Homework Helpers: Earth Science

Introduction

Welcome to Homework Helpers: Earth Science

Homework Helpers: Earth Science was written for the students who need a different presentation of Earth Science than what they've seen in class. This book is written less as a textbook and more as a conversation between the reader and a tutor.

Earth Science is the study of our natural surroundings of which we all have some familiarity. However, the important connections are often lost in the dry facts and abstract concepts. The discussions and examples in this book will give the reader the oh, of course! That makes sense, reaction.

This book is not to be read in one sitting or even in the order that it is presented. It is written as a supplement to your classroom experience. Pick up this book and review each topic as you work on it in class or in preparation for the chapter test. If you are finding your class particularly difficult, it will also come in handy to preview the topic before you see it in class.

Each section has practice questions and exercises designed to reinforce the new material. After the practice sections, you will find the answers and explanations of correct as well as incorrect answers. At the end of each chapter, there is a chapter test also accompanied by explanations of the answers.

Earth Science is something we are all immersed in every day and should not be a foreign subject. A firm grasp of the concepts of how our world works makes us partners in a relationship with nature, rather than victims of it.

Introduction to Earth Science

Lesson 1–1: Observation and Inference

An observation is any information that is gathered by using any of the five senses. Observations are the facts that are used in science. They tend to be dry facts, measurements, and statistics. Think of observations as evidence.

A measurement is a form of an observation. This is referred to as comparing to a standard because the definition of the unit you are using, such as a meter, is a standardized distance. In order that all measurements agree with each other, the definition of that unit can be found somewhere. For example, in the state Bureau of Weights and Measures, there is a metal bar that is measured very accurately to be as exact as humanly possible to a meter. This bar is the standard meter. All other meter sticks are compared to this one bar for accuracy. Whenever you use a ruler to measure a distance, you are comparing to a standard. Even though your 49-cent ruler may not be the most accurate, it is a fairly close representation of that bar in the Bureau of Weights and Measures. By the way, this is a huge leap from the old days of measuring a cubit as the length from your elbow to the tip of your middle finger or a foot as being the size of the king's foot.

Some Examples of Observations

The Sun rises due east on March 21.

The rock has a hardness of 7 on Mohs scale of hardness.

There is a quarter Moon in the sky.

An inference is a conclusion that is made based on your observations. It will typically answer the question why or how. When you make an inference you put the evidence together and explain what happened or what will happen.

Some Examples of Inferences

The rock was transported, by a glacier.

This sample of granite cooled slowly from magma inside Earth.

Based on today's weather trends, it will rain tomorrow.

Lesson 1–1 Review

Identify each of the following statements as either an observation or an inference:

The rock is dark brown.

The Moon is 386,000 km away from the Earth.

The Moon was created by a collision between Earth and another object in space.

It's raining today.

According to the graph, the world's population will double in 100 years.

A glacier gouged out this valley.

The wooly mammoth was hunted to extinction by primitive humans.

Figure 1.1. Cyclic Relationship

Lesson 1–2: Patterns of Change

In Earth Science we study many kinds of changes: changes in temperature, changes in the size of rocks as they wear down, the changing position of Earth throughout the year, and so on. Many of these changes follow some kind of pattern, which allows us to predict what will happen in the future.

A cyclic pattern is a repeating pattern. This is caused by repeating events and, when graphed, it appears as some version of a sine graph.

Examples of Cyclic Patterns

The hot and cold of the day and night.

The hot and cold of summer and winter.

The phases of the Moon.

The rise and fall of the tides.

A direct relationship is a pattern of change in which the cause and effect both increase together or both decrease together. The graph of a direct relationship will slope upwards towards the right.

"As X gets bigger,

Y also gets bigger."

An inverse relationship is a pattern in which one variable increases in value while the other variable decreases. When this relationship is graphed, it will make a line that slopes downward.

"As X gets bigger,

Y gets smaller."

Figure 1.2. Direct Relationships

Figure 1.3. Inverse Relationships

To extrapolate is to take a pattern and extend it beyond the current data. Extrapolation is used to make predictions. A classic example of this is to predict the world's population in 20 years. On a graph, extrapolation is as easy as extending the line or pattern.

Interpolation is another way of using data to make a good guess about a missing portion of information. Contrary to extrapolation (extra meaning outside or beyond), interpolation (inter meaning inside or between) does not extend the graph. It reads between the lines. For example, if you measured your height in fourth grade and you were 3 feet tall and in tenth grade you were 5 feet tall, even though you didn't measure yourself in seventh grade, it would be a good assumption that exactly between the fourth and tenth grade, you were exactly between 3 and 5 feet tall—or 4 feet tall.

Figure 1.4. Extrapolation. To extrapolate a graph, simply extend the line.

Figure 1.5. Interpolation

Making Graphs Without Using Numbers

Sometimes to show relationships graphs without numbers are used. But to make a numberless graph from scratch can be difficult until you know how to do it.

As an example, we'll use the relationship between temperature and density of a material. The first thing that you need to do is to label the axes: temperature and density. Then, label each axis with examples of extremes. For temperature, two extremes would be cold and hot, or if you are more comfortable with numbers use 0 and 1,000,000. And for density, some good labels are low density and high density, or fluffy and dense. Of course, the lower values are normally placed near the origin of the graph.

Figure 1.6

At this point all you need to do is ask, What is the density like for hot materials? Hot materials, like hot air, are light and fluffy, and they float. So, place a dot where hot and light cross. What is the density like for cold materials? Because cold materials sink, they are dense. Now, place a dot where cold and dense" cross.

Figure 1.7. Note that even though all three lines begin and end in one place there are different paths that the line can

Once you have two dots, you can connect them. Take note that the path between the dots can be straight or curved, but you will have the general relationship.

Lesson 1–2 Review

To make accurate predictions of the future, you need data that is

a) a random sampling.

b) a representation of part of a cycle.

c) a representation of one complete cycle.

d) made of several cycles.

The monthly changes in the phases of the Moon are

a) random.

b) cyclic.

c) not predictable.

d) highly variable.

Tide tables can be printed months in advance because tides

a) follow a predictable pattern.

b) are noncyclic events.

c) happen at the same place at the same time.

d) are based on the weather patterns.

The age of a baby and his or her size are

a) an inverse relationship.

b) a direct relationship.

c) a cyclic relationship.

d) multiples of each other.

For questions 5 and 6, use Figure 1.8, which shows the changing densities and volumes of a sample of air that is being pressurized.

Figure 1.8

5. What kind of relationship does pressure have with density?

a) inverse

b) direct

c) cyclic

d) no relationship

6. What kind of relationship does pressure have with volume?

a) inverse

b) direct

c) cyclic

d) no relationship

7. Which graph best shows the relationship between how large an object appears and how close it is to the observer?

Lesson 1–3: Metric Measurements

When collecting data, such as measurements, there is a wide variety of units that any one thing can be measured with. For example, length can be measured in inches, meters, furlongs, rods, fathoms, or even a stone's throw. To make sure that all scientific measurements are in the same units, the scientific community has adopted the Standard International (SI) system. It is based on the metric system and can be simplified to expressions of grams, meters, and seconds—or combinations of these three main units.

All scientific measurements are taken using the metric system (with the exception of American meteorology measurements). There are many advantages to using the metric system. It is used by most of the countries of the world and it allows easy communication between people who speak different languages. It is based on 10s and makes doing math work easy. The system is easier to rebuild from scratch if, for example, your thermometer breaks.

In Earth Science the basic units of the metric system are the meter and the gram. There are other units used, but these account for the majority of measurements taken for Earth Science calculations.

The metric system is based on water, the most common substance on Earth. Here is an example to illustrate how water can be used to recreate the metric system:

If you shaped 1 gram of liquid water into a cube, it would be a centimeter in each direction (also known as a cubic centimeter or cm³). One cm³ is also equal to 1 milliliter (1 mL). If you heat up 1 gram of water with 1 calorie of energy, it will raise the temperature 1°C.

Meter

The meter is the base unit for length. When measuring tiny distances, the meter is too big and is divided into 1,000 pieces called millimeters (milli means one thousandth). For distances a little larger, the centimeter is used. It is one hundredth of a meter or 10 millimeters. Centi means one hundredth. Just as there is 100 cents in a dollar, there are 100 centimeters in a meter. For larger distances meters are used, and kilometers are used to measure distances in thousands of meters (kilo means 1,000 times).

Know Your Sizes

A millimeter is about the thickness of your pinky nail.

A centimeter is about the width of your pinky nail.

A meter is just over a yard and is about the distance from the nose to the fingertips of an adult.

Grams

The mass of an object is roughly the measure of how many atoms are within the object. Mass is measured with a scale or balance and is expressed in grams. One thousand grams is one kilogram and is about the weight of a pineapple.

Volume

The amount of space an object takes up is volume. A good analogy of volume is to take a count of how many sugar cubes fit into an object. A sugar cube is roughly a centimeter on each side—or a cubic centimeter (cm³). With larger objects, volume is measured in cubic meters (m³) or even cubic kilometers (km³).

To measure the volume of an object, there are a few different methods depending on the nature of the object being measured. If the object is a geometric solid such as a block, sphere, or pyramid it is easy enough just to use a formula. For example, a block's volume would be found by using the equation:

Volume = length in centimeters × width in centimeters × height in centimeters

(or v = I × w × h)

This method will give the results in units of cubic centimeters (cm³).

To measure the volume of a liquid, you would use a graduated cylinder and the results would be in milliliters (mL). The tricky part of using a graduated cylinder is how exactly to read it. When water is poured into the tube, the water's surface will not be level. It will have a dip in it called a meniscus. The volume is read as the value of the bottom of the meniscus. The tubes are designed knowing that the water will dip so don't worry about it not being accurate.

To measure the volume of an irregular solid such as a rock, you would use the water displacement method. This measures the volume of the material by how much water is pushed out of a container when the object is submerged. In a lab setting this is done in a graduated cylinder. Fill the cylinder about half-way with water and note the volume of the water. Carefully insert the sample to be measured. When the water rises, note the new water level. The difference between the final level and the starting level is the volume of the rock.

Figure 1.13. In this example, the cylinder with only water has a volume of 35 mL. When the rock is inserted, the new volume is 55 mL. The difference, 20 mL, is the volume that the rock takes up. The rock has a volume of 20 cm³.

One confusing thing about using the water displacement method to measure the volume of a rock is that the units are still cm³ even though you are using the level of water to find the volume. Let me explain: 1 mL of liquid takes up exactly the same amount of space as 1 cm³. Therefore, they are interchangeable. Liquids are measured in mLs and solids in cm³.

Lesson 1–3 Review

Measure each line in centimeters (cm) and also in millimeters (mm).

a) Draw a line that is 1 cm long.

b) Now draw a line that is 10 mm long.

c) How many millimeters are there in 1 cm?

d) How do you change a measurement from centimeters to millimeters?

e) How do you change a measurement from millimeters to centimeters?

Lesson 1–4: Density

Density measures how tightly packed an object is. Technically speaking, it is how much mass is in a unit of volume. Some objects can be really dense and feel heavy for their size, whereas other objects are not as dense and feel lighter or fluffier.

Here are two examples of how an object can change its density. Take a piece of aluminum foil and lightly crumple it. Fell how heavy it feels. Now crumple it as hard as you can and feel how heavy it feels now. It will feel heavier. You have just made its volume smaller without changing its mass—it is now denser and feels heavier for its size.

For the second example, you start with an empty suitcase. It has a certain volume that it takes up, but because it is empty, it has very little mass. It feels light for its size. Now pack it with as many clothes as it will hold. Sit on it to compress to and zip it closed. The suitcase now has a much greater mass without changing its volume—it feels heavier for its size.

To calculate density, you divide the object's mass and by its volume. Because mass is measured in grams (g) and volume in cubic centimeters (cm³), density is measured in grams per cubic centimeter (g/cm³). The unit g/cm³ tells us how many grams of material are crammed into each cube the size of a sugar cube.

How to Use the Density Equation

The equation for density is .

How to use it for finding the volume or mass of a material? The first step is to put the equation into a triangle in this way:

Figure 1.14

In the equation mass, m, is the only variable that is on top of anything else so it goes into the top section of the triangle. The d and v go into the remaining spots and it doesn't matter which letter goes into which section.

In any equation, there is an unknown, which is what you are trying to solve. In the normal equation, d is unknown, which you need to find, and m and v are the values that you have. But if you need to solve for m or v, you need to solve a slightly different equation. Here's where the triangle comes into use. Simply use your finger to cover whichever variable you need to solve (you cover it because you don't know what it is). Once you cover the unknown, the remaining variables show you the new equation.

For example, if you need to know what the volume, v, is, cover the v and you are left with mass, m, over density, d. This means that volume is mass over (or divided by) density. If you are left with the two variables next to each other (d and v) then you multiply to find m.

Density: When the Volume Changes

To change the volume of a material, it will either have to be squeezed into a smaller size or expanded so that it takes up more room. But what happens to the density? When a material gets compacted, it packs the material into a smaller space. This might happen if it gets cooler or is put under greater pressure. When a material gets compacted, the atoms get closer together and the density increases. When the material expands, it takes up more room—the volume increases. As a result, the atoms get further apart and the density decreases. Materials will expand when they are heated or experience less pressure. When materials expand, the density decreases; it gets fluffier and has a tendency to float.

Density: When the Mass Changes

It is an unusual situation to change the mass of an object without affecting its volume, but it can happen. One of the more common examples would be releasing gas from a pressurized canister. When the gas escapes, the mass within the canister decreases but the volume stays the same (the gas within expands to fill the entire canister). When the mass decreases but the volume stays the same, the density will decrease. In the same situation, if more gas is pumped back into the canister, the volume will still stay the same but density will increase.

Lesson 1–4 Review

A sample of quartz has a density of 2.7 g/cm³. If the sample is cut in half, what will happen to the density of each of the two halves?

a) The densities of the two halves will be higher than the original.

b) The densities of the two halves will be lower than the original.

c) The densities of the two halves will be the same as the original.

d) There is not enough information.

Which of the following is the densest: water in the solid phase, liquid, or gaseous?

a) solid

b) liquid

c) gas

d) all are the same

The reason a hot air balloon rises is because when air is heated

a) it contracts, making its density lower.

b) it contracts, making its density higher.

c) it expands, making its density lower.

d) it expands, making its density higher.

Complete the following chart.

What is the density of the following sample?

Figure 1.15

Lesson 1–5: Gradient, Rate, and Time

In order to express how quickly values change, we use rate and gradient. Rate tells us how quickly a value changes from minute to minute, while gradient shows how quickly a value changes between two points on a map.

The change in value is simply subtracting one value from another. The order of which number is subtracted from which makes little difference. The only difference would be an answer with a negative sign in front of it, which would just get thrown out.

For example, to measure the weathering rate of a cemetery headstone, find the difference in thickness of the rock (subtract the worn thickness from the original thickness) and then divide by the amount time it took to wear down. If the headstone wore down 18mm in 50 years, then the equation would be:

Notice that the units are a combination of the top of the equation and the bottom. The unit mm/year is read millimeters per year and means that in one year the rock weathered .36 mm.

A good way to think of rate is that it means speed. It expresses how fast something happens.

Gradient works exactly the same way rate does except instead of time, the values change with the distance on a map. Subtract the two values and divide by the distance between the two values.

As with rate, the units for gradient are a combination of the units on top of the equation and the bottom. This can make some strange combinations such as m/km (meters per kilometer) or m/m (meters per meter). When this happens, there is no need to combine like terms. (Meters per kilometer tells that the slope of a mountain rises so many meters for every kilometer across the map.)

Rate and Time

In Science, it is critical to express ourselves clearly and accurately. One of the most difficult things to express is the difference between rate and time. People often mix up the two. Rate tells us how quickly a value changes. Because rate is a speed, we can say the value changes quickly or fast.

Time expresses how much time it takes for an event. Time can never go fast or slow (except if you are Einstein). But you can have a short time or a long time.

One reason why the two terms are often confused comes from their relationship with each other. Time is a straight measurement of time: t. Rate is a value over time: x/t. In Math class, they would call these two terms multiplicative inverses, which means that they are exact opposites. If the time gets bigger, the rate gets smaller and vice versa.

For example, if you take a trip to Grandma's house and it takes a long time then you were traveling at a slow rate or speed. On the way back from Grandma's, the same trip takes a shorter amount of time—you were traveling at a faster rate.

Rate means speed. When you hear rate think of the dial of a speedometer and use words such as faster and slower.

When you think of time, think of a stopwatch and use phrases such as a longer time or a shorter time. Never use words such as quicker or slower to express time.

Lesson 1–5 Review

Exercise A: Gradients

For all problems, show all work and label the answers with the proper units.

Write the equation for gradient.

Two cities are separated by 300 miles. City X has a temperature of 42°F and city Y has a temperature of 60°F. Calculate the temperature gradient between the two cities.

New Earth City has a temperature of 65°F; Monolith City, 42 miles away, has a temperature of 58°F. Calculate the temperature gradient between the two locations.

Chicago is 1,500 miles away from New York. The two areas have a difference in air pressure of 7.5 mb (millibars). What is the pressure gradient?

Two cities are 900 miles distant from each other. What is the pressure gradient if the air pressure at one city is 29.21 inches and in the other city it is 29.84 inches?

The air pressure inside a tornado can drop 30 mb from the pressure outside it. If an F5 tornado is 1 mile across (5,200 ft), what is the pressure gradient in mb/ft from the outside to the center (half the diameter) of the tornado?

Exercise B: Rates

Complete the following data chart, graph the data (see Figure 1.16 on page 26), and then answer the questions. You will plot two lines on the graph: time and rate. Make your graphs with the time on the left vertical axis and the rate on the right vertical axis.

7. Write the equation for rate of change.

Figure 1.16

8. Which hardness takes the longest time to weather?

9. Which hardness has the fastest weathering rate?

10. How does the rate of weathering change as hardness increases?

11. How does the time needed for weathering change as hardness increases?

12. Is the relationship between hardness and weathering time direct or inverse?

13. Is the relationship between hardness and weathering rate direct or inverse?

Lesson 1–6: Percent Deviation

All measurements have some error associated with them. Sometimes it is valuable to know just how large the error is. For example, if you measured a length and you were off by 50 cm, would that be a good measurement? If you just measured a sheet of paper that is about 30 cm long, it would be a horrible measurement. However, if you measured the diameter of Earth (1,275,600,000 cm) and were off by 50 cm, it would be a very good measurement! One way to express error is percent deviation or percent error.

Percent deviation takes the value of the error and compares it to the correct value for the measurement.

For example: A student measures a rock to have a mass of 54 g while it is actually 50 g.

at this point, the grams cancel out

Lesson 1–6 Review

Write the equation for percent deviation.

What does accepted value mean?

A student weighed a rock and found its mass to be 30 g. When checked, she found out that the rock really has a mass of 25 g. What is the percent deviation?

A student measured a table to be 150 cm wide. The correct width is 175 cm. What is the percent deviation?

Original satellite technology measured the Earth's circumference to be 14,504 km. What is the percent deviation if the actual circumference is 14,564 km?

Yor was a Viking. He had to cut wood for a boat. Each piece was to be 22 meters long, but Yor measured them to be 21 meters. What was his percent deviation?

Chapter Exam

If a mountain grows at a rate of 400 cm in 100 years, what is its growth rate per year?

The lip of Niagara Falls is worn backwards by 900 cm in a month. What is its erosion rate per day (assume a