**Mass, Weight, Volume, and Density**

**The United States Transport Safety Board released the report into the New York crash. It states that the estimated weight on board the helicopter when it took off was 1464kg, a figure which exceeds the manufacturer’s maximum of 1451kg. The helicopter which was flying sightseers over New York plunged into the East River, New York on 4 October 2011.**

**I'm not fat!**

I have big bones!!

I have big bones!!

Why should we care if we can measure the weight or mass of an object?

The United States Transport Safety Board released the report into the New York crash. It states that the estimated weight on board the helicopter when it took off was 1464kg, a figure which exceeds the manufacturer’s maximum of 1451kg. The helicopter which was flying sightseers over New York plunged into the East River, New York on 4 October 2011.

Matter and Mass

The term matter refers to anything that has mass and takes up space. This is a very general characteristic that describes virtually everything you will ever see on Earth.

The term mass describes the amount of matter in an object. The standard unit (SI unit) for mass is the kilogram (kg).

1,000-2,000 kg

about 12 kg

Kilograms and Grams

We have just learned that the kilogram is the standard unit to be used when measuring an object's mass. However, most of the things you guys have measured were far less than a kilogram. For smaller measurements of mass, it may be convenient to use the Gram for these types of measurements.

1 kilogram is equal to 1,000 grams. Notice the word kilogram is simply the word "gram" with the prefix "kilo" at the beginning. Remember, prefixes can have a huge impact.

Measuring Mass

In this class and most laboratories, the mass of an object is calculated or measured using a mass balance scale like the ones pictured below.

Are Mass and Weight the Same?

NO!

Mass and weight are often used in the same way, but they mean two totally different things in scientific terms. As we learned earlier, mass is the amount of matter an object has.

Weight refers to the amount of gravitational pull on an object. Your mass is constant throughout the universe, but what about your weight?

Mass versus Weight

Mass is a fundamental property of an object measured in kilograms (kg). Weight is a force that depends on the pulling force of gravity and is measured in Newtons (N)

Mass

Weight

Amount of matter in an object

Stays the same unless you gain mass

SI unit : kilogram (kg)

The force of gravity acting on an object's mass

Changes when gravitational force changes

SI unit = Newton (N)

Similarities

Property of matter

Can be measured

1 kg = 9.8 N = 2.2 lb

Volume

Volume is the amount of space an object takes up. The SI unit for volume is the cubic meter (m ). However, this unit is too large for most of the measurements we will make in this class. A better unit to use is the cubic centimeter (cm )

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Measuring Volume

Liquids

You can measure the volume of liquids by pouring them into a graduated cylinder. The markings on a graduated cylinder represent milliliters (mL).

Solids

You have probably already measured the volume for solid shapes that were in convenient geometrical shapes like cubes, pyramids, and spheres.

What if I need to measure the volume of an object that isn't in a nice geometrical shape?

Measuring the Volume with

Water Displacement

When you add an object to a container with water, you increase the volume in that container. When the object is added, the water level will rise depending on the volume of the object. This "rise" in the water level can be measured to determine the volume of the object in question.

Beware the Meniscus!!!!

When you have liquid in a graduated cylinder, you will notice that the surface of the liquid forms a curve rather than a straight line. This curve is called the meniscus. You need to read the volume at the center of the meniscus

Mass and Volume are not the Same!

Sometimes, we assume a large object will be very heavy or we assume a small object will be extremely light. This is not the case however. It depends on the material that the object is made of . This leads us to our next concept, which is density.

Density describes how much mass is in a given volume of a material. Steel has high density but aluminum has a much lower density. This means that a brick of aluminum is easier to lift than a same sized brick of steel.

Density

Density describes how much mass is in an object. It is a ratio of an object's mass to its volume. The units for density will be g/mL. Remember, 1 mL is equal to 1cm, so the units can also be written as g/cm .

Sometimes, you need to calculate the density of a large object and will need to use kg/cm. To convert from g/cm to kg/cm , you simply need to multiply by 1,000.

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High density vs Low density

Material density is independent of shape

Density is a property of material that is independent of shape or quantity. A steel nail and a steel cube have different shapes and may have different masses, but the density for both objects will be the same.

Density of Liquids and Solids

The density of a liquid is usually a little less than the density of the same material in solid form. The density of a liquid is less because the atoms are not packed as tightly. This looser packing is why the density is lower and the liquid can flow. Water is an exception to this rule. The density of ice is actually less than the density of water. This is because of the way water freezes. When it freezes, the molecules form a pattern that has large, empty spaces.

Calculating Density

To find the density of a material, you must know its mass and volume for the sample. After that, you simply use the following equation.

Density = ______________

Mass

Volume

Mass = 78 grams

Volume = 10 cm

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Density = _______

78 g

10 cm

Density = 7.8 g/cm

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Graphing

Why do we use Graphs?

In this class, we have been learning how to measure and gather data. Having the data is great, but now what? If we want to share our data, how can we share it with others?

Graphs are a great way to visually represent data so that others can grasp it more easily.

The different types of Graphs

Bar Graph

Pie Chart

Scatterplot

Line Graph

Bar Graphs, Pie Charts, and

Line Graphs

A bar graph compares groups of information.

A pie chart shows how a whole is divided up into percentages.

A line graph is often used to show trends in data over time. This graph usually does not show cause and effect.

Scatterplot Graphs

A scatterplot graph is used to determine if two variables are related. For example, if we wanted to know if there was a relationship between the size of a shoe and how much it weighs, we could use a scatterplot to show this relationship.

Scatterplots show how a change in one variable (shoe size) influences another variable (shoe weight).

Indepedent and Dependent

Variables

The independent variable is the variable you believe might influence the other variable. This is the variable that is controlled during the experiment. It is sometimes called the manipulating variable.

The dependent variable is the variable that may be influenced by the independent variable, and can also be called the responding variable.

The X- and Y-axes

The vertical line on a graph is the Y-axis and the horizontal line is the X-axis. When creating a graph, the first thing one does is assign the X- and Y-axes.

The independent variable is always on the X-axis. The dependent is always on the Y-axis.

dependent variable

independent variable

What type of Relationship is it?

When you have your scatterplot graphed. You should be able to understand how the two variables are related.

Direct relationship- in this type of relationship, if the independent variable increases, the dependent will also increase and vice-versa. If you have a job that pays an hourly wage, the amount of hours worked and the amount of your paycheck is a good example of a direct relationship. If you work more hours, your check will be higher.

What type of Relationship is it?

What if the two variables seem to move opposite of one another?

Inverse relationship- In this relationship, the dependent variable will decrease when the independent variable increases and vice-versa. Consider the price of a sandwich for an example. If I continue to raise the price of the sandwich, what will happen to the number of sandwiches I sell?

Make a Scale

When talking about a graph, scale refers to the size of the intervals on the X- and Y-axes. You must first look at the range of your data (the smallest to the largest data) and decide a good interval that will display and separate your data so that the graph is visually appealing and not confusing.

Usually, you can try counting by ones, then twos, then fives, then tens. One of these will probably work, but you may need to use decimals if the data is quite small.

Value per box on graph = ___________________________

data range

number of boxes on axis

Plot Your Data

Once you have assigned your axes and you have created your scale, you are ready to plot your data on the graph.

First, find the x-value by moving left to right until you find the appropriate value on the x-axis. Once you reach that point, find the y-value by moving up the axis until you find the appropriate value for your data. The point where these two intersect is where you would plot that particular data.

After you have plotted your data, the last thing to do is give the graph a title/name and label the axis with the appropriate units. The title should be related to the graph and not something cute or funny.

Strong versus Weak relationship

If there are noticeable changes in the dependent variable when the independent variable changes, you probably have a strong relationship. If there seems to be no predictable effect, then the relationship is probably weak.

Using graphs to make Predictions

If everything has been set up correctly, you can actually use a graph to make a prediction about future data. Suppose you know the constant speed of a car, you can graph this data and make predictions about how far the car has traveled in the future.

Problem Solving

Life is full of problems and somebody has to solve them. The great problem solvers of the world do not stumble upon the solution or get lucky. They use methods or processes for solving their problems.

Examples of Problem Solvers

Doctors collect information about patients to figure out what is causing their pain or sickness.

Mechanics gather information about a car to figure out how to fix the engine.

To solve a problem, you use what you already know to figure out something you want to know.

A 4-step Process

1. What do you want to find?

2. What do you know?

3. Identify useful relationships

4. Solve the problem!

What do you want to find?

What is the problem asking for? Figure out what variables or values need to be in the answer.

What do you know?

What information are you given? Sometimes this includes numbers or values. Other times it includes descriptive information to interpret.

Identify some relationships.

What relationships exist between what you are asked to find and what you are given? Suppose you are given mass and volume and you are asked to find the density. Do you know a relationship that would help you?

Solve the problem!

How did he know!!

He has the spear!

Combine the relationships with what you know to find what you are asked for. Once you complete steps 1-3, you will be able to see how to solve most problems.

Lets solve a problem together!

A 6-gram marble, placed in a graduated cylinder of water, raises the water from 30 mL to 32 mL. Calculate the marble's volume and density.

Example: A caper in which the detective must solve the mystery of the missing Spear of Destiny!!!

The two types of problems

we will face.

A formula problem has a single answer. You apply what you know to the information you are given to solve the problem.

A design problem is more challenging (and more fun, too). You have to use what you know to design or create a solution that solves the problem. There are usually many different solutions and you are limited only by you creativity, ingenuity, skill, and patience. You are trying to make something that "gets the job done"

Examples of Design Solutions

Dr Ricketts' Hydrogen Car

Dr Ricketts converted this Toyota Tercel into a vehicle that ran on water instead of gas. He completed a trip from Knoxville to Memphis using this car. It averaged 45 miles per gallon. And its cost of fuel (water) was about $2.50 per gallon. His design may be something that is widely used in the future.

Solving Design Problems

1. Write down everything your solution needs to accomplish.

2. Write down every constraint that must also be met. These are limits on cost, size, time, materials, etc.

3. Think up an idea that might work. Talk with others, do research, and try things out.

4. Follow the design cycle.

The Design Cycle

Idea

Design

Prototype

Test

Analyze