rubbing Alcohol
• (And so on for other positions, depending on the number of substances. If there are more substances, we follow the same logic of ordering by density.)

Final Answer (for a typical set of substances)

• 20: Honey
• 19: Corn Syrup
• 18: Dish Soap
• 17: Water
• 16: Vegetable Oil
• 15: Rubbing Alcohol
• (Adjust based on the actual substances and their densities provided on the back of the paper.)

Answer:

To solve the problem of creating a density column, we follow these steps:

Step 1: Recall the formula for density

The formula for density is $
ho = \frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume.

Step 2: Gather data for each substance

(Assuming we have substances like honey, corn syrup, dish soap, water, vegetable oil, rubbing alcohol, etc. with their respective masses and volumes. For example, let's take some common values:

• Honey: $m = 142\ \text{g}$, $V = 100\ \text{mL}$
• Corn syrup: $m = 136\ \text{g}$, $V = 100\ \text{mL}$
• Dish soap: $m = 116\ \text{g}$, $V = 100\ \text{mL}$
• Water: $m = 100\ \text{g}$, $V = 100\ \text{mL}$
• Vegetable oil: $m = 92\ \text{g}$, $V = 100\ \text{mL}$
• Rubbing alcohol: $m = 78\ \text{g}$, $V = 100\ \text{mL}$)

Step 3: Calculate density for each substance

• Honey: $

ho = \frac{142\ \text{g}}{100\ \text{mL}} = 1.42\ \text{g/mL}$

• Corn syrup: $

ho = \frac{136\ \text{g}}{100\ \text{mL}} = 1.36\ \text{g/mL}$

• Dish soap: $

ho = \frac{116\ \text{g}}{100\ \text{mL}} = 1.16\ \text{g/mL}$

• Water: $

ho = \frac{100\ \text{g}}{100\ \text{mL}} = 1.00\ \text{g/mL}$

• Vegetable oil: $

ho = \frac{92\ \text{g}}{100\ \text{mL}} = 0.92\ \text{g/mL}$

• Rubbing alcohol: $

ho = \frac{78\ \text{g}}{100\ \text{mL}} = 0.78\ \text{g/mL}$

Step 4: Order substances by density (highest to lowest)

The order from highest density to lowest density is: Honey ($1.42$), Corn Syrup ($1.36$), Dish Soap ($1.16$), Water ($1.00$), Vegetable Oil ($0.92$), Rubbing Alcohol ($0.78$).

Step 5: Assign positions in the density column

• Position 20 (bottom, highest density): Honey
• Position 19: Corn Syrup
• Position 18: Dish Soap
• Position 17: Water
• Position 16: Vegetable Oil
• Position 15: Rubbing Alcohol
• (And so on for other positions, depending on the number of substances. If there are more substances, we follow the same logic of ordering by density.)

Final Answer (for a typical set of substances)

• 20: Honey
• 19: Corn Syrup
• 18: Dish Soap
• 17: Water
• 16: Vegetable Oil
• 15: Rubbing Alcohol
• (Adjust based on the actual substances and their densities provided on the back of the paper.)