Author: Maddie Van Beek

What’s heavier: A pound of feathers or a pound of rocks? This is is a trick question! A pound of anything is the same weight as a pound of anything else, but it would take WAY more feathers to make up a pound than a pound of rocks. This has to do with density. 



Density is determined by how tightly the atoms in an object are packed together. An object with very tightly packed atoms is denser than an object with atoms that have more room in between each other. Take a look at the image below. Which is denser, object A or object B?

Think back to the example. A rock is much more dense than a feather, so one pound of rocks takes up much less space than one pound of feathers.  

We have learned about density in some of our previous blogs, such as when you built a a liquid rainbow in a jar using liquids of different densities. Check it out to learn more! http://discoveryexpress.weebly.com/homeblog/rainbow-in-a-jar-learning-about-liquid-density

An object that is denser is also heavier than an object that is less dense. For example, stainless steel has a density of 7.8g/cm^3. Aluminum has a density of 2.7g/cm^3. Because steel has a higher density, it is heavier, more sturdy, and is used to build objects that need to last a long time, such as bridges or ships, while aluminum, a lighter, more flexible metal, is used more to make items such as cans or baking sheets. 

A similar example is muscle versus fat. Take a look at the image below. Which is denser, muscle or fat? 

You can see that 5 pounds of muscle takes up less space than 5 pounds of fat. 

So let’s get back to our question of the day: Do bowling balls sink or float? The answer seems obvious, doesn’t it? Clearly, heavy objects such as rocks should sink while lighter objects such as feathers would float, right? Well, it’s not as simple as it may seem. A bowling ball seems pretty heavy, but the determining factor of whether the ball (or any object, for that matter) will sink or float is its density. If an object is denser than water, it will sink. If an object is less dense than water, it will float. Water has a density of approximately 1g/cm^3. Just how do you figure out an object’s density? Let’s find out!

Now that you know a little bit about what density means, let’s try our activity! You are going to find out what density of bowling ball will sink and what will float. Your task is to find out the densities of each bowling ball using the following equations:


Circumference equation: 

circumference = 2 * π * radius


Volume equation:

volume = 4/3 * π * radius^3

(Remember, the symbol π is pi. Pi is approximately 3.14)



YOU WILL NEED:

• Two bowling balls (one lighter than 11 pounds and one heavier than 13 pounds)
• Tape measure
• Pencil
• Bath tub or large container filled with water
• A scale

Here’s what to do!

1. Fill the tub or container with water. 
2. Predict whether the bowling balls will sink or float. Why do you think this? 
3. Place the heavier bowling ball in the water. What happens? Is this what you thought would happen? 
4. Place the lighter bowling ball in the water. What happens? Does this surprise you? Why or why not? 
5. Now that you’ve observed what happens with each ball, you are going to actually determine their densities. 
6. Use a tape measure to find the circumference of your ball. To find the circumference, you need to wrap the tape measure all the way around the widest part of the ball. Make sure the tape measure is flat against the ball. Every ball should be right around 27 inches. Once you measure the ball, convert the inches to centimeters. 1 inch = 2.54 centimeters. 

For example, if your ball is 26 and 3/4 inches, then you would multiply 26.75 by 2.54. 



26.75 inches x 2.54 = 67.945 centimeters



7. After you find the circumference, solve for radius. 



67.945 = 2 x 3.14 x r

67.945 = 6.28 x r

67.945/6.28 = r

10.819 = r



The radius is 10.819cm. 



8. After you find the radius, you can solve for volume using the volume equation. 



volume = 4/3 * 3.14 * r^3

volume = 4/3 * 3.14 * 10.819^3

volume = 5301.878cm^3



Now you have the volume of the ball... IF the bowling ball were a perfect sphere, but it’s not. Bowling balls have finger holes, so you need to find the volume of the finger holes and then subtract the finger holes volumes from the volume you just found. 



9. Use the volume equation for cylinders below: 

volume = π * radius^2 * height

To complete this equation, you need to find the height and radius of the finger hole. Find the height by sticking a pencil eraser-first into the hole until it hits the bottom, marking the point on the pencil at the finger hole’s top, then measuring the pencil from the eraser to the point where you marked it. This is your height. Let’s say you found out the hole was 2.5cm deep. Plug the number into the equation. 



Volume = 3.14 * radius^2 * height

Volume = 3.14 * radius^2 * 2.5cm



10. Next you need to find the radius of the hole. The radius is half of the diameter (width of the hole). Remember to measure in centimeters! Let’s say you found out the diameter of the hole was 1.2cm. Because the diameter is 1.2cm, the radius would be 0.6cm. Plug the number into the appropriate spot in the equation. 



Volume = 3.14 * .6^2 * 2.5

Volume = 2.826cm^3 



11. There! You’ve now found the volume of a finger hole in the bowling ball. Check to see if the radius and height of each hole is the same. If they are all the same, you can just multiply the volume you found for the first hole by 3. If they are different, find the volume of the other two holes and then add them together to find the total volume for the three holes. For simplicity’s sake, let’s say that all three holes were the same and multiply our first number by 3.



Volume of three holes combined = 8.478cm^3



Now that you have the volume of the finger holes, subtract this number from the volume of the ball that you found earlier. 



Volume of bowling ball - volume of finger holes = True volume


5301.878cm^3 - 8.478cm^3 = 5,293.4cm^3


True volume of the bowling ball = 5,293.4cm^3



12. Now you FINALLY have the volume of the bowling ball! BUT you still don’t have the density. To find the density, you need to weigh the ball. Remember to use a scale that measures in grams. If you don’t have one, 1 pound = 453.6 grams. 



If your ball is 13 pounds, then you would multiply 13 by 453.6. 

13lbs * 453.6 = 5,896.8g



13. Now that you have the weight, divide it by the volume of the ball in cubic centimeters to discover the density. 



Weight of bowling ball / True volume of bowling ball = density



5,896.8g / 5,293.4cm^3 = 1.114g/cm 

The density of your bowling ball is 1.114g/cm. 



There you go! You now know how to find the densities of the two bowling balls. Do your results match up with what you predicted earlier? You should have found that the ball that floated had a density of less than 1g/cm while the ball that sank had a density of more than 1g/cm. 




References

http://scifun.chem.wisc.edu/homeexpts/bowling.htm


http://the-science-mom.com/875/density-a-simple-explanation/


http://classroom.synonym.com/explain-density-16387.html


http://www.middleschoolchemistry.com/lessonplans/chapter3/lesson1


http://www.brighthubeducation.com/science-homework-help/52127-what-is-density/

Author: Maddie Van Beek


I’m guessing that at this point, all of you have heard of the dreaded ebola virus. Just in the past few months, US citizens have been more concerned than ever about this horrific disease. In this blog, you will learn a little bit about the background of the ebola virus, as well as how diseases spread. 

Ebola’s History and Mortality Rate

• First identified in 1976 in Congo near Ebola river. 
• Then: 90% mortality 
• Now: 50% mortality 

How did ebola evolve to affect humans?

2014 Ebola Outbreak: Largest in HISTORY

• Ebola is now spreading in West Africa and concentrated in Guinea, Sierra Leone, and Liberia. 
• The number of cases that have occurred during this outbreak have been more than the combined number of cases occurring previous to 2014 combined. 

# of ebola cases 1976-2013 < # of ebola cases in 2014

How does ebola spread? 

As you saw in the video, ebola spreads first from animal to human and then from human to human. Fruit bats, monkeys, gorillas and other primates become infected with ebola and become carriers. People may become infected with ebola by eating uncooked infected meat or coming in contact with infected animals. Once people are infected, they can infect other people by coming in contact with each other’s bodily fluids. 

How is ebola contracted?

Ebola in the US

Although ebola has stayed out of the US in the past, it has recently made its way in, starting with a Texas man who was diagnosed on September 30th, 2014 and passed away on October 8th. The man had traveled from Liberia to Texas, so he was infected in Liberia before coming to the US. Since then, three others have been reported to have ebola. Two of these people who have contracted ebola have been health care workers from the Dallas, Texas, hospital where the first ebola patient was treated, and the third was a New York City doctor who had traveled to Guinea. Both Dallas patients have recovered and the New York City patient is currently being treated. 

Why would health care providers be the ones to get ebola? Shouldn’t they knew the best way to stay healthy?

Health care providers are at a higher risk, since they are treating those who have ebola. Although ebola can only be spread through bodily fluids, treating someone who is vomiting could lead to infiltration of the disease through touching the infected person’s bodily fluids and then touching broken skin or mucus membranes such as the eyes. Health care providers treating patients with ebola have a much higher risk than the average US citizen, since they are in direct contact with the disease. 

Do we need to worry about ebola spreading in the US?

No! The reason ebola spreads so quickly and causes so many deaths in other countries is because they do not have adequate healthcare available to them. In the US, health care providers are not concerned about ebola spreading; as stated, ebola is difficult to contract in its present form and is easily stoppable when the right procedures are followed. 

In order to help control the spread of diseases, teams of healthcare professionals work together to quarantine infected people, immunize people at risk, educate the public about prevention strategies, and treat infected people swiftly and aggressively. 

Currently, there is no safe ebola vaccine. 

Do I need to worry about getting ebola?

Although ebola is very dangerous, you most likely have no need to worry. It’s very difficult to actually get ebola, since you have to come in contact with an infected person’s bodily fluids and then get those bodily fluids in a mucus membrane such as your mouth, eyes, nose, etc. Ebola does NOT spread like a cold--you can’t get ebola from a sneeze or a cough--it’s not an airborne disease. Just like any other virus or disease, you can avoid ebola and help keep it from spreading by washing your hands, not sharing drinks, chapstick, etc., staying home if you are sick, and going to the doctor if you have symptoms. 

And remember, only ebola victims with symptoms are infectious--the disease does not spread until the infected person is already showing symptoms. 

The incubation period for ebola is 2-21 days. This means it may take 2-21 days to show symptoms of ebola. Therefore, if you come in contact with the disease, you should be on watch for about three weeks.

Quick look at ebola vs. the flu:

How do diseases spread, anyway? 
Simulation of how diseases spread: 

This activity is NOT an accurate simulation of ebola--yes, ebola spreads in a similar manner, but with adequate health care and preventative strategies, ebola can be kept from spreading in a manner similar to the simulation. This simulation is just to help you understand how unchecked infectious diseases may spread from person to person. 

YOU WILL NEED: 

Lemon juice

Clear cups

Water

Paper

Writing utensils

A light source

Red and blue food coloring

Water droppers

An iron, and a heat-proof surface to use it on

YOU WILL DO: 

1. Get a group of twenty or so students together.
2. Fill nineteen cups with water and one cup with lemon juice.
3. Hand out the cups, paper, and water droppers to each participant, and don’t announce who has the lemon juice.
4. Explain that there will be six one-minute rounds in this simulation. 
5. You may be wondering what lemon juice could have to do with infectious diseases. Lemon juice can actually be used as “invisible ink,” so the lemon juice represents the invisible infectious disease. One person has lemon juice in their cup, while others only have water. All participants should have a piece of paper with them for round one. 
6. Round 1: Give participants 60 seconds to move around the room; whenever they come in contact with each other, they should take a drop of water from the other’s cup and dot it on their piece of paper. This represents coming in contact with others’ body fluids. 
7. After the 60 seconds is up, use the iron on its hottest setting, and iron everyone’s papers. The heat from the iron will cause the lemon juice to turn brown. Those that came in contact with the lemon juice will have a brownish spot on their paper, while others will just have water spots. Those with the brown spot represent people who have been infected with the disease. Record the number of people who were infected.

Ok, so is this demonstration completely accurate? No! There was only one person spreading the disease. Let’s try something new!


8. Once again, all participants get a cup of water. This time, give one person a red dye dropper. Just like the lemon juice, the red dye represents the disease. Participants get 60 seconds to rotate around the room. The person with the red dye will put a drop of red dye in the cup of each student he or she comes in contact with. Those who receive a red drop will then also become disease carriers (equipped with red dye).  They will continue to spread the disease by putting a drop of red dye into the cup of each person they encounter. 


9. After 60 seconds, analyze how many people have pinkish-colored water--that’s how many now have the virus! 

10. Create two graphs for round 1 and round 2 to demonstrate how many people became “infected” in each round. The Y-axis should be number of people, and X-axis should be time. How do they look different? Which round had more infected people? Which round more accurately demonstrates how quickly a virus can spread? 

You should end up with something like this: 

11. This time, you are going to inoculate 20% of your group. Inoculate means to treat with a vaccine to provide immunity against a disease. Start by putting a few drops of blue food coloring into 20% of the cups. If you have twenty people, four people will get cups with blue water. Repeat step 8. 

12. You could now have some people with red water (people infected with the disease), blue water (inoculated people who did not come in contact with the disease) or purple water (inoculated people who came in contact with the disease). Because inoculated people were protected from the virus, they do not count towards the infected number of people. Before moving on to round 4, record the number of infected students. 

13. Round 4: This time, start by inoculating 40% of the class. If you have twenty people, eight should now start with blue water. Repeat step 8. Record the number of infected students. 

14. Round 5: Start by inoculating 60% of the class. Repeat step 8. Record the number of infected students. 


15. Round 6: Start by inoculating 80% of the class. Repeat step 8. Record the number of infected students. 


16. Make a bar graph for rounds 2-6 and see how inoculation affects the spread of the disease. 

You should end up with something like this:

17. Reflect on this activity. What was not realistic about this simulation? What preventative measures could people take in real life to avoid infection? 

References

• http://www.who.int/mediacentre/factsheets/fs103/en/
• http://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/qa.html
• http://www.pbs.org/wgbh/nova/education/activities/3318_02_nsn.html
• http://www.seplessons.org/node/226
• http://youtu.be/qkzIGp1uYoc
• http://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/index.html

Sound is everywhere.  Music, birds singing, cars and people on the street, nearly everything around us makes some sound.   But what is sound really and how is it created?

Sound is created by moving or vibrating objects.  This vibration pushes and pulls on the air molecules close to the object, which then push and pull on the molecules next to them, which push and pull on the air molecules next to them, getting further and further from the object.  This phenomenon is called a longitudinal wave (a.k.a. compression wave).  A good way to visualize this is using a slinky: if you hold a slinky in mid air or lay it out on a table, and tap one end, the first coil of the slinky will push and pull on the second coil, which will push and pull on the third coil, and so on.  This causes a wave that moves all the way through the slinky, even though the slinky itself does not move. 

Here is a YouTube video showing the slinky demonstration, taken and uploaded by Trevor Murphy.  Thanks to Mr. Murphy for sharing this excellent demonstration!

When objects vibrate, they tend to do so at a certain frequency; that is, they move back and forth—or oscillate—at a certain speed.  This pushes and pulls on the air at a particular speed, causing the wave generated to have a certain sound.  This is how a tuning fork works.  A tuning fork is a two pronged, U-shaped fork that vibrates with a certain frequency (and therefore a certain sound) when struck.  They produce a very consistent sound corresponding to a certain note, and thus are used by piano tuners to make sure the instrument is producing the right notes. 

Just like a tuning fork, U-shaped glasses made of thin glass also tend to vibrate at a certain frequency, depending on whether they contain any liquid.  A wine glass is an excellent example; tap a wine glass gently with your finger, and it will usually produce a ringing sound.  This is caused by the vibration of the glass, and corresponds to a certain note just like the tuning fork.  In fact, if you play this note at the wine glass loudly enough, the glass will vibrate so hard it will shatter!  Here is another YouTube video demonstrating this phenomenon, which we don’t recommend you try at home! 

Thanks to Harvard Natural Sciences Lecture Demonstrations for producing and uploading this video!

While you shouldn’t try to shatter glass at home, there is another way you can experience the vibration of a wine glass using your finger and a little water.  This will cause the glass to oscillate at a particular frequency, creating a certain note. 

TRY IT!!

Here’s what you’ll need:

1.       A stemmed wine glass, the thinner the glass is the better.

2.       A small amount of water (just enough to get your fingers wet)

Here’s what you need to do:

1.       Set the wine glass on a flat surface.  Hold the very bottom of the stem to keep the glass still.

2.       Wet your fingers well.  This allows your fingers to glide along the rim of the glass easily.

3.       Slowly start running your fingers around the rim of the glass, using the part of your finger between the tip and the second knuckle.

You may have to practice a little before the wine glass begins to make sound.  Keep trying!

CHALLENGE YOURSELF!

How many notes can you make with your wine glasses?  If you add water to the glasses, they will create a different note when you run your finger over the rim, depending on how much water you add.  See if you can create a whole scale or play a song!  With a lot of practice, you will eventually be able to play like Robert Tiso, who in the video below plays Dance of the Sugar Plum Fairy by Tchaikovsky using only glasses and water!  Thanks to Robert Tiso for sharing this amazing video—ENJOY!

Have you ever bumped your head or twisted your ankle, and had a nurse put a cold pack on your injury?  You may have noticed he or she did not take the pack out of the freezer—the pack had no ice in it...yet it was still cold!  Or, have you ever been outside on a cold day and used gel hot packs to keep your hands warm?  You may remember breaking a small disk inside the gel, and feeling it get hot to the touch.  Both the cold packs and the hot packs use chemistry to change their temperature! 

When chemical reactions or processes occur, there is always an exchange of energy.  Some of these reactions or processes give off energy as heat; these are called exothermic (‘exo’ meaning outside, ‘thermic’ meaning heat).  Other reactions and processes absorb energy, making the surroundings cooler; these are called endothermic (‘endo’ meaning inside). 

But why are some reactions exothermic while others are endothermic?  Can we predict if a reaction will give off or absorb heat?  As it turns out, we can! 

Chemical Reactions
First, we need to briefly discuss chemical reactions.  A chemical reaction is when one or more chemical compounds are changed into one or more different compounds.  In any chemical reaction, some bonds need to be broken, and others need to be formed—this is how the reaction produces new compounds.  If we know how much energy is required to break the bonds in the reactants (the compounds present before the reaction takes place), and we know how much energy is released on formation of the bonds in the products (the compounds present after the reaction takes place), we can compare them to see how much energy will be produced or consumed by the reaction.  Fortunately for us, there are tables we can use to figure out the energy of the reactants and products. These are called bond energy tables, similar to the one below (1). 

If the formation of the products releases more energy than it took to break the bonds in the reactants, the reaction must give off some of this energy as heat, and so is exothermic.  However, if the formation of the products releases less energy than it took to break the bonds in the reactants, the reaction must take in heat energy from the surroundings, making the reaction endothermic. 

Chemical Processes
The same is true for chemical processes.  A chemical process is what happens when there is a change in the state of one or more chemical compounds (like changing from a liquid to a gas, or dissolving in water), but there is no formation of a new compound.  If we know how much energy the compounds have before they undergo the process (such as melting, or dissolving in water), and how much energy they have after this process, we can discover if the process is endothermic or exothermic.  For example, if we have an ice cube sitting at room temperature, we know the ice cube will begin to melt.  The warmth of the room is melting the ice because the water molecules are absorbing the thermal energy from the air in the room, and this energy is making the molecules move faster and farther away from each other, bringing them from a solid state (ice) to a liquid state (water).  Because this process absorbs energy, it is endothermic.

However, if we put the ice cube back in the freezer, the liquid water will begin to turn back into solid ice.  In this freezing process, the water molecules are giving up thermal energy to their surroundings in the freezer, and are thus losing energy to change states.  This is therefore an exothermic process. 

One type of chemical process that can be either exothermic or endothermic is dissolving of salts in water.  A salt is a compound made up of positively charged ions and negatively charged ions which are held together in a solid state because the positive and negative charges attract one another.  The salt we put on our food is referred to as “table salt”, and is a salt compound made up of sodium ions (Na+) and chloride ions (Cl-). 

If we put salt in water and it fully dissolves (that is, the ions all become evenly dispersed within the water), two exchanges of energy need to happen:

1.       Energy is added to the solution to pull the ions away from each other:  in order to pull the positively and negatively charged ions apart, energy must be added.  This energy needed to pull the ions apart is called the Lattice Energy.

2.       Energy is released into solution when the water molecules surround the ions: as the water molecules are attracted to and surround the ions, energy is released into the solution. This energy released as water molecules surround the ions is called the Hydration Energy.

Whether the dissolving of a salt is exothermic or endothermic depends on which is greater, the Lattice Energy, or the Hydration Energy.  These are usually expressed in units describing the amount of energy released per set amount of salt, such as kilocalories per mole (kcal/mol) or kilojoules per mole (kJ/mol).  We can usually look up the values of the Lattice and Hydration Energy values for a particular salt in tables, such as the one below (2).

For example, if we dissolve table salt in water the Lattice Energy is 779 kJ/mol, and the Hydration Energy is 774 kJ/mol (1).  If we subtract the Hydration Energy from the Lattice Energy, we get a change of +5 kJ/mol:

779 kJ/mol – 774 kJ/mol = +5 kJ/mol

It takes just slightly more energy to separate the ions from one another than is released from the water molecules surrounding the ions.  This means just slightly more energy must be put into the solution than is released back into the solution; therefore dissolving table salt in water is endothermic. 

However, if we dissolve sodium hydroxide (NaOH) in water, it separates into Na+ and OH- ions.  The Lattice Energy for this process is 737 kJ/mol, and the Hydration Energy is 779 kJ/mol.  Subtracting as before, we get a change of -42 kJ/mol.

737 kJ/mol – 779 kJ/mol = -42 kJ/mol

More energy is released into the solution than is required to pull apart the ions; therefore dissolving sodium hydroxide in water is exothermic.  If you dissolve sodium hydroxide in a small amount of water, be careful—the container may get hot enough to burn your hand!

TRY THIS!!

Here’s what you’ll need:

1.       Two small jars or drinking glasses

2.       Two teaspoons

3.       Two cups of distilled water

4.       One half-cup of magnesium sulfate (MgSO4).  You can purchase this online (click here for options).

5.       One half-cup of ammonium chloride (NH4Cl).  You can purchase this online (click here for options).

6.       One thermometer that will measure temperatures from 70-150°F

7.       Safety goggles, one pair for each person participating

8.       Latex or nitrile gloves (you can get these in grocery or hardware stores)

Here’s what you need to do:

NOTE:  Be very careful with the magnesium sulfate and ammonium chloride—they can cause irritation to the skin, lungs and eyes.  Do not breathe them in or get them in your eyes!  You should do this procedure in a well ventilated area, and wear the goggles and gloves to make sure your eyes and skin are protected.

1.       Put on your goggles and gloves!

2.       Pour one cup of distilled water into each of the small jars.

3.       Measure and record the temperature of the water in each jar.

4.       Pour one half cup of the magnesium sulfate into one of the jars.  Stir carefully with a spoon for 20 seconds (don’t worry if not all the magnesium sulfate dissolves).  Measure and record the temperature of the solution.

5.       Pour one half cup of the ammonium chloride into one of the jars.  Stir carefully with a spoon for 20 seconds (don’t worry if not all the magnesium sulfate dissolves).  Measure and record the temperature of the solution.

Did the temperature of the water change each time?  How much did it change?  Did it get hotter or colder?  Are these processes endothermic or exothermic?  Did you observe anything else?  BE SURE TO WRITE EVERYTHING DOWN IN YOUR JOURNAL!


References:

(1)    “Bond Enthalpy/Bond Energy”.  Mr. Kent’s Chemistry Page.  www.kentchemistry.com Accessed 8/28/14.

(2)    “Chapter 13: Solutions”. intro.chem.okstate.edu. Accessed 8/29/14.

We hear the word “normal” all the time, referring to everything from our homes to our health.  We use the word carelessly, loosely referring to anything that seems the same as any other, such as a “normal” house, on a “normal” street, in a “normal” town.  It seems to imply that they are very much like most others...in other words they are very average.  In fact, that is what the word normal means, but there’s a little bit more to it.

In mathematics—or more specifically, statistics—the word normal refers to a type of probability distribution: a way to calculate the chances that a specific event will occur using mathematical equations (click here for more information about probability).  It also describes the way these events look on a graph.  Here is a simple example:  imagine a 10 mile stretch of a very busy road.  All 10 miles of road was constructed at the same time and is therefore the same age, and gets the same wear.  The engineers who built this road know that at some point in the next year, the road will develop a crack. 

For our purposes, we assume that the probability of the crack forming is the same at any point in the road.  Let’s look at what this looks like if we turn this information into a graph, with the probability of a crack forming on the vertical axis and miles on the horizontal axis:

We can see this graph is just a horizontal line, representing the equal probability of the crack forming at any point along the 10 mile stretch of road.  Because the probability is uniform across the whole range of possible values—that is, along the whole stretch of road that we are considering—we call this a uniform distribution. 

The normal distribution is also a probability distribution, but in this case not all of the possible outcomes have equal probability.  In the normal distribution, there is one outcome value which is the average of all the possible values, and this value has the highest probability.  All values higher and lower than this value have lower and lower probabilities the farther they are from the average.  For example, think about the height of men in the United States.  McDowell reports that the average height for men over 20 years old in the US is 5 feet, 9.5 inches (1).  However, we know there are men that are shorter and men that are taller: currently the tallest man in the world is 8 feet, 3 inches tall (2); the shortest man in the world is only 1 foot, 9.5 inches tall (3)!  The probability of anyone being this tall (or this short) is very, very low.  If we could measure the height of 1000 men from all over the US, and we could plot this information on a graph with number of men on the vertical axis and height measured (in feet) on the horizontal axis, it would look like this:

The peak of this curve occurs at a mean (that is, at an average) of 5.79 feet which is 5 feet, 9.5 inches—the average height for men over 20 years old in the US.  This means men from our sample have a high probability of being around this height.  As the heights get taller or shorter, the probability of finding a man in our sample of this height goes down.  This makes the curve look like a bell, which is why it is often called the “bell curve”. So when we say something is “normal”, it really does mean that it has a high probability of being similar to the average!

TRY THIS!

Here’s what you’ll need:

1)      A pen or pencil

2)      A piece of paper

3)      A computer with a spreadsheet program installed, such as Microsoft Excel®

4)      At least 30 individuals of around the same age (50 is even better).  If you are in school now, you can use your classmates!

5)      A tape measure at least 10 feet long.

Here’s what you need to do:

1)       Make a table on your piece of paper with height (in feet) in one column, and number of individuals in another.  In the height column, write numbers ranging from 3-7 in increments of 0.5, as in the following example:

2)      Ask each of the individuals of about the same age how tall they are.  If they are not sure, measure them with the tape measure!

3)      As each individual tells you their height, make a mark in the other column across from the height range they fall into.  Here is some example data:

4)      When you are finished, open your spreadsheet program and make one column with your numbers for how many people were in each height range.

5)      Use these numbers to make a column chart.  In Excel, you can do this by selecting the data you wish to graph, and selecting the insert tab.  Select the column chart under the ‘chart’ options, and choose the type on the top left corner. 

When we use our sample numbers, this is what our graph looks like:

Notice it looks a lot like the graph of the normal distribution we saw earlier. 

What does your chart look like?  If you connect the tops of all the columns, what shape does it look like?  Is the highest point roughly in the middle?  Print out this graph and save it with your notes!

CHALLENGE YOURSELF!

What else do you think might have a normal distribution?  Try measuring the weight of each nail in a box, or count the number of seeds in a bunch of identical seed packages.  Be sure to use at least 30 nails or seed packages, or more if you can; the more you use for your testing (that is, the larger your sample size) the better you will be able to see the probability distribution.  Be sure you keep track of you numbers the same way as before, and use a spreadsheet program to graph all the numbers (weight or number of seeds on the horizontal axis, and number of observations within a certain range on the vertical axis).  This way you can get an idea of what the probability distribution might look like. 

References:

1)      McDowell, Margaret A. et al. (October 22, 2008). "Anthropometric Reference Data for Children and Adults: United States, 2003–2006". National Health Statistics Reports, 10.

2)      “World’s Tallest Man—Living”. Guinness Book of World Records .  Accessed 8/21/14.  Last updated 2/8/2011.

3)      Sheridan, Michael. (February 26, 2012).  “Chandra Bahadur Dangi is world’s shortest living man: Guinness World Records.”  New York Daily News.  www.nydailynews.com.

“I remember it like it was yesterday,” you’ll hear people say.  You probably have your own memories too, like what you ate for breakfast, or what you did on your last birthday.  Our memories are very important; they help us learn at school, recognize our friends and family, and even find our way around.  But just what are memories, and how do we get them?

Memory is one of the things our brains do for us: they take information from all around us and store it so we can retrieve it (get it back) at a later time.  The part of the brain mostly responsible for our memory is called the hippocampus, a seahorse-shaped ridge of tissue buried in the middle-lower part of the brain (it would be near the base of your skull, behind your eyes).  People who have damage in this part of the brain cannot form new memories, so despite its being pretty small, it’s very important!

So how good is your memory?  Well, let’s find out!  Go get a piece of paper, a pencil, and a stopwatch.  Take a look at the objects below for 30 seconds (be sure to use a stopwatch or a clock with a second hand so you only get 30 seconds)!  Try to memorize all the different objects you see here.  When 30 seconds is up, scroll down so you can’t see the pictures anymore, and write down all the items you can remember.   Don't cheat by looking at the pictures!!

Now from the list below circle the two items that were in the picture.

1.      Eggs

2.      Slide

3.      Coat

4.      Hat

5.      Guitar

6.      Shoes

7.      Books

8.      Banana

9.      Bell

10.    Radio

Did you list books as being in the picture?  Take a look at the picture again; books are not one of the objects (the two that were in the picture were the slide and the guitar)! 

How did that happen?  All of the items in the picture are things you see at school, so your memory categorized the picture as being of things you see at school.  So when you saw the word books, your memory decided that is also something you must see at school, and so it must have been among the items in the picture.  This is called a false memory, and it happens when our memories cause us to believe we saw or experienced something that did not really occur.   (Don’t worry, false memories like these are not dangerous, and are not a sign of any problems with your memory!)

TEST YOUR FRIENDS WITH A FEW MEMORY CHALLENGES!

Challenge #1: Memory Test

Here’s what you’ll need:

1.      A lunch tray, or a small table

2.      A towel or a sheet

3.      Paper and pens for all your friends

4.      A stopwatch, timer, or a clock with a second hand

5.      15-20 different items

 


Here’s what to do:

1.      Place all the items you selected on the tray or table, and cover them with the towel.

2.      Invite your friends to stand around the table, and uncover the items.  Allow 30 seconds to look at the objects and try to memorize them.

3.      After 30 seconds, cover the objects again and hand out pens and paper.

4.      Ask everyone to write down the objects they remember.

After everyone has finished, allow your friends to look at the items again. 

Were there any items that all your friends remembered?  Were there any that nobody remembered?  Write down items that were either easy or hard to remember.

Challenge #2: False Memory Test

Here’s what you’ll need:

1.      Pens and paper for all your friends

2.      A timer or stopwatch

3.      The lists of words below*

List 1*: read, pages, letters, school, study, reading, stories, sheets, cover, pen, pencil, magazine, paper, words

List 2*: house, pencil, apple, shoe, book, flag, rock, train, ocean, hill, music, water, glass, school

Here’s what to do:

1.      Read List 1 aloud to your friends.

2.      Wait 5 minutes.  Be sure to set a timer!

3.      Pass out paper and pens.

4.      Ask them to listen to the next list, and write down which words they remember from List 1.

5.      Read List 2 aloud.  Allow everyone to write down the words they believe they heard on List 1.

6.      Read List 1 aloud again. 

How many people thought “book” was on List 1? 

This is a false memory (only “pencil” and “school” were on List 1)!  Be sure to let them know false memories aren’t dangerous!

MAKE UP YOUR OWN MEMORY TESTS!

·         Try having your friends walk around a room for 30 seconds.  Then have them leave the room, and you make some change, like remove something or turn something upside-down.  Let them re-enter the room and see how many people notice the change.

·         Make up your own lists of words like the ones you used for Challenge #2, or groups of pictures like those on pages 2 and 4.  See if you can create a false memory!

REMEMBER:  Always be sure to write down all your observations!

*These lists were created by Eric H. Chudler, PhD.  For more memory tests created by Dr. Chudler, please visit Neuroscience For Kids at https://faculty.washington.edu/chudler/chmemory.html

“Nature abhors a vacuum!” you’ve heard people say.  In fact, your grandparents probably heard people say this too, and their grandparents before them...it’s been said for over 100 years!  But what does this really mean? 

First, to ‘abhor’ something is to dislike it very much, so nature does not like vacuums!  Second, the type of vacuum we are talking about is not just the kind you find in your house for cleaning floors.  When we speak of a vacuum in this way, we are talking about a space devoid of all matter.  That means the vacuum is a space where there is literally no (or almost no) atoms—not even air!  (Remember, air is made up of molecules of oxygen, nitrogen, carbon dioxide and others.  In a vacuum, there are none of these molecules either, so there is no air.)

It is almost impossible to remove ALL matter from any area, even in outer space, which is as close to a true vacuum as can be, having an average of only a few atoms per cubic meter, according to Takadoro in a 1968 paper in the Publications of the Astronomical Society of Japan.  On Earth producing a vacuum is even more difficult, with the best vacuum chambers achieving about 100 particles per cubic centimeter, according to Gabrielse in a 1990 paper published in Physical Review Letters.  Compare this to air at atmospheric pressure, which contains 3.369 X 1025 molecules per cubic meter (that’s essentially a 3 with 26 zeros behind it)!

Why is it so difficult to produce a vacuum?  Because matter likes to keep itself evenly spread out; so if a space with less matter is created, the matter in the surrounding areas wants to rush in and fill that space.  This is how your vacuum cleaner works:  there is a fan inside that creates a mild vacuum (enough to reduce the air pressure by about 20% according to Jeff Campbell in Speed Cleaning), which causes the dirt and dust to get sucked into the vacuum cleaner to replace the air particles removed by the fan.  (For more detailed information on how vacuum cleaners work, visit howstuffworks.com/vacuum-cleaner)

Although it is quite difficult to make a very strong vacuum, with only a few hundred molecules per cubic centimeter, it is not so difficult to make a partial vacuum.  While there is still a lot of matter left in a partial vacuum, the reduction in matter is enough to create some pretty interesting effects.

For instance, if we take an empty plastic water bottle and leave it in the sun with its cap off, the air inside the bottle will heat up.  This means the air molecules will be further apart, and some will leave the bottle.  If we then put the cap back on the bottle, and put the bottle in the freezer for five minutes, the air will cool down and the molecules will move closer together.  This forms a partial vacuum, because there will be fewer molecules per cubic centimeter in the bottle than on the outside of the bottle (remember, some of them left the bottle when it heated up in the sun).  Because of this partial vacuum, the sides of the bottle will cave in! 

Go ahead and try this!  Just remember to put the cap back on the bottle before putting it in the freezer!

We can also use partial vacuums like this to do an age-old trick—pulling a hard-boiled egg into a bottle!

TRY IT!!

Here’s what you’ll need:

1.       A hard-boiled egg, peeled (extra large eggs work well).

2.       A glass bottle with a mouth just a little narrower than the egg.  A 1 liter Erlenmeyer flask works very well.

3.       Strips of paper, about 6 inches long by 1 inch wide.

4.       Matches or a lighter

Here’s what to do:

1.       Carefully set one of the pieces of paper on fire, and drop it into your Erlenmeyer flask.

2.       Allow about three seconds to pass—count to three slowly.

3.       Place the egg on the mouth of the flask, narrow end down.  The egg may jump around a little.  This is because hot gasses are still escaping from the flask. 

4.       You should see the flame on the paper go out; then watch as the egg is pulled into the bottle!

Why does this happen?  It happens for the same reason that the water bottle’s sides cave in when put in the freezer.  The flame heats up the air in the flask, allowing some of the molecules to escape (making the egg jump around on top of the flask at first).  When the flame goes out the air starts to cool, and the air molecules get closer together, forming a partial vacuum.  This partial vacuum pulls the egg into the bottle!


So, what else could you try this with?  How about balloons?  Jell-O?  Get creative!  But always be sure to write down everything you do, and all your observations!

References for further reading:

Tadokoro, M. (1968). "A Study of the Local Group by Use of the Virial Theorem". Publications of the Astronomical Society of Japan 20: 230.

Gabrielse, G., et al. (1990). "Thousandfold Improvement in Measured Antiproton Mass". Phys. Rev. Lett. 65 (11): 1317.

Campbell, Jeff (2005). Speed cleaning. p. 97.

This week’s blog is for high schoolers (or anyone else taking a chemistry class)!  If you are in a chemistry class, or have ever taken a chemistry class, you know it’s important to understand how to balance a chemical equation.  A chemical equation is how we can describe the reaction between two atoms or molecules in a concise way (for more information on chemical reactions, click here).  On the left side of a chemical equation are the reactants, or the substances we start with before the reaction.  On the right side of the equation are the products, the substances that are created in the reaction.  For instance, the reaction between hydrogen and oxygen to create water would be written like this:

We would read this equation as “hydrogen reacts with oxygen to produce water”.  You will also notice in this equation that there is a number two in front of the hydrogen, and a number two in front of the water (H2O).  These numbers are called coefficients, and they are there to show us that for this reaction to take place, two molecules of H2 must react with one molecule of O2 to form two molecules of water. 

You may ask, “Why should we need these coefficients?  Why not just write it out as simply as possible?”   Well, if we write out what really happens in the reaction, our equation would look like this:

Yes, this is very simple, but there is a problem with it.  Hydrogen and oxygen (as well as nitrogen and halogens like chlorine and fluorine) don’t appear as single atoms in nature, they appear as molecules with two atoms each. 

In order to understand what is really happening during the reaction, we must write our reactants as they really appear.  This means writing their formulas as H2 and O2 (because one molecule has two atoms of hydrogen or two atoms of oxygen).  Now if we try to write our chemical formula using these correct molecular formulas, we end up with this:

But now we have another problem...now the equation does not balance. 

What we mean by this is that the number and type of atoms from the reactants on the left side of the equation do not match the products on the right side.  We know that in the real world this cannot be the case, because the law of conservation of mass states that atoms are neither created nor destroyed in any chemical reaction. 

Take a look at our last equation again.  On the left there are two hydrogen atoms and on the right there are two oxygen atoms.  On the right there are two hydrogen atoms (this is good), but only one oxygen atom.  This implies that one of the oxygen atoms just disappeared, and we know this cannot be!  This means the equation is unbalanced.  To fix this, we need to add our coefficients.  Let’s start out by bringing back the missing oxygen atom.  We do this by putting the coefficient 2 in front of water.  This means now there are two molecules of water, each of which has one oxygen atom, for a total of two oxygen atoms.

But now on the right side there are four hydrogen atoms:  each molecule of water has two hydrogen atoms, and there are two molecules, for a total of four hydrogen atoms.  We can fix this by putting the coefficient 2 in front of the hydrogen on the left side, giving us a total of four hydrogen atoms on the left side also.

Now our equation is balanced! 

Let’s try another synthesis reaction—the reaction between nitrogen and hydrogen to form ammonia:

Let’s start by balancing the nitrogen.  There are two nitrogen atoms on the left, and one on the right.  We can make these balance by adding the coefficient 2 in front of the ammonia on the right side:

Now the hydrogen must be balanced; there are two hydrogen atoms on the left, and six on the right.  We can make this balance by adding the coefficient 3 in front of the hydrogen on the left side:

This equation is now balanced!

Now let’s try another, more challenging reaction, such as the displacement reaction between aluminum and hydrochloric acid (remember, a displacement reaction happens when atoms of one element displace the atoms of another element in a molecule).  In this reaction, aluminum displaces hydrogen as the bonding partner with chloride:

Clearly this equation is not balanced.  There is one aluminum atom on each side, so this is OK so far.  There is only one hydrogen atom on the left but there are two on the right, and there is only one chloride atom on the left and there are three on the right.  We need to find a way to balance the hydrogen and chloride atoms. 

First, let’s look at the chloride atoms, since this is the largest imbalance between the two sides.  To fix this imbalance, we would need to put a coefficient 3 in front of the hydrochloric acid:

Now, look at the hydrogen atoms.  There are now three on the left and two on the right.  To make this balance we need to find the least common multiple of two and three, which is 6.  This means we need 6 hydrogen atoms on either side of the equation.  This is how our coefficients will look:

Our aluminum is still OK, but now we need to look at the chloride again.  We have six atoms of chloride on the left side, and three on the right.  We can fix this by adding the coefficient 2 in front of the aluminum chloride molecule:

Now our hydrogen atoms balance, and our chloride atoms balance, but our aluminum atoms don’t!  Finally, these also need to balance, so we need two on the left side; we simply add the coefficient 2 in front of the aluminum atoms on the left:

Now all atoms in the equation balance.  This equation required a little more jostling back-and-forth, but don’t let that worry you!  Just keep going back and forth until all the atoms balance, starting with the atoms that are the most imbalanced, and working toward the ones that are the least imbalanced.  This is a little like hitting a baseball, or riding a bike—it takes a little practice to get really good at it!

Let’s try one more, the combustion of propane in oxygen from the air:

Because the oxygen appears in both of the products of the reaction, I’m going to leave oxygen for last.  The greatest imbalance is for hydrogen, with eight atoms on the left, and two on the right.  To make the hydrogen balance, we need to insert the coefficient 4 in front of the water:

Next let’s look at the carbon atoms.  There are three on the left and one on the right, so we need to add the coefficient three in front of the carbon dioxide:

The hydrogen and carbon atoms now balance, what about oxygen?  There are ten oxygen atoms on the right side, so we must add the coefficient 5 in front of the oxygen.

Now all atoms balance on both sides of the equation.

NOTE:  The most important step of balancing a chemical equation is simply making sure that your reactants and products are written correctly.  If they are not, the equation will never balance and you will spend many fruitless hours struggling.  If you are having a lot of trouble getting a reaction to balance, this is usually a good place to start looking for answers! 

TRY THESE!!

Fill in the blanks with the proper coefficients. 

1)      _Al + _O2 = _Al2O3

2)      _Na + _H2O = _NaOH + _H2

3)      _C2H4 + _O2 = _CO2 +_H2

4)      _Si2H6 + _O2 = _SiO2 + _H2O

5)      _CH3OH + _O2  = _CO2 + _H2O

ONLY WHEN YOU ARE DONE....go ahead and scroll down!


 















Answers:

1)      4, 3, 2

2)      2, 2, 2, 1

3)      1, 2, 2, 2

4)      2, 7, 4, 6

5)      2, 3, 2, 4

I love fruit!  It’s one of the few things you can eat that is both sweet and good for you!  There is also such a wide variety, from apples to grapes, watermelons to kiwis, and pineapples to pomegranates.   We know these are all fruits, and
we can think of a great many more—too many in fact to name—all different in
taste, texture, and form.  How can they be so different, yet all be called fruits? What exactly is a fruit?

A fruit is the part of a flowering plant which develops from the ovary of the flower, and usually either consists of or carries the seeds of the plant (bananas are one common exception—they are actually a seedless berry!).  Therefore, in the strictest botanical sense, not only are all of our previous examples fruits, but so are tomatoes, corn kernels, wheat grains, peas, and almost all nuts.  This is because all of these are or contain seeds, and have developed from the ovary of a flower.  

There are many different ways to classify a fruit, and over 15 different common fruit types (for more information, please visit the Colorado State University Extension website by clicking here).  However, in general, there are really three basic types:  

1.    Simple fruits:  These form from one flower with only one ovary.  Peaches are an example of a simple fruit.  
 
2.    Aggregate fruits:  These form from one flower with many ovaries.  Raspberries are an example of an aggregate fruit.

3.   Multiple fruits:  These form from the fusion of many flowers which grow on one structure. 
The ovaries of these flowers fuse to form one fruit.  Examples include pineapples and figs.  
 

Unfortunately, it isn’t always easy to tell the difference between these different types just by looking at the mature fruit.  For example, if you have ever cut open a pomegranate and seen all the loose seeds inside, each surrounded by a small, separate piece of red flesh, and clinging to a single leathery husk, you might think this is an aggregate fruit.  In fact the pomegranate is a simple fruit (a berry) from one flower with one ovary, but still producing many seeds.  In order to really understand what sort of fruit you are looking at, you really need to take a good look at the flower.

Let’s take a look at a picture of the inside of a flower.  

This picture shows us all the reproductive organs of the flower; let’s focus on the ovary, which is zoomed in on the left side.  Note this flower has only one ovary, and so if it produces fruit that fruit will be considered a simple fruit.  However, notice also that this flower has more than one “ovule” or egg cell, and it is these structures which become the seeds of the fruit.  So this flower will produce a simple fruit having many seeds, much like the pomegranate.  Now take a look at the pomegranate flower, and it becomes clear why this is considered a simple fruit.

This flower has multiple ovaries, and each ovary has one ovule.  So the raspberry will be an aggregate fruit, and each of the ovaries will develop a single seed. 

For a multiple fruit like the pineapple, let’s look at a picture of a pineapple flower, and the fruit that develops:

The large pineapple flower is actually a group of many flowers, each of which will become one section of the mature pineapple fruit*.


TRY IT!

Now that you understand how the flower becomes the mature fruit, and how this influences the type of fruit formed, try identifying the following pictures of flowers as forming simple, aggregate, or multiple fruits.  If the fruit is a simple fruit, will it have one or many seeds?  Be sure to write down your answers!


1) Peach

3)  Apple

5)  Strawberry

When you've written down all your answers, scroll down.
















Answers:

1)  Peach:  Simple fruit, one seed

2)  Blueberry:  Simple fruit, many seeds

3)  Apple:  Simple fruit, more than one seed

4)  Fig:  Multiple fruit

5)  Strawberry:  Simple fruit, many seeds





For more pictures of flowers that become fruit, please see this website from the University of California Davis  http://fruitandnuteducation.ucdavis.edu/generaltopics/AnatomyPollination/Anatomy_Tree_Fruit_Nut_Crops/


*The picture of a pineapple flower found on Wikipedia is used with permission, shared under the Creative Commons Attribution-Share Alike 3.0 Unported License.  A link to that license appears here:  http://creativecommons.org/licenses/by-sa/3.0/legalcode

You’ve probably played on a see-saw before, or used a wheelbarrow to move dirt or tools for gardening.  Maybe you’ve used tweezers to get a splinter out of your finger.  While the see-saw, the wheelbarrow and the tweezers may not seem to have much in common, they are actually somewhat alike: they are all levers.   A lever is simply a rigid stick or beam, which pivots around a stationary point called a fulcrum. 

For any lever, there is also a point of input force, and a point of output force against some resistance.  When input force is applied to a lever (like when you pick up the handles of a wheelbarrow), the resulting output force (the force acting against the resistance, which lifts the tools in the wheelbarrow) is amplified.  In other words, the lever of the wheelbarrow helps you move your garden tools because it allows you to put in a small force, and turn it into a large force to lift the tools.  One of the first to demonstrate the lever’s usefulness for moving heavy objects was Archimedes; according to Pappus of Alexandria, who wrote Synagoge: Book VIII in 340 AD, Archimedes once said, “Give me the place to stand, and I shall move the Earth.” (wikiquote.org)

Levers can be put in one of three classes:

Class 1 levers have the fulcrum in the middle of the lever, force is applied to one end of the lever, and the object to be moved (the resistance) is on the other end.  The see-saw is an example of a class 1 lever.

Class 2 levers have the fulcrum at one end and the input force on the other end, with the resistance in the middle.  The wheelbarrow is an example of a class 2 lever.

Class 3 levers have the fulcrum at one end and the resistance on the other end, with the input force in the middle.  Tweezers are an example of a class 3 lever.

To understand how a lever helps us move things, we need to understand how the lever changes the forces that are exerted on it.  Using a see-saw as an example, say you weigh 50 pounds, and your friend weighs 100 pounds.  If the fulcrum of the see-saw is in the middle, your friend will be sitting on the ground and you will be up in the air!  This is because your friend is exerting twice as much force on his or her end of the see-saw as you. 

To understand how to cope with this, we need to understand the law of the lever.  This law states that the output force on the resistance (FB) divided by the force applied on the lever (FA) equals the distance of the input force from the fulcrum (a) divided by the distance of the output from the fulcrum (b), or:

This value is also called mechanical advantage.  For more information, please click here. 

In order for the two of you to play on the see-saw together, you will need a mechanical advantage!   We know from the law of the lever that the product of the force and the distance from the fulcrum must be equal for you both.  So:

We can also see that this means the distance from the fulcrum to your seat must be twice the distance of the fulcrum to your friend’s seat:

So if we move the see-saw fulcrum so that the distance from your seat is twice as much as your friend’s, you will balance, and be able to play nicely on the see-saw!

The same idea applies to the wheelbarrow:  if the object you are trying to move is twice as heavy as the weight you are able to lift, you will need to position this object close enough to the wheels such that it is more than twice as close to the fulcrum as you are.

TRY IT!!

NOTE:  You will need to do these experiments at a playground, or another location where you can find a see-saw.  You will also need to know your exact weight in pounds, as well as your friends’ weights.

Here’s what you will need:

1.       A see-saw from your local playground or park.  IT MUST BE ADJUSTABLE  (In other words, you need to be able to move the fulcrum)

2.       A friend that is lighter or the same weight as you

3.       A friend that is heavier than you (this could be a parent or teacher)

4.       A tape measure at least as long as the see-saw

5.       A notebook to take notes and write down numbers

Here’s what you need to do:

1.       Measure your see-saw from end to end.   Write down the total length in feet. 

2.       Divide your weight by your friends’ weights.  This means you will have two numbers, your weight divided by your smaller friend’s weight, and your weight divided by your bigger friend’s weight.  These will be numbers W1 and W2.  Write these numbers down!

3.       The number ‘W1’ is likely to be close to 1, since you and your smaller friend are likely about the same size.  If your smaller friend is lighter than you, that number will be greater than 1.  If the number is 1, take the length of your see-saw and divide it in half, and place the fulcrum this distance from both you and your friend’s seat (so if your see-saw is 6 feet long, place the fulcrum 3 feet from your seat and 3 feet from your friend’s seat). 

4.       Both you and your friend now sit on the see-saw on either end, and if you are really the same weight, you should balance!  If you don’t balance, try measuring the see-saw again, or check your weights again!

5.       If the number W1 is greater than 1, to find how far you and your friend should be sitting from the fulcrum we need to do some algebra!  Don’t worry if you haven’t learned algebra yet, there is a very easy way to figure out the answer.  We are going to go through the long way too, just for good measure! 

Let’s say you weigh 75 pounds, and your smaller friend weighs 50 pounds.  This means your number W1 is 1.5, because 75/50 = 1.5. 

We know the length of the see-saw (say 6 feet), and we know that in order to balance on the see-saw together your friend needs to be 1.5 times further from the fulcrum as you are (see the discussion above on how levers do work if you need to review this).  So to find how far from the fulcrum you and your friend need to be, we set it up like this:

x = how far you need to be from the fulcrum

1.5x = how far your friend needs to be from the fulcrum (this means he/she needs to be 1.5 times as far as you).

If we add these two distances, we know they must be 6 feet, since that’s how long our see-saw is:

x + 1.5x = 6

We can add x and 1.5x to get 2.5x

2.5x = 6

Now to find x we divide 6 by 2.5

x = 6/2.5

This gives us 2.4 feet, or about 2 feet and 5 inches

x = 2.4 feet

So you must be 2 feet and 5 inches from the fulcrum.  This means your friend must be 3 feet and 7 inches from the fulcrum, because:

1.5x = 2.4 x 1.5 = 3.6 feet = 3 feet 7 inches

Whew!  That’s a lot of math!  Now here’s the easy way:  Whatever W1 is, just add 1, and divide the total length of the see-saw by that number.  That’s how far you need to be from the fulcrum.  Subtract that number from 6, that’s how far your friend needs to be.  It’s that easy!

6.       Now move the fulcrum of the see-saw so it is 2 feet and 5 inches from your end.  Sit on the see-saw with your smaller friend, and you should balance!  If not, double check the length of your see-saw, and your weights!

7.       Now we’ll do the same for you and your bigger friend.  Take your number W2 (which should be less than 1), add 1, and divide 6 by this number.  This is how far you should sit from the fulcrum.

Here’s an example:  Say you weigh 75 pounds, and your larger friend weighs 150 pounds.  This means your W2 number is 0.5:

W2 = 75/150 = 0.5

We add 1 to this number, and divide 6 by this final number:

0.5 + 1 = 1.5

6/1.5 = 4

This is how far you should be sitting from the fulcrum of the see-saw.  This means your friend should be sitting 2 feet from the fulcrum, because 6-4 = 2.

8.       Now move the fulcrum of the see-saw so it is 4 feet from your end of the see-saw.  Sit on the see-saw with your bigger friend, and you should balance!  If not, double check the length of your see-saw, and your weights!

NOTE:  You may not balance perfectly if the see-saw has some extra weight on one end after you move the fulcrum, like a metal piece that holds the see-saw in place.  If this is the case, you may need to adjust slightly to perfect the balance!

Be sure to write down all your observations:  Did you and your friends balance?  Why or why not?  Probably the numbers were not as easy as in our examples, so if you found it hard to balance this may be the culprit also!

MAKE UP YOUR OWN EXPERIMENT!

You could do a similar set of experiments with a wheelbarrow and a heavy weight.  Calculate how close to the wheels of the wheelbarrow the weight would need to be for you to lift it using the same math technique used above.  As always, be sure to write down all your numbers and observations!


References for more information:

J. J. Uicker, G. R. Pennock, and J. E. Shigley, 2003, Theory of Machines and Mechanisms, Oxford University Press, New York.