For every solid object, there is a point where it appears that all the weight of that object is concentrated.  That point is called it’s “center of gravity.”  The center of gravity is the point at which you can balance the object.  An object which is moved outside of it’s center of gravity will become very unstable.

Materials Needed:   You; a friend.

Procedure:   With your friend watching, place your feet together and stand up straight.  Bend over and touch your toes. 

Next, stand with your back and heels against a wall.  Again, try to bend over and touch your toes.  Can you do it?

Now have your friend to do what you have just done.  Watch the position of  his or her body.  What is different when your friend is against the wall?

What Happened: Neither of you should have had any trouble bending over when you were away from the wall, but with your back against the wall, it was impossible.  When you bent over away from the wall, your legs bent backwards and your backside moved backwards as well.  This counteracted the weight of your upper body moving forward, and kept your weight balanced near the center.  However, when you stood against the wall, you could not move your backside backwards and your center of gravity shifted forward causing you to fall forward.

---

Finding the Center of Gravity of a Rectangle and a Circle

Materials Needed:   Thin cardboard; ruler; compass; scissors; sharp pencil.

Procedure:   Cut a rectangle from your piece of cardboard.   Using your ruler, draw a straight line from one corner to the opposite corner.   Now draw another line between the other two opposite corners.  Press the point of your pencil into the point where the two lines intersect (cross) to make a small indentation.  Now carefully try to balance the rectangle on your pencil point where you just made the indentation.

Next, use the compass to draw a circle on the cardboard.  Press the compass point firmly into the cardboard to make a small indentation at the center of the circle.  Carefully cut out the circle.  Try to balance the circle on the pencil point at its center.
 
What Happened: You found the geometric center of the rectangle and the circle.  Both should have balanced on the pencil point at their center.  The center of gravity of a regular shaped geometric figure, such as a rectangle or circle, is the same as it’s geometric center.

Going Further: See if you can construct a square, a pentagon, a hexagon and an octagon from cardboard and locate their geometric centers.  Is this the center of gravity for each figure?  (NOTE: If you don’t know what each of these figures is, you may want to get some help from a math teacher.  Your teacher may also be able to help you locate the center of each.  To keep it simple, make sure that all the sides of each figure are of equal length.

---

Finding the Center of Gravity of an Irregular Flat Object

Materials Needed: Cardboard; scissors; string; push pin; small washer, nut or other small weight; pencil.
 
Procedure: Cut out an irregular shape of cardboard similar to the one shown.  

Cut a piece of string about one and a half times longer than the widest part of the cardboard. Tie one end of the of string to your weight, and tie the other end to the straight pin near the head.

Punch a hole in the cardboard with the pin, anywhere near the edge.  Hold on to the pin, but allow the cardboard to swing freely.  When the cardboard stops swinging, draw a line on the cardboard where the string is hanging.  Remove the pin and stick it in at another point along the edge and do the same thing again.  Do this a third time.  If you have done this carefully, all three lines should intersect at the same point.  If they don’t, check your lines again.  Make sure that the cardboard is free to swing when you hold the pin.

Press the point of your pencil into the cardboard where the lines intersect to make a small indentation.  Now try to balance this object on your pencil at this point.
 
What Happened: You have located the center of gravity of an irregular flat object.  An object that is allowed to swing freely will move so that it’s center of gravity moves to it’s lowest point.  Therefore, the center of gravity will be located somewhere along the line of your string. (Remember the plumb bob?)  When you move the pin to another point, the center of gravity will again be located somewhere along the line of the string.  Where the lines intersect is where the center of gravity is located.

Going Further: Can you use this method to find the center of gravity of the circle or rectangle?  Is it where you expected it to be, based on the last experiment?

---

Exploring the Center of Gravity Outside of an Object

Materials Needed: Two forks; coffee stirrer; large radish; drinking glass.

Procedure: Place the two forks and the coffee stirrer in the radish as shown.  Move the coffee stirrer along the edge of the glass until the forks balance.  Looks unusual doesn’t it?

What Happened: The center of gravity of the forks and radish was somewhere along the edge of the stirrer between the two forks.

Materials Needed: Small pail such as a toy sand bucket; water.

Procedure: This experiment should be done outside.  You should also find a bucket with a sturdy handle and no leaks!

Fill the pail about 1/4 full of water.  Holding the pail, stretch your arm out and it spin around in a horozontal circle.  Watch the water as you do.  What happens?

Next, swing the pail around in a vertical circle.  What happens?
 
What Happened: The water stayed in the bucket, even when you swung the pail over your head.  Centrifugal force is a force which tends to push an object away from the center of it’s rotation or revolution.  In this experiment, the water was pushed toward the bottom of the pail as it was spun around.  This force was greater than the force of gravity, so the water did not come out of the pail, even when the pail was upside down and over your head.

Going Further:  It is centrifugal force that keeps you from falling in many carnival rides such as those that quickly turn you upside down and back up again, or those that spin you around while the floor drops out from under you.  Can  you think of any other such rides?

A pendulum is a swinging weight suspended from a fixed point.  Two common examples of the pendulum are a child’s swing and a clock pendulum.  The following experiments will help us see how pendulums work. 

---

A Simple Pendulum

Materials Needed: String; small washer, nut or other small weight; meter stick, yard stick or long dowel; two chairs.

Procedure:   Tie the small weight  to one end of an 80 cm piece of string.  Measure 75 cm from the weight and tie the other end of the string to the dowel or stick.  You should try to have as close to 75 cm of string from the weight to the stick as possible.

Place the backs of two chairs a little over 75 cm apart, and place the stick over the two chair backs as shown.   Pull the weight to one side and let it go.  You have made a simple pendulum.  In order to study pendulums, there are a few terms you will need to understand.

First, the length of the pendulum is the distance from the point where it is suspended to the center of gravity of the weight.  In this pendulum, the length is 75 cm.

Second, the period of the pendulum is the time it takes the pendulum to make one complete swing from one side to the other and back again.

Third, the frequency of a pendulum is the number of periods or complete swings per second.

Finally, the amplitude of a pendulum is the distance from the low point or center of the pendulum to the highest point of the swing.

Materials Needed: String; small washer, nut or other small weight; meter stick, yard stick or long dowel; two chairs; watch that measures seconds.

Procedure: Make a pendulum as you did in the last experiment, but with a length of 50 cm.

Move the pendulum weight  5 cm from the center.  Release the weight and time how long it takes for the pendulum to complete ten complete periods.  

Repeat for 10 and 15 cm.
 
What Happened: The time should have been the same regardless of amplitude.  You may have noticed minor differences, but these may have been due to small amounts of friction or air resistance or both. 

The time required for the pendulum to make one complete cycle or period is the same regardless of amplitude.  You measured the time required for ten periods instead of just one, because it was easier to measure. If you divide this time by 10, you will get a more accurate time for 1 period than you would if you tried to time a single period.

Materials Needed:   Setup from the last experiment; a second identical weight.

Procedure: Move the pendulum weight 10 cm from the center and again time how long it takes for the pendulum to complete ten complete periods.

Next, add the second weight to your pendulum to double it’s weight.  Again, move the pendulum 10 cm from the center and time how long it takes for the pendulum to complete ten periods.  Is there a change?

What Happened: Changing the weight had little or no effect on the period.  Again, small differences may be seen due to friction or air resistance or a combination of the two.

The period of the pendulum is the same regardless of it’s weight.

Going Further: Try this experiment using other weights.

Materials Needed:  Setup from the last experiment with only one weight.

Procedure:   Start with the pendulum at 50 cm long.  Move the pendulum weight 15 cm from the center and release it.  Time how long it  takes the pendulum to complete ten periods.

Shorten the pendulum length to 40 cm and repeat.  Do the same thing for 30 and 20 cm.  How does the length of the pendulum affect the period?
 
What Happened: Shortening the pendulum length shortens the pendulum’s period.

A clock that uses a pendulum to keep time depends on this property of a pendulum that allows us to adjust the pendulum’s period.  If you observe a grandfather clock, you will see that the period of the clock’s pendulum is one second. 

Going Further: This is a challenge for you, and there may be another science project here.  If we know the pendulum length, we can calculate the period using the following formula:

T is the period in seconds, π ( pronounced “pie”) is a constant which is about 3.14 (and that's close enough for our purposes), L is the length of the pendulum, and g is the constant for the acceleration due to gravity on earth which is 9.8 meters/second².  This formula reads, "T is equal to 2 times π (or 3.14) times the square root of the length of the pendulum, all that divided by g (or 9.8 meters/second²).

This formula is a little harder to use than the earlier ones we used, so you may want to get a math teacher to help you, particularly if you don’t understand square roots or how the math is done. Once you have learned how the math is done, try calculating T for several different pendulum lengths.  Then, make pendulums of those lengths and measure the period of each.  See how closely your measurements and your calculations agree.

In this experiment, you will construct a pendulum that has a period of one second.

Materials Needed: The pendulum setup from the last experiment; a watch that measures seconds.

Procedure: Starting with a length of 50 cm, begin shortening the length of your pendulum until ten cycles or periods take exactly ten seconds.  Once you have determined the correct length, measure it.

Going Further:   Here is another real challenge! There is another way to determine how long the pendulum should be other than by trial and error.  To calculate the length using math, we use the formula:

Here, L is the length of the pendulum, T is the period in seconds, π is a constant which is about 3.14, and g is the constant for the acceleration due to gravity or 9.8 meters/second².  If this looks a little like the formula in the last experiment, it is because it is the same formula.  It has just been rearranged.  You may want to get a math teacher to show you how.  You may also need some help doing the math.

Sir Isaac Newton was a famous scientist whose work formed the basis for much of what we know about gravity and forces today.  Among the things he discovered was his third law of motion.  This law states, “For every action, there is an equal and opposite  reaction.”  But what does this mean? 

Have you ever tried to step out of a small boat without holding on to something?  If so, you may have found that as you tried to step out of the boat by stepping forward, you also pushed the boat backward.  The force generated by your feet and legs propelled you forward, but it also pushed the boat backward with an equal amount of force.  (In the process, it may have given you a swim as well!)  This is an example of Newton’s third law.  The next few experiments will provide a few more examples.

---

Newton’s Third Law in a Bottle

Materials Needed: Three or four round pencils; a “long neck” glass bottle with a flat side; rubber or cork stopper to fit the bottle; vinegar; baking soda; paper towel.

Procedure:   This experiment can get a little messy, so it should be done outside on a smooth level surface.

Place the pencils parallel to one another on a flat surface close enough to each other to lay the wide part of the bottle across them as shown. 

Fill the bottle 1/4 full of vinegar.  Place 8 ml (1 tsp) of baking soda in a small square piece of paper towel and twist the corners of the paper towel to seal it inside.

Drop the paper towel and baking soda in the bottle.  Quickly stopper the bottle and place it on the pencils.  Keep clear of the cork and the mouth of the bottle.

What To Look For: Notice what happens when the cork pops out of the bottle.

What Happened: The vinegar and baking soda reacted to produce carbon dioxide gas.  As this gas was produced, pressure built up inside the bottle, pushing in all directions.  When the pressure was great enough, the cork was pushed out of the bottle. When the cork was pushed backward, the bottle was pushed forward.  The popping of the cork was the action, and the rolling of the bottle was the reaction. 

The forces involved were equal but opposite.

Going Further: You probably noticed that the cork went much father than the bottle. If the forces involved were equal, then why did the cork go further than the bottle?  

The answer is actually pretty simple.  The cork was much lighter than the bottle, and the same amount of force would move it much father than the heavier bottle.

If you can find an old roller skate or toy car, you might be able to make a "cradle" to hold the bottle.  This would probably work better than the pencils, and it could be the start of a good science project to investigate how the reaction would be affected by different weights and sizes of bottles and corks..

---

Newton’s Third Law and Space Ships