Math / Numbers & Operations

QuestionProblem 7 A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?

Studdy Solution

STEP 1

What is this asking? We've got a rock, and we want to figure out how much water it pushes out of the way, how big it is, and how dense it is.
Then, we'll check if it could be made of granite. Watch out! Don't mix up mass and volume!
Mass is how much "stuff" is in the rock, while volume is how much space it takes up.
Also, remember the units: grams for mass, milliliters or cubic centimeters for volume, and grams per milliliter or grams per cubic centimeter for density.

STEP 2

1. Displaced Water Mass
2. Rock Volume
3. Rock Density and Granite Check

STEP 3

Alright, let's start with the mass of the water displaced!
When the rock goes into the water, it pushes some water out of the way.
That's called displacement!

STEP 4

The mass of the water displaced is exactly equal to the difference between the rock's mass in air and its apparent mass in water.
It's like the water is "holding up" some of the rock's weight.

STEP 5

So, let's calculate the difference: $\text{Mass}_\text{displaced} = \text{Mass}_\text{air} - \text{Mass}_\text{water}$ $\text{Mass}_\text{displaced} = 540 \text{ g} - 342 \text{ g} = \textbf{198 g}$ The rock displaces 198 g of water!

STEP 6

Now, let's find the rock's volume!
Since the density of water is $\textbf{1 g/mL}$ , the volume of water displaced is equal to its mass.

STEP 7

This means the rock's volume is the same as the volume of water displaced.
Pretty cool, right?

STEP 8

So, the rock's volume is $\textbf{198 mL}$ , which is the same as $\textbf{198 cm}^3$ .
Remember, $1 \text{ mL} = 1 \text{ cm}^3$ .

STEP 9

Time to calculate the rock's density!
Density is how much mass is packed into a certain volume.
The formula is: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

STEP 10

We know the rock's mass in air is 540 g and its volume is 198 cm³.
Let's plug those values in: $\text{Density} = \frac{540 \text{ g}}{198 \text{ cm}^3} \approx \textbf{2.73 g/cm}^3$

STEP 11

The density of granite is typically between $2.65 \text{ g/cm}^3$ and $2.75 \text{ g/cm}^3$ .
Our rock's density falls right in that range!

STEP 12

(a) The mass of water displaced is 198 g. (b) The volume of the rock is 198 cm³. (c) The rock's average density is approximately 2.73 g/cm³.
This is consistent with the density of granite.

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QuestionProblem 7 A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?

Studdy Solution

STEP 1

STEP 2

1. Displaced Water Mass
2. Rock Volume
3. Rock Density and Granite Check

STEP 3

Alright, let's start with the mass of the water displaced!
When the rock goes into the water, it pushes some water out of the way.
That's called displacement!

STEP 4

The mass of the water displaced is exactly equal to the difference between the rock's mass in air and its apparent mass in water.
It's like the water is "holding up" some of the rock's weight.

STEP 5

So, let's calculate the difference: $\text{Mass}_\text{displaced} = \text{Mass}_\text{air} - \text{Mass}_\text{water}$ $\text{Mass}_\text{displaced} = 540 \text{ g} - 342 \text{ g} = \textbf{198 g}$ The rock displaces 198 g of water!

STEP 6

Now, let's find the rock's volume!
Since the density of water is $\textbf{1 g/mL}$ , the volume of water displaced is equal to its mass.

STEP 7

This means the rock's volume is the same as the volume of water displaced.
Pretty cool, right?

STEP 8

So, the rock's volume is $\textbf{198 mL}$ , which is the same as $\textbf{198 cm}^3$ .
Remember, $1 \text{ mL} = 1 \text{ cm}^3$ .

STEP 9

Time to calculate the rock's density!
Density is how much mass is packed into a certain volume.
The formula is: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

STEP 10

We know the rock's mass in air is 540 g and its volume is 198 cm³.
Let's plug those values in: $\text{Density} = \frac{540 \text{ g}}{198 \text{ cm}^3} \approx \textbf{2.73 g/cm}^3$

STEP 11

The density of granite is typically between $2.65 \text{ g/cm}^3$ and $2.75 \text{ g/cm}^3$ .
Our rock's density falls right in that range!

STEP 12

(a) The mass of water displaced is 198 g. (b) The volume of the rock is 198 cm³. (c) The rock's average density is approximately 2.73 g/cm³.
This is consistent with the density of granite.

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QuestionProblem 7 A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?

Studdy Solution

STEP 1

STEP 2

1. Displaced Water Mass2. Rock Volume3. Rock Density and Granite Check

STEP 3

Alright, let's **start** with the mass of the water displaced!When the rock goes into the water, it pushes some water out of the way.That's called displacement!

STEP 4

The mass of the water displaced is *exactly* equal to the *difference* between the rock's mass in air and its apparent mass in water.It's like the water is "holding up" some of the rock's weight.

STEP 5

STEP 6

Now, let's **find** the rock's volume!Since the density of water is 1 g/mL\textbf{1 g/mL}1 g/mL, the volume of water displaced is equal to its mass.

STEP 7

This means the rock's volume is the *same* as the volume of water displaced.Pretty cool, right?

STEP 8

So, the rock's volume is 198 mL\textbf{198 mL}198 mL, which is the same as 198 cm3\textbf{198 cm}^3198 cm3.Remember, 1 mL=1 cm31 \text{ mL} = 1 \text{ cm}^31 mL=1 cm3.

STEP 9

Time to **calculate** the rock's density!Density is how much mass is packed into a certain volume.The formula is: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass​

STEP 10

We know the rock's mass in air is **540 g** and its volume is **198 cm³**.Let's plug those values in: Density=540 g198 cm3≈2.73 g/cm3\text{Density} = \frac{540 \text{ g}}{198 \text{ cm}^3} \approx \textbf{2.73 g/cm}^3Density=198 cm3540 g​≈2.73 g/cm3

STEP 11

The density of granite is typically between 2.65 g/cm32.65 \text{ g/cm}^32.65 g/cm3 and 2.75 g/cm32.75 \text{ g/cm}^32.75 g/cm3.Our rock's density falls right in that range!

STEP 12

(a) The mass of water displaced is **198 g**. (b) The volume of the rock is **198 cm³**. (c) The rock's average density is approximately **2.73 g/cm³**.This is consistent with the density of granite.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Displaced Water Mass
2. Rock Volume
3. Rock Density and Granite Check

Alright, let's start with the mass of the water displaced!
When the rock goes into the water, it pushes some water out of the way.
That's called displacement!

The mass of the water displaced is exactly equal to the difference between the rock's mass in air and its apparent mass in water.
It's like the water is "holding up" some of the rock's weight.

Now, let's find the rock's volume!
Since the density of water is $\textbf{1 g/mL}$ , the volume of water displaced is equal to its mass.

This means the rock's volume is the same as the volume of water displaced.
Pretty cool, right?

So, the rock's volume is $\textbf{198 mL}$ , which is the same as $\textbf{198 cm}^3$ .
Remember, $1 \text{ mL} = 1 \text{ cm}^3$ .

Time to calculate the rock's density!
Density is how much mass is packed into a certain volume.
The formula is: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

We know the rock's mass in air is 540 g and its volume is 198 cm³.
Let's plug those values in: $\text{Density} = \frac{540 \text{ g}}{198 \text{ cm}^3} \approx \textbf{2.73 g/cm}^3$

The density of granite is typically between $2.65 \text{ g/cm}^3$ and $2.75 \text{ g/cm}^3$ .
Our rock's density falls right in that range!

(a) The mass of water displaced is 198 g. (b) The volume of the rock is 198 cm³. (c) The rock's average density is approximately 2.73 g/cm³.
This is consistent with the density of granite.