The Science Notebook
Forces - Part 1

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 On this page...
INERTIA
A Body at Rest
Inertia "Magic"
A Body In Motion
Inertia - Why You Need a Seat Belt
Inertia and Bombs
 
FRICTION
Friction on Smooth and Rough Surfaces
Reducing Friction with Oil
Reducing Friction Mechanically
Friction and Surface Area   
Reducing Friction Using a Cushion of Air
 
COLLISIONS
 Using Air Pucks To Study an Elastic Collision
More on Elastic Collisions
Another Elastic Collision
Elastic Collisions and Direction
A Messy (But Fun ) Inelastic Collision

GRAVITY
 Gravity - Where Is It Pulling Us To?
Gravity - Direction of Fall
How Falling Objects Are Affected By Gravity
Slowing Gravity's Pull
Gravity and a Parachute
Forward Motion and Gravity
Exploring Falling Objects Using Simple Math
Exploring A Curved Path Using Simple Math 
INERTIA

Inertia is a property of matter that you experience every day.  In fancy words, it is “the tendency of a body at rest to remain at rest, and of a body in motion to keep moving at that same speed and direction until acted on by an outside force”.  But what does that mean? 

“Tendency” means what something is likely to do.  For example, little kids have a tendency to like candy.  To a scientist studying forces and motion, a “body” is any object.  It may be a solid, liquid or gas.  “At rest” means that the object is not moving.  “In motion” means just that - the object is moving.  So another way of defining inertia is to say that is “an object that is not moving is likely to stay put, and a moving object is likely to keep moving in the direction it’s moving, and at the speed that it is moving.”  All this may not mean a whole lot to you now, but once you do these experiments, you should be able to understand exactly what this means.


A Body at Rest


Materials Needed: Large coin such as a quarter; small piece of cardboard such as a 3x5 card; small glass, cup  or jar.

Procedure: Place the cardboard on top of the container.  Put the coin on top of the cardboard.   Thump the edge of the cardboard.  Watch what happens to the coin.

What Happened: The coin on top of the cardboard was an object at rest.  It was not moving.  When the cardboard was thumped, it moved out from under the coin, but because of inertia, the coin had a tendency to remain at rest instead of moving forward with the cardboard.  Since the coin did not move forward, it dropped into the glass when the cardboard was removed from underneath it..

Going Further: Why did you have to thump the paper quickly?  What would happen if you didn’t? 


Inertia “Magic”

You have probably seen a magician pull a tablecloth out from under dishes set on a table.  The dinnerware “magically” stays in place.  However, there is really nothing magical about it at all.  In this experiment you will do the same thing - on a smaller scale.  Just to be on the safe side, though, you should use an unbreakable dish.

Materials Needed: Sheet of paper; unbreakable dish such as a cup, saucer or glass; smooth counter top or table.

Procedure:   Place the paper on the counter and place your dish on top of the paper.  Quickly pull the paper out from under the dish.  What happens?

What Happened: Because of inertia, the dish “at rest” didn’t move when the paper was pulled out from under it.

Going Further: Why did you have to pull the paper quickly?  What would happen if you didn’t?  We’ll see a little later.


A Body In Motion

Materials Needed:  A friend; piece of tape; smooth flat surface, such as a driveway or gym floor.

Procedure:   Place the strip of tape on the driveway or floor.  Have your friend to back up about 30 meters (100 feet) behind the tape.  Instruct him or her to run toward the tape as fast as possible and to stop exactly on the tape.  Position yourself beside the tape and observe your friend.
 
What To Look For: Notice what happens when your friend tries to stop.

What Happened: When your friend approached the tape at a run and tried to stop at the tape, you should have seen his or her body lean forward.  Your friend may not have been able to stop at the tape.  Your friend was “a body in motion”.  Because of inertia, he or she had to expend some energy to stop.  Even so, your friend’s body had a tendency to keep going forward.


Inertia - Why You Need a Seatbelt


Materials Needed: Toy car or truck that rolls smoothly; small object that can be placed on top of the vehicle such as a small coin; a hard cover book.
 
Procedure:   Place the book on a flat surface.  The book should not be as high as the top of the vehicle.  Position the car or truck four or five feet away from the books.  Then, place the small object on the roof of vehicle and give it a slow push it into the book.  What happens to the object on top of the vehicle?

What Happened: If you pushed too fast, the car moved, but the object was left behind, just like the coin and the dish in the experiments above.  However, if you pushed the car slowly, the object stayed in place until the  “crash”.  When the toy car “crashed”, the object was thrown forward.  Once the vehicle started rolling, the object on top of the vehicle began moving with the vehicle because it was acted on by an outside force - the push of your hand.  Once moving, it had a tendency to keep moving, even when the vehicle was stopped by the book. 

In the same way, you have probably been in a car with your seat belt on when the driver applied the brakes suddenly.  If so, you no doubt felt yourself pushed forward against the seat belt.  You were a moving object.  When the vehicle braked, it slowed down but you continued to go forward until restrained by your seat belt.  Without  the seat belt, you could have been thrown into the windshield and seriously hurt. 

Going Further: What happens when you are in the back seat of a car going around a sharp curve?  Why?


Inertia and Bombs


Materials Needed: Food tin; several small coins.

Procedure:   Stand directly over the tin.  Try to drop the coins into the can one by one.  Practice this until you are able to hit the tin nearly every time.  Next, place the tin about 3 meters (ten feet) away.  Walk toward the can and try to drop a coin in the can as you walk by.  If you miss the can, make a note of where the penny falls.  Keep trying until you are able to get a coin to go into the can every time.  What did you have to do?

What Happened: You were probably able to drop a coin into the can while standing over the can with little or no practice.  However, trying to drop a coin into the can while you were moving was much harder.

When you walked while carrying the coin, both you and the coin were “in motion”.  When you let the coin go, it had a tendency to keep going forward at the same speed as you even while it was falling, so it actually fell along a curved path as shown in the diagram.  Because of this forward motion, in order to get the coin to fall into the can, you actually had to release it before you got over to the can.

Because of inertia, when bombs are dropped from a plane, they continue to move forward at the same speed as the plane.  If the plane doesn’t change speed or direction, the bombs will hit the ground almost directly underneath the plane, although air resistance will slow their forward motion down some.

Going Further: Have a friend who doesn’t know what is supposed to happen to do this same experiment while you watch.  Can you see the curved path of the coin when your friend drops it.


FRICTION

Objects in motion can be stopped because of a property of matter called “friction”.  Friction is caused when two types of matter “rub” against one another.  No surface is perfectly smooth.  If you look at most any solid surface that appears to be smooth to the naked eye, and then look at that same surface under a microscope, you will see that it often has small bumps or ridges.  When these bumps or ridges rub against the bumps and ridges of another surface, they cause the two surfaces to resist movement against each other.  This resistance is called friction.  The rougher the surface, the more resistance, and the greater the friction between the two surfaces.


Friction on Smooth and Rough Surfaces

Materials Needed: Two glass microscope slides or two pieces of glass from small picture frames; two pieces of sand paper.

Procedure:
Rub the two microscope slides together.  How easily do they slide back and forth?  Do the same thing with the two pieces of sand paper. 

What Happened:
When you rubbed the two pieces of glass together, they were able to move against each other much easier than the two pieces of sandpaper, but there was still some resistance.  With both the sandpaper and the glass, the resistance comes from the fact that the surfaces are not completely smooth.  Whenever two objects come in contact with one another, we often want to reduce the rubbing or friction as much as possible.  There are several ways to do this, as we will see.


Reducing Friction with Oil

Materials Needed:  Two microscope slides or two pieces of glass from small picture frames; two pieces of sand paper; cooking oil.

Procedure:   Place a drop of cooking oil on one of the two microscope slides and try rubbing them together again.  Do you notice any change from the last experiment?

Cut two 3 cm (1 in) squares of sandpaper, and place several drops of oil on the rough surface of one of them.  Rub the rough surfaces of the two squares together.  Do you notice any change from the last experiment?

What Happened: You should have noticed that the two surfaces were able to slide against each other more freely.  The most improvement should have been seen on the glass surfaces, but you should have seen some improvement even in the sandpaper.  Here, the oil was used as a “lubricant” by filling in some of the gaps between the rough spots on the rough surface of each piece of sandpaper allowing them to move more freely against one another.

Going Further: Try placing a drop or two of water between the slides.  Does this work better than the oil?  Why or why not? Also, try placing some softened butter or margarine between the sandpaper squares.  Does this work better than the oil?  Why or why not?


Reducing Friction Mechanically

Materials Needed: Old toy car that rolls smoothly; rubber band; tape.

Procedure:   Tape the rubber band to the front of the car by running a piece of tape through the loop of the rubber band.  Place the car upside down on a smooth hard floor and give it a steady pull.  As you do, notice how easy or difficult it is to pull the car.  Also notice how far the rubber band stretches.

Now turn the car right side up on its wheels and pull it over the same surface.  Again, notice how easy or difficult it is to pull the car.  Also, observe how far the rubber band stretches with a steady pull.

What Happened: You could tell that the car was much easier to pull when it rolled on its wheels.  Wheels are mechanical devices that reduce friction.  You also saw that the rubber band stretched farther when the friction was greater.  The distance the rubber band stretches is a measure of the amount of force required to overcome friction.  The more force  required to overcome friction, the farther the rubber band stretches.
 
Going Further: If you can, borrow a spring scale from your school.  Repeat this experiment using the spring scale instead of the rubber band.  See whether you can measure the amount of force required to move the car by observing the reading on the scale.


Friction and Surface Area

  
 

Materials Needed: Hardcover book; rubber band; string; table top.

Procedure:   You should use an old book that you don't care to keep since there is a slight risk that the book could be damaged.

Run the string through the rubber band and tie it to the rubber band.  Next, loop the rubber band inside the book between two pages somewhere in the middle of the book so that the string is in the middle of the spine on the outside.  (NOTE:  The illustration above shows the book with the rubber band looped around the top and bottom of the book, instead of inside the book, and this is not correct.  If you follow the illustration, part of the friction will be due to the rubber band underneath the book.  A new illustration will be provided soon.)  Place the book flat on the table and pull it steadily along the table top.  Notice how far the rubber band stretches.  

Now place the rubber band around the outside of the book.  Turn the book upright so that the spine is vertical and the string is again lined up with the middle of the spine.  Now carefully pull the book across the table top again.  How much does the rubber band stretch now?

What Happened: The rubber band probably stretched much farther when the book was flat on the table.  This indicates that more force was required to overcome friction when the book was flat.  The more surface area that is in contact between two objects moving against one another, the greater the friction between those two objects.

Going Further:  If you can borrow a spring scale from your school, repeat this experiment using the spring scale and a loop of string instead of a rubber band and see whether you can measure the amount of force required to move the book.


Reducing Friction Using a Cushion of Air


CAUTION!  Always use sharp objects such as knives or scissors with adult supervision only!  Hold any sharp point away from your body, particularly your eyes.

Materials Needed: Old compact disc (CD) or 10 cm (4 in) diameter cardboard circle; plastic soft drink bottle top; glue; balloon; sharp knife or scissors.

Procedure:   If you don’t have an old CD, use a compass to draw a 10 cm (4 in) diameter circle on a piece of thin stiff cardboard.  Cut out the circle and cut about a 1 cm (½ in) circle from the center. 

The bottle top should be made of soft plastic and have just a slight flare around the edge.  Most soft drink tops have this slight flare and will do very nicely. Glue the bottle top to the very center of the cardboard disc or CD.  You should use a good strong glue.  The author used glue from a hot glue gun, but any strong general purpose glue except “Super Glue”® type adhesives should work.  Super Glue® is very strong, but it won’t work very well on these surfaces.  Also, if you are not very careful, it is easy to get Super Glue® stuck to your fingers where it does stick all too well.

Allow the glue to dry completely.  Then, carefully punch a hole in the bottle top.  You should start with a small hole.  If you need to make it larger, you can do so once you’ve tested it, but you can’t make it smaller once it’s too big!

Inflate the balloon and hold your finger over the hole in the cap. Keep the balloon pinched so as not to let out the air while you stretch the mouth of a balloon over the bottom of the cap.  You may need to have someone to help you with this.

Remove your finger from the hole in the cap.  Quickly place the disc on a table top and give it a slight push.

What To Look For: The disc should skim across the table with very little friction.  If it doesn’t, you should remove the balloon and enlarge the hole a little bit at the time until it does.

What Happened: The air leaving the balloon created a thin cushion of air between the disc and the table top.  The disc glided along on this cushion of air with very little friction to slow it down.  In fact, it was much more likely to be slowed down by the air resistance and inertia of the balloon.

You have just made an air puck.  This air puck works on the same principle as the air pucks used in air hockey games.  An air hockey puck glides along on a cushion of air coming through the holes on the surface of the table from underneath. This is also the principle used by a hovercraft to skim over water or land on a cushion of air created by large fans.

Going Further:   There are lots of ways you can experiment with the design of your air puck.  You can try using different materials such as plastic sheets or foam board, and you can also try changing the size and shape of the puck.  In fact, if you keep careful records, you can probably design an experiment to test the different designs which could turn into a good science project.


COLLISIONS

Air pucks such as the one you just made can help you to study collisions without the interference of friction.

There are two types of collisions - elastic and inelastic.

In an elastic collision, neither of the objects is permanently changed or altered by the collision.  This is the case with bowling pins and a bowling ball.  When they collide, the pins and balls may go off in different directions, but they are not altered.  This is also true of marbles and billiard balls.

On the other hand, in an inelastic collision, one or both of the objects are altered by the collision - usually be being dented, cracked or broken.  This is the case with a car crash, for example.


Using Air Pucks To Study an Elastic Collision


Materials Needed:   Two air pucks.  (See previous experiment.)

Procedure:   You will need to make a second air puck just like toe one you made in the last experiment.  Inflate the balloons and place the two air pucks about a 30 cm (1 ft) apart on a smooth tabletop.  Push one into the other and observe what happens.  Do the balloons have any effect?

What Happened: When the moving puck collided with the stationary one, it stopped or at least slowed down, and the second puck moved away.  The energy from the first puck was transferred to the second puck, causing the second puck to move away.

Going Further: Try this same experiment using two marbles on a smooth surface instead of two air pucks.  Do you get the same result?  Also, if you know someone who has an air hockey game, you might want to try this experiment, and the next few, using the air hockey table and pucks.  If you do, are your results the same or different?  Why?


More on Elastic Collisions

Materials Needed:   Two air pucks; modeling clay.

Procedure: Place three small lumps of clay on one of the pucks.  The lumps should be the same size, and should be placed the same distance from the center and from each other so that when the puck moves, it is balanced and does not drag on one side.  You may have to work on this for a while,.  If you put too much clay on the puck, it will be too heavy to glide, so take your time getting this one right.

Inflate the balloons on both pucks and place them about 30 cm (1 ft) apart on a smooth tabletop.  Next, push the heavier puck into the lighter one and observe what happens.

What Happened: When the heavier puck hit the lighter stationary one, it had considerable energy stored in it.  Because it was heavier, it took a stronger push to get it going.  Because of this, not all of it’s energy was transferred to the lighter puck.  Although the lighter puck moved off as before, the heavier puck may have continued to move also.  It did not move quite as fast, however, because it transferred some of its energy in the collision to the lighter puck.
 
Going Further: Try using different amounts of weight on the heavy puck.  If you have a balance, you may want to weigh the pucks before each collision.  In fact, with a little careful  thought, you might be able to design a science project around elastic collisions.  The next experiment may also give you some ideas.


Another Elastic Collision

Materials Needed: The two air pucks from the last experiment; extra modeling clay.

Procedure: Inflate the balloons and place the air pucks about a 30 cm (1 ft)  apart as before.  However, this time push the lighter air puck into the heavier one.  Before you do this, what do you think will happen?  Why?

What Happened: The heavier air puck may have moved away when it was struck by the lighter one, but probably not nearly as fast or as far.  The lighter one probably moved off in a different direction or stopped moving.

The heavier air puck absorbs all, or nearly all, of the energy of the lighter one, so the lighter puck stops moving or slows down considerably.  However, since the second puck was heavier, the energy transferred from the lighter puck was not enough for the heavier puck to move off at the same speed, so it moves away slower and did not travel as far as the lighter one would have.

Going Further:  Again, you may want to repeat this experiment  using different amounts of clay. 


Elastic Collisions and Direction


Materials Needed: A marble; smooth tabletop; a heavy hardcover book.

Procedure: Place the book flat on the tabletop.  Roll the marble toward the spine at an angle as shown, and observe the direction it moves after the collision.

What Happened: The marble moved away from the book in the opposite direction.  If you were to draw an imaginary line at a right angle away from the book where the marble hit, the angle of the marble as it approached the book would be the same size as the angle made when the marble moved away.
 
Going Further: Try this experiment at different angles.  Is the angle of the marble as it bounces off the book always the same size as the angle going toward the book.  If it isn’t, why not?  You can also try this using a billiard ball on a pool table, or using an air puck against the book.


A Messy (But Fun) Inelastic Collision


Materials Needed: A toy car that rolls; an egg.

Procedure: This experiment must be done on a smooth surface such as a flat driveway where it is OK to break an egg.  Once the egg is broken, you should clean it up immediately and rinse the area with water.  Dried raw egg is tough to clean up, and after only a little while in the sun, it can smell really bad!

Place the egg a couple of feet away from the toy car.  Roll the car into the egg SLOWLY!  Observe what happens.

Repeat this several times, slowly increasing the speed of the toy car until the egg breaks.

What Happened: The first few collisions were elastic.  The egg was able to absorb the energy by rolling away.  However, as the energy you put into the car was increased and the car went faster, a point was reached where the egg was unable to absorb all of the energy and transfer it into movement.  When that point was reached, the egg broke, and the collision became an inelastic one.


GRAVITY

Gravity is a force we experience all of the time every day.  It is that force which holds us to the ground and keeps us from flying off into space.  These next few experiments will help us to explore some of the properties of gravity and how it works.


Gravity - Where Is It Pulling Us To?


Materials Needed: Metal nut or other small object; string.

Procedure:  Tie the nut to one end of a 1 meter (3 ft) length of string.  Hold the other end and let the nut hang freely. In which direction are the string and nut pointing?

What Happened: Your first response is probably to say that the nut is pointing down, and you would be right.  But more specifically, the nut is pointing toward the center of the earth.  The force of gravity exerted by the earth tends to draw all objects under it’s influence toward the center of the earth.

Going Further:   The string and nut combination is a simple device known as a “plumb bob”.  A plumb bob is used to insure that an object is perfectly straight up and down or vertical.  You can use this simple plumb bob to straighten picture frames on a wall.

Gravity - Direction of Fall


Materials Needed: Food tin; marble; piece of cardboard; book; table; plumb bob from the last experiment.

Procedure: Cut a hole in one end of a piece of cardboard large enough for the marble to drop through freely.   Place the cardboard on the edge of the table with the hole off the edge.  Place a book on the other end to hold the cardboard in place.

Place the nut on the end of the plumb bob through the hole and lower a short distance above the floor. Position the can so that the plumb bob is over the center of the can.  Remove the plumb line.

Drop the marble through the hole.  Where does it go?  Next, have a friend to drop the marble through the hole while you watch.  What do you see?

What Happened: In each case, the marble fell straight down.  The earth’s gravity pulls all objects directly toward the center of the earth.  In general, all falling objects near the earth fall toward the center of the earth.


How Falling Objects Are Affected By Gravity


Materials Needed: Two rocks of different size and weight; chair; a friend.

Procedure: This experiment should be done outside on a driveway or on the ground.  Stand on a good steady chair and hold both rocks at the same height above your head, one in each hand.  Let both rocks go at the same time while a friend watches the ground underneath.  Have your friend to note which rock hits the ground first.  Then, have your friend repeat the experiment while you watch.
 
What Happened: Both rocks hit the ground at the same time or nearly so.  The force of gravity will cause all objects to fall at the same rate of speed, regardless of how much or how little they weigh.  However, there is one other force that can affect the speed of the fall, as you will see in the next experiment.

Going Further: Try this with a variety of objects such as coins, pens, pencils or small hardware.


Slowing Gravity’s Pull


Materials Needed: Two identical sheets of notebook paper; chair; a friend.

Procedure: Crumple one of the sheets of paper into a ball.   Stand on a good sturdy chair and hold one piece of paper in each hand at the same height above your head.  While your friend is watching, drop both pieces of paper.  Have your friend notice which hits the ground first.  Have your friend to repeat the experiment while you watch.

What Happened: The crumpled paper hit the floor first, while the flat sheet of paper fell much slower.  The difference was caused by air resistance.  As the flat sheet fell, it’s surface area exposed to the air was much greater than the surface area of the crumpled piece.  As both pieces fell, they were slowed down by the air, but the flat sheet was slowed more because of the greater surface area. All objects falling through air are slowed by air resistance, but objects that are very light, or those which have a large surface area compared to their weight, are affected more.

Air resistance allows a parachute to work as it does.


Gravity and a Parachute


CAUTION!  Always use sharp objects such as knives or scissors with adult supervision only!  Hold any sharp point away from your body, particularly your eyes.

Materials Needed: Handkerchief or other small piece of light cloth; light thread; nut or other small weight.  (HINT:  You can substitute a square cut from a plastic grocery bag for the cloth.)

Procedure: Cut four pieces of thread each about twice the length of one side of the handkerchief.  Tie one end of each piece of thread to each corner of the handkerchief.  Tie the other end of each string to the weight to make a small parachute.

Roll up this small parachute and throw it as high as you can.  What happens?

What Happened: If the parachute opened properly, it fell gently down to the ground. The surface area of the handkerchief presented a large surface area for air resistance to oppose the pull of gravity and slow the fall just as a real parachute does.


Forward Motion and Gravity


Materials Needed: Two baseballs or softballs; a friend.

Procedure: Have you friend stand some distance away and to one side of you.  Hold one ball in each hand.  At the same time, drop one ball and throw the other ball as straight ahead of you as possible.  Be careful that you throw the ball as level as you can, rather than have it arch upward.  Have your friend to observe when each hits the ground.  Repeat this two or three times.

Next, have your friend to repeat the experiment while you watch.  What do you see?

What Happened: If you were careful to throw the ball straight ahead, and if you released both balls at the same time, the balls should have hit the ground at the same time.  It isn’t all that easy to throw a ball straight ahead without arching it up a little bit.  It also will take some practice to throw and release at the same time, so the two balls might not have hit at exactly the same time.  You may need to do this a few times before it works. 

The forward speed of an object does not affect the force of gravity on that object.  It still falls at the same rate as one which is not moving forward.  Even a very fast moving object, such as a bullet fired from a gun, falls at the same rate as it would if it were not moving forward.  This is because there are actually two separate forces at work on the moving ball at the same time.  One is the forward force given by your hand and the other is the downward force of gravity.  The two forces combine to produce a curved path for the ball. 

Going Further: Explore the curved paths with a friend by taking turns throwing the ball and observing the thrower.  Notice the path that a ball takes when it is thrown straight ahead and when it is thrown upward and forward.  Can you sketch these paths?


Exploring Falling Objects Using Simple Math


In this experiment, you are going to use a simple math formula to measure how much distance a falling object covers over time.  The formula we use to do this is:

     t2g
  
d    =   ---      
         2  
 

This formula may look complicated, but it isn’t.  “d” is the distance an object falls in meters when dropped.  That is what we are looking for.  “t” is the time in seconds and in this formula, it is squared (or multiplied times itself).  “g” is the number that represents how fast gravity increases the speed of an object as it falls.  “g” is a constant which means it’s value doesn’t change.  For objects here on earth, “g” equals 9.8 meters/second2.  What this means is that for every second an object falls, it speed increases 9.8 meters per second over it’s speed the last second.

Now let’s see how it all works.

Materials Needed: Tennis ball; stopwatch; a friend; a building with several stories; small weight; roll of string; meter stick; marker; calculator (optional).

Procedure:   Find a building that is several stories tall and that has windows from which you may SAFELY drop a tennis ball.  This should never be done when there is anyone nearby who could be struck by a falling or bouncing ball!

You will need a friend to help you with this experiment.  Start at a first floor window.  Tie a small weight to the string and lower the string from the bottom of the window to the ground, a meter at a time.  Use the marker to make a mark on the string every meter.  When the weight has reached the ground, note the distance to the ground.  Drop the ball out the window even with the bottom windowsill.  Start the stopwatch at the same time.  Use the stopwatch to measure how long it takes from the time you release the ball until it hits the ground.  Do this several times and average the times.

Repeat this for the second and third floors.  For safety reasons, you should not go past the third floor.

To calculate distance the ball fell from each floor (and thus the height it was dropped from), use the formula explained above.  For example, suppose it took the ball two seconds to hit the ground.  Using the formula:

    t2g
d =  ---  
       2   

     22 x 9.8 m/sec2  
d =  ------------------      
 2

        4 x 9.8 m/sec2
d =    ------------------  
            2   

      39.2 m    
d =   ---------    
      2   

d = 19.6 meters

Compare the distance you measured with the string with the distance as calsulated using this formula.  The two should be close.

Going Further: If you live near a tall bridge or cliff, you can use this same formula to calculate how far the bridge or cliff is from the ground.  If you try this, though, be sure to always keep safety in mind and only do this with the help of an adult.


 Exploring A Curved Path Using Simple Math


The formula from the last experiment may also be used to determine how high a ball is thrown.

Materials Needed: Ball; a friend with a good pitching arm; stopwatch.

Procedure: Have your friend to pitch the ball as high as he or she can straight up.  Use the stopwatch to time how long it takes for the ball from the time it leaves your friend’s hand until it strikes the ground.  Do this a couple of times.

Have your friend to throw several high arching curves while you again time how long the ball is in the air.

What To Look For: When your friend throws the ball straight up, notice how long it takes for the ball to go up, and how long it takes for the ball to come back down.  You should see that the times are the same or nearly so.  This is because an object moving against the force of gravity is slowing down at the same rate that an object is accelerating when it is moving with the force of gravity.  Because of this, to figure out how high the object went, you should divide the total time in half.

Keeping this in mind, use the formula

t2g
d = ----      
     2    
just as you did in the last experiment to figure out how high the ball went each time.

Going Further:   Try this same experiment using a toy dart gun.


This is only half the story about forces.  To learn more, visit the Forces - Part 2 page!


"The Science Notebook"  Copyright 2008-2017 - Norman Young