Physics 3 Using Vectors To Show Forces

You are asked to join a game of tug of war by one friend. Each of you grabs an end of the rope and starts pulling. Neither of you can pull the other one.

Another friend comes over and grabs the rope with your friend. What happens?

At first the forces you and your friend exert on the rope are the same and opposite. The result is no force.

Let’s show this using vectors.

A vector is an arrow pointing in the direction the force is going. In tug of war the forces go away from each other as both sides are pulling on the rope.

When the third person starts pulling, one force stays the same. The other force doubles. Can vectors show this?

There is one vector arrow for each tug of war participant. Each arrow points the way that person is pulling. Two of the arrows are equal and opposite cancelling each other out. That leaves one arrow to show what happens in the game.

When you put the vectors together, they show what happened in your game of tug of war.

What Is a Vector?

As you can see, a vector is an arrow. The arrow shaft shows the amount of the force. You can do this with labels or drawing to scale.

The head of the arrow shows the direction the force is acting in.

Let’s Draw some Vectors

Materials:

Paper or Graph paper

Pencil

Ruler

Drawing the Vectors:

Draw your block from Project 1

From the bottom center of the block draw a line 2 cm long straight down

Every object on Earth has this vector arrow pointing down. If that force didn’t exist, everything would float into space.

Put the head of the arrow on the end going down

What does this arrow show? What force is holding the block on the table?

You made the block move by pushing on it. Draw a line to the side of the block. How long should the line be?

Using vector arrows for forces makes it easy to see how strong a force is, which direction it is going and how it is acting on an object.

The block moved. Think back to the game of tug of war. As long as the two forces were the same, the forces cancelled each other out.

If the force line showing you pushing the block is shorter than the gravity arrow, will the block move?

Your push vector must be longer than your gravity vector. Let’s make it 3 cm long. Now put the head of the arrow on.

Where does this go? Which way did the force push? It pushed against the block so the head of the arrow points at the block.

Can you draw the pulling force on the block using vectors? Try it. My drawing will be down below.

Using Vectors for Changing Forces

Put your block out on the table. This time push on the block from two adjacent sides at the same time.

Gravity always pulls on objects on Earth. This time we are interested in two forces pushing on two adjacent sides of the block at the same time. Which way will the block move? Can vectors be used to tell us?

Which way did the block go?

Draw your block on the graph paper again. This time have two pushing forces on adjacent sides on the block.

Now, copy one of the vectors from the tip of the opposite corner. Make sure it points in the same direction and is the same length.

The vector arrows are the same ones as before only moved. they point the same way and are the same length. Moving the vectors lets you draw a resultant vector showing the actual path the block took when acted on by two forces.

Next copy the other vector with the end starting at the point of the other vector. Make sure it points in the same direction and is the same length.

If you draw a final vector from the point of the block to the point of the last vector, you have the direction the block moved when you pushed on it with two forces.

The vector arrow for gravity still points down. The other vector arrow now points away from the block as you were pulling on it.

Why Use Vectors?

You can see the forces acting on your block, right? You can see some of them but not others.

Using vectors makes what is happening easier to see. As we go on to look at work and simple machines, we will often use vectors to better understand what the forces are doing.

Physics 2 Putting Forces Together

Do you like to fly paper airplanes? The beginner model doesn’t fly very well. A modified one zips along.

What do paper airplanes have to do with physics and forces? They can show us how putting forces together changes the strength of the forces.

Introducing my helper for this physics project Tyler Green.

Question: How does putting forces together change them?

Materials:

Paper airplane

Fan

Tape

Large room

Procedure:

Make your favorite paper airplane

Set up the fan at one end of the large room

Stand by the fan, not turned on, and fly your paper airplane

Paper airplanes have several forces working on them. Air pushes them up and back. Your hand pushes them forward. Gravity pulls them down. Tyler isn’t thinking about this as he practices flying his airplane.

Put a piece of tape where it lands

Repeat this two more times

Turn on the fan

Fly your paper airplane several times over the fan so the moving air catches it

Mark where the airplane lands each time

Walk out from the fan to about where your paper airplane would land with the fan off

Fly your paper airplane toward the fan and into the stream of air several times

Mark where it lands each time

Observations:

Describe where the paper airplane lands

Without the fan

With the fan

Against the fan

Describe how the paper airplane flies

Without the fan

With the fan

Against the fan

Conclusions

What forces are acting on your paper airplane when it flies without the fan?

Does the air from the fan provide a force?

Who says physics is boring? Not Tyler. His paper airplane really took off when the fan’s air current helped push it aloft and across the room.

What happens when this force is added to your paper airplane?

What happens when this force acts against your paper airplane?

How does putting forces together change the force acting on an object?

What I Found Out:

It is hard to fly a paper airplane and take pictures of it flying at the same time. I asked Tyler Reed for help. He was a bit young for the physics but very enthusiastic about flying the airplanes.

A paper airplane launched into the air has several forces acting on it. One is the push you give it to make it go called thrust. Another is gravity pulling it down to the ground. Another is the air which helps hold it up but pushes against it slowing it down.

Tyler had a lot of thrust so the paper airplanes, two styles, flew very well without the fan. They zipped along moving up a little then going lower until they hit the floor at the laundromat where I do the physics projects as there is so much more room than at home.

With the fan turned on the paper airplanes flew higher and farther before. This depended on Tyler throwing the planes near the fan so the fan’s air could push on them.

Tyler threw the paper airplane at the fan. If you look carefully you can see the airplane off to the right side and slightly below the fan pushed there by the air current.

Then Tyler threw the paper airplanes at the fan. The air was still being pushed out from the fan. Now the air stream was pushing against the airplanes. They tended to go up over the air current, turn aside out of the current or dive bomb into the floor.

Putting forces together changes how an object moves. When the forces act in the same direction, they add up to a bigger force so the object moves farther. When the forces act against each other, they make the object go slowly, stop or turn aside from the force.

Physics1 Defining Forces in Physics

The word force has lots of meanings. Most of them have nothing to do with physics. How are forces in physics defined?

The block is sitting not moving on the table. Is a force acting on it?

Question: What are forces in physics?

Materials:

Block of wood

Table

Wire with a crook at the end

Procedure:

Set the block of wood on the table

Observe the block for a minute

Push on the block

Pushing on the block made it move across the table. Pushing is another kind of force.

Use the wire with the crook to pull the block

Push the block off the edge of the table

Observations:

What the block of wood does sitting on the table:

What the block does when you push on it:

What the block does when you pull on it:

What the block does when you hit the table:

What the block does when you push it off the table:

Conclusions:

What makes the block move?

Is a force acting on the block as it sits on the table?

Why doesn’t the block move because of this force?

How do you know a force is acting on the block?

How does a force act?

How do you think forces in physics are defined?

I forgot to grab my wire to pull the block across the table. Fingers do work to apply force by pulling.

What I Found Out:

My block of wood did not move sitting on the table. It only moved when I pushed or pulled it.

A force is working on the block as it sits on the table. When the block is pushed off the table this force pulls it to the floor. The only reason the force couldn’t move the block before is because the table was in the way.

A force acts by pushes and pulls.

What Are Forces in Physics?

Physics defines force as a push or a pull. There are many kinds of forces but they all act by pushing of pulling to move an object.

Can you think of some other kinds of force?

Gravity is one. It pulls objects down to the ground.

Magnets have force. They can be used to push or pull each other around.

Electricity especially static is a force. Think about what happens when you rub a balloon and touch it to a wall.

For the next fourteen physics projects we will look at physical forces, pushing and pulling and how we can use this through simple machines to make work easier.

Physics 28 Building Arches

Lots of bridges have arches under them. The Romans used arches under their aqueducts for thousands of miles carrying water to their cities. What’s so special about arches?
Question: How does an arch work?
Materials:
Paper
Tape
Procedure:
Make two small diameter paper tubes

The two tubes should be a small diameter and about the same diameter.

Overlap the ends 2 cm and tape them together [You will need to flatten the ends.]

The two tubes only need 2 or 3 cm overlap but must be flattened for the overlapping part.

Bend this long tube into an arch but don’t fold it

The tape must extend over the paper joint on both sides.

Place one end of the arch against a book or other heavy thing
Hold the other end lightly to make it an arch
Press down on the center of the arch letting the end move if it wants to
Hold the end of the arch firmly in place
Press down on the center of the arch
If you can, suspend a cup from the center of the arch and fill it with weights
Observations:
Describe what happens to the end of the arch when you put pressure on the top:

Force applied to the top of an arch flows down each leg into the ground or other base under the arch.

Describe what happens when you hold the ends firmly and put pressure on the arch:
Conclusions:
Where does the pressure go when you press on the arch?
How does this make the arch a good way to build a bridge?
What must a builder do to use an arch safely?

When weight or force is applied to an arch, the base of the arch tends to spread. This tendency must be countered when the arch is used in construction.

If two arches are side by side, what happens to the forces acting on the bottom of one arch?

What I Found Out:
My arch tried to fold at the sides of the flattened part a little making the top look a little flat. When I pressed on the center of the arch the first time, the free end moved out letting the arch flatten.
The pressure I put on the arch went down both legs of the arch. The one leg was trapped against the box and wall so the force pushing that leg out was stopped by force from the wall. The free end had no force acting against it so the end moved outward.

Arches are more rounded than this paper version but this one shows how arches move forces so they can support a lot of weight.

When I held the second leg firmly in place, I supplied the force against the outward force. The arch held firmly.
I could not suspend weight from my arch but think the cup would hold a lot of weight. The force from the weight would go down the legs into the table and the wall and my hand.
Since an arch moves the force from weight off the bridge, the bridge can carry a lot of weight. Since the arch has an opening in the middle under it, other traffic or water can move freely below the bridge.
The problem with using an arch is the outward force acting on the legs. There has to be something strong pushing back to keep the arch in place.
Two arches side by side will do this for each other. The outward force from one leg pushes against the leg from the next arch which is pushing back as weight force moves onto it.

Physics 27 Making Walls Stronger

Changing the shape of a sheet of paper made it much stronger. But people don’t live or walk on tubes or folds. People live in buildings with walls.

The sheet of paper got stronger when forces were moved from the center to the edges of the paper. Can walls do the same thing?

Question: How can walls be made stronger?

Materials:

Paper

Tape

Ruler

Scissors

Procedure:

The physics project will use nine tubes of about the same diameter.

Make 9 small diameter long tubes of paper

The four tubes for the square must be shorter than the two used for the diagonal pieces. The distance diagonally across the square is farther than across a side.

Trim 6 cm off the ends of four tubes

I put each left tube on top of the right tube so the square would be close to a square not a rectangle. You can do the opposite as long as you do the same for each corner.

Tape the four trimmed tubes into a square

A strip of tape across each corner on both sides held the tubes in place. The tape wrapped around the tube at each end about half way.

Hold the square in one hand or with the bottom on a table

The tape crossing each corner holds the square together. Is the tape strong enough to hold the square together?

Push the side

Pushing on one side of the square makes the side slope. All the pushing force goes across the top tube to push on the top far corner making it buckle.

Tape a tube diagonally across the square

The diagonal tube is taped into place. Notice the tape itself stiffens the corners.

Hold the square in one hand or with the edge on a table

Putting a diagonal inside the square wall cut it into two triangles. Pushing on one side with another side of the triangle on the table is like pushing on the triangle. The side does not move.

Push gently on one side then the other side of the square

Tape a tube diagonally across the square in the other direction

Both diagonals must be flattened a little in the center so the two diagonals will lie flat.

Hold the square as before

Push gently on one side then the other side of the square

Laying the tubes out for the triangle shows that each corner has less angle than those of the square.

Tape three tubes into a triangle

The tubes meet at an angle so I flattened the tips a little and taped over the top of the joint.

Hold the base of the triangle in one hand or on the table

Push on one side then the other side of the triangle

Observations:

Describe how the square feels to hold

Describe what happens when you push on the sides

Describe how the square with one diagonal feels

Pushing on the side of the square with one diagonal going up makes the square twist. The pushing force tries to push on the far corner but the diagonal tries to take the force back to the table not letting the corner move.

Describe what happens when you push on the sides

Describe how the square with two diagonal feels

Describe what happens when you push on the sides

Describe what the triangle feels like when you hold it

Describe what happens when you push on the sides of the triangle

Conclusions:

Is a plain square very stable? Why do you think so?

Why did you have to trim the four tubes for the square?

What has the square become when you add a diagonal?

The triangle side does not push over. The force goes down the other side and into the table.

Compare how the square with a diagonal and the triangle act when pushed on.

Compare how the square with two diagonals and the plain square feel when you hold them.

Compare how the force of a push on the plain square compares to the force of a push on the square with one or two diagonals.

Why do you think the diagonals make a wall stronger?

Can you think of another way to make a square wall stronger with out using diagonals?

Try your idea out and see if it works. Compare your method to the diagonal method.

What I Found Out:

The plain square was very flimsy. It was easy to push the side over turning the square into a rhombus. This is not very stable.

The longer tube fit into the square. If the sides had not been trimmed, the longer tube would not have been long enough to reach across the diagonal.

Once the diagonal is in place the square becomes two joined triangles. It feels much stiffer than the plain square did. The sides do not push. The square does twist when I push on the side.

The sides of the triangle did not move when I pushed on them. The triangle felt rigid.

The square became two triangles with the diagonal in place so the sides did not want to move. But pushing on the top triangle made the side twist because it was not flat on the table.

Pushing on the side of the square with two diagonals in it has the forces being split so some goes across the top, some from the top to the bottom down the diagonal even some into the second diagonal. The square will not push.

With two diagonals in it, the square is stiff. It feels rigid, not at all flimsy like the plain square. The sides do not move when pushed. It does not twist.

When I pushed on the side of the plain square, all the force went across the top tube to push on the other side tube. It moved.

When I pushed on the side of the square when the diagonals were in place, some force still went across the top. But some of the force went down the diagonal to the base of the square.

Diagonals make the square stronger by redirecting the force, breaking it up. That way less force pushes on the top of the side tube and it doesn’t move easily.

The square gets stronger if the corners do not move. Diagonals move the forces around. If the corners are reinforced somehow, it would take a lot more force to move them.

One way would be to put small diagonals across each corner. Another way would be to put a solid piece over the entire square to hole the tubes in place.

Physics 26 How Strong Is a Paper Bridge?

We met force as a push or a pull. When we balanced forces, we found we could set two forces against each other. The new force was found by adding those forces up.

When an engineer builds a building or a bridge, forces are very important or the structure will fall down. How can an engineer move forces around to keep a structure standing?

Question: How strong is a sheet of paper bridge?

Materials:

Several sheets of paper

Tape

Plastic yoghurt cup or plastic cup of similar or slightly larger size

Marbles or other small weights – enough to fill the cup, over 3 pounds worth

String

Scissors

Scale

2 Chairs

Small blanket or several bath towels

Procedure:

Put the two chairs back to back with a gap between them two thirds as big as the paper is long

Place the two chairs back to back so they are parallel. The towels are to catch the marbles or rocks when they fall.

Place the blanket or folded towels on the floor between the chairs

Place a sheet of paper across the gap

A sheet of paper suspended over the gap between the chairs sags down in the center.

Carefully set the cup on the sheet of paper

If the paper stays put, add a marble

The sheet of paper seemed to fall even before the cup was set on it.

Continue adding marbles until the bridge falls down

Mass the cup and any marbles in it [You may have to pick these up.]

The sheet of paper couldn’t hold even the 11.7 g cup.

Take the sheet of paper and fold it lengthwise so the fold is 1.5 cm

Now make a second fold the other way 1.5 cm

The folds are made lengthwise to span the gap. If the folds went across the paper, would they change how the sheet of paper acted? Probably not.

Repeat this until the paper is accordion folded [This is called concertina.]

Put the folded piece of paper across the gap between the chairs

The concertina bridge is straight across the gap between the chairs. The cup sits up on the folds.

Carefully set the cup on the sheet of paper

If the paper stays put, add marbles until it falls down

Mass the cup and marbles

Put four small holes [big enough for the string.] equal distances apart around the rim of the cup

If the four strings are the same length, the cup should be close to level when suspended. This lets the weights distribute evenly and not tip out.

Cut 4 pieces of string about 45 cm long

Tie knots in one end of the strings

Put the untied ends through the holes, one piece in each hole

Tie the ends together [You might want to tape it together too so the knot doesn’t untie.]

Take another piece of paper and roll it up lengthwise so the roll is 10 cm in diameter

Note: The diameters don’t have to be exact. You need a large, medium and small tube.

The tube sizes can vary but one is large, one small and one in the middle. A couple of short pieces of tape keep the tubes from unrolling.

Tape the roll so it won’t unroll

Roll another sheet of paper into a 7 cm diameter tube

Roll another sheet of paper into a tube with a 1 cm diameter

Put the 4 cm roll through the string loop of the cup and suspend the cup between the chairs

The cup is suspended below the middle of the bridge. An interesting comparison could be done putting the cup at different places along the tube. Each attempt would use a new tube of the same size.

Add marbles one by one until the bridge fails

Using a wide top cup made it easy to add the rocks. Another advantage was having my hand inside the strings so I caught the cup as it fell before the rocks were scattered over the towels.

Mass the cup and marbles

The large tube bridge held 478.3 g, an increase of 75.4 g over the concertina bridge.

Repeat this with the 2 cm and 1 cm tubes

Observations:

Describe how the sheet of paper looks suspended between the chairs

Mass of cup and marbles the sheet of paper held up

Describe how the concertina or folded paper looks suspended between the chairs

A single additional rock caused the folds to flatten under the cup. The concertina bridge did hold several more rocks before crashing down to the floor.

Describe what happens to the concertina as you add marbles to the cup

Mass of cup and marbles the concertina held up

Describe how the 10 cm tube acts before and as you add marbles to the cup

Mass of cup and marbles the tube holds up

Describe how the 7 cm tube acts before and as you add marbles to the cup

Mass of cup and marbles the tube holds up

The medium tube bridge held up 699.7 g which was 221.4 g more than the large tube.

Describe how the 4 cm tube acts before and as you add marbles to the cup

Mass of cup and marbles the tube holds up

Conclusions:

Compare how the plain sheet of paper and the concertina looked suspended.

Where was all the force from the cup focused on the sheet of paper?

Where was all the force from the cup focused on the concertina bridge?

Note: Think about how the tops and bottoms of the folds act.

How is the force from the cup focused with the tubes?

Adding rocks to the cup below the large tube bridge caused the tube to flatten.

What happens to the tube bridges to make them fail?

What do you think would happen if you could make an even smaller diameter tube?

How do you think the forces would focus if the tube were a solid cylinder?

Why is a hollow tube stronger than a solid cylinder?

What I Found Out

I didn’t have enough marbles so I went out to the creek and gathered pieces of gravel about the size of marbles.

The sheet of paper barely stayed up suspended between the chairs. It bowed down in the middle. The 11.7 g cup never really sat on it before the paper fell to the floor.

After the sheet of paper was folded into the concertina, it went straight across between the chairs. It did not sag. The cup sat on it as though it was on a table.

The only difference between the sheet of paper and concertina bridges were the folds yet the weight capacity increased a lot.

I started adding rocks. Finally the folds buckled under the weight. A few more rocks and the concertina fell. It held up 402.9 g of cup and rocks.

All the force of the cup was in the middle of the sheet of paper and it couldn’t hold it up. The folds of the concertina bridge let the force push and pull between the top and bottom of the folds. The folds carried a lot of the force away from them to the chairs. This let the concertina carry weight until the folds finally broke. Then the force was more in the center and it fell down.

The tube bridges acted much the same but the small tube took longer to change. They were straight across the gap. As the rocks were added, the tubes began to flatten. As the tube bridges failed, the tubes crushed.

The force of the weight is spread around the tube bridge and passed on to the chairs. As the tube collapses, more of the force is concentrated on the middle where the strings are. When the tube fails, all the force has moved to where the strings are crushing the tube and making it bend.

I did have some more rocks but couldn’t get them to stay on the pile. The tube had started to flatten so the small tube bridge was approaching its weight capacity.

The smallest tube had not failed when the cup was filled to overflowing with rocks. Perhaps I could have added some small lead wheel weights at the beginning so the tube would fail.

An even smaller diameter tube should hold more weight as long as the center is hollow. This lets the force of the weight move away from where the strings are hanging and go into the chairs. The forces on a solid tube would stay mostly where the strings are hanging putting the weight on the bar there until the bar would break.

Physics 21 Balancing Forces

Many Projects ago we defined a force as a push or a pull. We found forces could add to or subtract from each other. This Project we will try balancing forces so an object does not move when pulled by three forces at the same time in different directions.

Question: How do forces balance?

Materials:

Metal or other rigid ring

3 Spring scales [You can use three identical rubber bands but will not be able to measure the forces instead measure the rubber bands]

Protractor

Procedure:

This Project works well with friends to help. If you are working alone like I do, you will need tape to fasten the scales in place.

A simple spring scale has a pull strip to zero the scale and two scales. One is in grams for obtaining mass. The other is in Newtons, a unit of force.

Secure one scale to the table

Attach the secured scale and another scale to the ring

Pull on the second scale until it reads the same force as the first scale and  stops moving around the ring balancing forces

Record the measurements on the two scales

Note: I have three spring scales that measure forces in three levels of magnitude. If this is how your scales are, check your measurements carefully as each scale will look different.

Secure the second scale to the table

Attach the third scale to the ring

Pull on the third scale until it has the same force reading as the other two scales again balancing forces

Pull the third scale a little more and record the forces shown on the three scales

Secure the scale to the table

Use the protractor to measure the angles between the scales

Observations:

Record the force you use on your scales (or length of rubber bands):

Draw out where the two scales are on the ring

Draw out where the three scales are on the ring

Measurement of angles between the three scales

Record what happens to the three scales when you pull harder on one

Conclusions:

Do you think you could move one of the two scales pulling on the ring so they were not opposite and still balance the forces? Why do you think this?

Even if the second scale is next to the first one when hooked to the ring, it will shift to opposite the scale balancing forces with equal and opposite vectors.

If you used vectors to show the forces of the two scales, would they be the same length? Would they point the same direction?

What happened when you started pulling with the third scale?

What happened when you pulled harder on one scale?

What do you think would happen if you pulled on the ring with a fourth scale? Try it and find out.

What I Found Out:

All three of my scales used a gram and a Newton scale. All three would register .5 Newtons so I decided to use this amount of force.

I attached one scale to the table, put the ring on the hook and put the hook of another scale on the ring. As soon as I started pulling with the second scale, the hook slid until the two scales were exactly opposite of each other. The scales had to be opposite each other for the forces to balance each other so I couldn’t move one scale.

If I drew vectors to show the forces, the arrows would be the same length because both scales pulled with the same force. The arrows would point in opposite directions.

Adding a third scale causes the ring to shift. Having the same force with each scale balances the forces. Putting a ruler from the end of one scale to the next will create an equilateral triangle.

The second scale was attached to the table. I put the third scale’s hook on the ring and started to pull it. The hook slid around the ring until the three scales were the same distance apart around the ring.

Whatever force I pulled with on the third scale, the other two scales showed the same force.

Physics 11 Circular Motion

Things move in different paths. So far we’ve looked at straight motion and pendulum motion. What if a pendulum didn’t swing back and forth but went all the way around? This is circular motion. How is circular motion different from pendulum motion?

Question: How does circular motion work?

Materials:

String

Nut

Procedure:

Cut a piece of string 1.5 m long

Measure off 1.5 m of string. My string unravels easily so I put a piece of tape over the end to hold it together.

Put a loop in one end big enough to fit on your wrist

The loop at the end of the string needs to be big enough to slide over a hand but small enough to not slip off the wrist easily.

Tie the nut to the other end of the string [I taped the knot as my string doesn’t hold a knot well.]

The nut is tied to the end of the string. Be sure to secure the knot so it will not come loose while you are swinging the nut around. I used tape.

Measure up the string 0.5 m and make a small knot

The first knot is tied 0.5 meter from the nut.

Measure up the string 1 m and make a small knot

The second knot is tied at 1 meter from the nut.

!Warning!: Getting hit by the nut can hurt. Hitting something else with the nut can get you into a lot of trouble picking up broken things off the floor.

Put the loop around your wrist

Hold the string at the first knot

Swing the nut back and forth like a pendulum but keep adding force until the nut goes all the way around

Swing the nut around in a circular path several times

Stop the string

Hold the string at the second knot

Swing the nut back and forth like a pendulum but keep adding force until the nut goes all the way around

Swing the nut around in a circular path several times

Stop the string

Observations:

How did you have to move your hand to add force to increase the swing of the nut?

The nut swings at the end of the string. The hand holding the string keeps the nut moving at a fixed distance so it travels in a circular path.

Describe any differences for the longer string

Describe how it felt as the nut moved in a circular path

Describe any differences for the longer string

Conclusions:

Why do you loop the string around your wrist?

If you put a little bit of force into making the string swing, does the nut go all the way around?

Does the nut want to continue in a circular path or does it try to leave that path? Why do you think so?

What will the nut do if you let go of the string? If you decide to test this, be sure you are outside and not swinging the nut toward anything like a window. Take the loop off your wrist, swing the nut so it is going in a circle and let go of the string as it tops the circle. You can get a little idea of what it does by leaving the loop around your wrist, swing the nut by the first know and letting it go at the top of the circle. Be aware the nut could hit you when you do it this way.

Compare the speed of using a short string and using a long string. If you decide to time the swings, have a friend use the stopwatch. It would be easier to get an accurate time if your friend times three to five revolutions instead of one.

Try drawing the vectors to show how the nut travels in a circular motion. Remember one vector will follow the string as it holds the nut in the pathway. Which way will the nut’s forward vector point? Will it be curved or straight? Does gravity have much of an effect on this motion?

What I Found Out:

The nut was easy to put on the string. If it hits something breakable like a window, this is bad news. Keeping the string attached to my wrist and taping the knot holding the nut on the string made sure it couldn’t fly off and hit anything or anyone.

My hand swung back and forth to make the nut swing. This hand movement could turn the nut into a pendulum, even one that went very high. It did not make the nut go around in a circular pathway.

I had to move my hand in a circular path to get the nut to go around. With the short string, the nut went around very easily. It was very hard to slow down enough for the nut to not go around.

The longer string took more and bigger movements of my hand to get it started going around. If I slowed down at all, the nut would make only a partial circle and fall down toward the ground.

Once the nut was going around on the long string, I could make the same small movements with my hand to keep it going as long as I kept it going fast enough to go around.

I think gravity pulls on the nut. When the nut is going fast enough, gravity can’t pull hard enough to make it fall. If the nut slow down, gravity takes over and pulls it down.

I could feel the nut pulling on my hand as it went around. There was a bigger pull with the longer string.

When I let go of the string, the nut flew out away from the circular path. I had to keep the loop around my wrist doing this so the nut hit the end of the string and fell to the floor.

The nut was traveling fairly fast around the path making timing challenging. The short string gave me 3.09 sec and 3.06 sec for five times around. The long string times to 3.62 sec and 3.56 sec. The longer string seemed to give a longer time for each revolution. I would wonder how accurate this is because I could not measure the force used to make the nut go around so this may have been very different for the long and short strings.

There are three vectors interacting in circular motion. One points in to the center of the circle holding the object in its circular pathway. One is the pull of gravity. One is the straight line motion path the nut would take if the other two forces did not exist.

Drawing the vectors depends a little on where the nut is on the circular pathway. One vector arrow must point down toward my hand. I know this because I had to hold onto the string and felt the nut trying to pull free.

One vector arrow will point down toward the ground. This is gravity. It is a smaller arrow as the nut is going around, not falling straight to the ground.

The last vector arrow goes straight out from wherever the nut is. The nut is trying to go in a straight path. The vector arrow pointing to the hand keeps it from flying off so the straight vector is bigger than the gravity arrow and smaller than the one going to the hand.

Physics 4 Vectors

Forces hold things in place and make them move. Some of the forces we can see. Others we know are there but can’t see. We need a way to show all of these forces. That is what vectors do.

Question: How do vectors show forces?

Materials:

Paper

Pencil

Ruler

Procedure:

Open your Journal and write Project 4

Remember Project 1 where the block sits on the table

Draw a table with legs sitting on the floor

Your drawing doesn’t need to be fancy. A simple set of boxes will work like this will work fine.

Draw the block sitting on the table

Gravity pulls down on the block so draw an arrow pointing down from the block

Gravity pulls down on the block so it sits on the table. The vector arrow points down.

Note: Gravity always points toward the center of the Earth which is usually down

If only gravity was pulling on the block, it would fall to the ground so some force is pushing back on the block. The table is pushing back so draw another arrow next to the other arrow but pointing up.

The table pushes back against the block just as hard as gravity pulls it down so a vector arrow the same size pointing up is added to the block.

How long should this arrow be? Vectors show speed and direction. We are not measuring speed but only showing direction in this Project.

Gravity pulls down. If the arrow pointing up is longer showing greater force, there would be more force pointing up than down. The block would float up off the table. It didn’t so the arrow isn’t longer than the gravity arrow.

If the arrow is shorter than the gravity arrow, the force of gravity would be greater than that of the table. The block would pull through the table and fall to the floor. It didn’t so the arrow isn’t shorter.

The arrows must be the same length as the forces are equal and opposite to each other.

Since the table is not floating away, gravity is pulling down on the legs so a vector arrow pointing down is put in each leg.

Since the table isn’t floating away, gravity must be pulling down on it too. Draw vector arrows for gravity to hold each table leg on the floor.

The floor pushes up against the table legs just as hard as gravity pulls down on the legs so the arrows are the same length as those vectors but pointing up.

Since the table isn’t sinking into the floor, the floor is pushing back against the table legs. Draw those vector arrows.

A vector arrow showing the push on the block is added aimed at the block which was the direction of the force.

Next remember what happened when you pushed on the block. Your finger was a force acting on the block. Draw a vector arrow for that force.

Did the block move? Which way did it move? Since the block moved, there was no force pushing back against your finger so there will be no arrow.

Every pair of force vectors have the arrows equal and opposite except for the last pair. The pushing force arrow must be longer than the block resistance force arrow for the block to move.

Now wait a minute! When I pushed against my block of wood, the end of my finger flattened so the block did push back. But the block moved so the force the block pushed against my finger was much less than the push my finger gave the block. I will draw a little arrow from the block toward my finger.

Paper airplanes are fun to fly. They fly and fall because of forces pushing and pulling on them. Those forces can be drawn as vectors.

Now let’s draw vectors for a paper airplane:

Draw the airplane flying

What force made the airplane fly?

You threw it so you exerted a force on it. Draw that arrow pushing the back of the airplane.

Throwing a paper airplane pushes it forward so the vector arrow pushes against the tail end.

Is gravity acting on the airplane? Gravity acts on everything on Earth so draw an arrow pointing down for gravity.

Like the sheet of paper, air pushes up on the wings of the paper airplane so the vector arrow points up toward the wing.

What is pushing up on the wings to keep the airplane up? Air pushes up.

Does the air keep the airplane up all the time? It didn’t keep mine up. So there is an arrow for the air pushing the wings up but it is less than the gravity.

The paper airplane doesn’t fly forever so gravity pulls down on it which the vector arrow shows.

Where would the arrow for the fan pushing the airplane go? Draw it in.

Notice that this arrow is with the one from you throwing the airplane so the two add up.

When the air from the fan pushes the paper airplane, the vector arrow pushes against the airplane’s tail adding to the thrust vector from you throwing it.

Where would the arrow go for when the fan pushed against the airplane? For my airplane it would be the same length as the one for throwing the airplane because I did see it stop my airplane once.

When the air from the fan blows against the paper airplane, the vector arrow must point toward the airplane.

This last set of drawings shows one way vectors help a physicist understand the forces acting on an object. When forces act together, they add up. When forces act against each other, they cancel each other out.

Another way vectors show how forces work is shown with the car going down the ramp.

Draw the ramp with a car on it.

The car is racing down the ramp so the vector arrow goes down the ramp. Or does it?

The car is moving down the ramp so the vector arrow points down the ramp but is this correct?

Gravity is pulling the car down but gravity pulls straight down. So there should be an arrow pointing down from the car.

Gravity pulls down on the car so a vector arrow points down from the car.

But the car moved down the ramp. So there is another arrow from the tip of the gravity arrow to the ramp spot where the car will be after a certain amount of time.

The gravity arrow and the forward arrow meet at the vector arrow on the ramp’s point as the two add up to that vector.

In this case vectors show the movement of the car is made up of two different vectors, one pulling down and one pulling across.

About Vectors

Vectors usually show both direction and acceleration. They are a way to see how forces add and subtract from each other so you can tell where an object will go when several forces push or pull on it at the same time.

For now the accelerating force we will work with will be gravity. The next Project will look at some ways gravity pulls objects down.

Physics 1 What Is a Force

Be sure to start a Physics Journal to keep track of all your physics projects. Sometimes one Project will ask you to take another look at a Project you did earlier. A Journal makes this easy to do.

A physics journal doesn’t have to be fancy, just full of paper to write on. That way all or your observations are in one place, easy to find.

Physics can be very hard with lots of difficult math. But some parts of physics are much easier. Those are the ones we will be doing this year.

Physics tries to explain forces. What is a force? The easiest definition of a force is: A force is a push or a pull.

Since physics is about forces, we will start with some simple forces and how they work.

Question: What is a force?

Materials:

2 Small blocks of wood

Ball

Scale

Procedure:

Open your Physics Journal and write the Project number

In my Physics Journal I put only the Project number and question. then I list the observations, analysis and conclusions. If I did not have the materials and procedure on the computer, i would put those in my Journal too.

Set a block of wood on a table then leave the room

Left setting on a table a wood block sits there not moving.

Come back in the room and look at the block of wood

Did the block of wood move?

Push on the block of wood with a finger

Does the block of wood move?

Pushing on the wood block caused the block to move in the direction of the push.

Pull the block of wood using a finger

Does the block of wood move?

Hold the ball in your hand

Does the ball stay in your hand?

Drop the ball

What does the ball do?

Place one block of wood on the scale

Block 2 has a weight of 57.57 g. It wavered between 57.56 g and 57.57 g but finally settled on 57.56 g.

Place the second block of wood on the scale

Put both blocks of wood on the scale

Observations:

Did the block of wood move?

What happens when you push the block of wood?

What happens when you pull the block of wood?

What does the ball do in your hand?

What does the ball do when you drop it?

How much does one block of wood weigh?

Block 1 had a weight of 32.13 g.

How much does the second block of wood weigh?

How much do both blocks of wood weigh?

Analysis:

Add up the masses of the two blocks of wood

Together the wood blocks have a weight of 89.69 g.

Conclusions:

What makes the block of wood move?

Why doesn’t the block of wood float off the table?

Why does the ball sit in your hand?

A ball sits in the hand as long as it is held there.

Why does the ball drop when you let it go?

A contact force is a force you apply directly to an object. A non-contact force is a force applied to an object without touching it. Which of the forces applied to the block of wood and the ball were contact forces and which were non-contact forces? Explain why you think this.

Compare the masses of the two blocks on the scale and the two masses you added up. Do masses combine? Why do you think so.

Weight is a measurement of the pull of gravity. Do you think forces combine? Why do you think so?

What I Found Out

My block of wood didn’t move by itself. It did move when I pushed or pulled it. Pushing or pulling the block makes it move. It sits on the table because of gravity.

Pulling on the wood block caused the block to move across the table in the direction it was pulled in.

The ball sat in my hand because I was holding it until I dropped it. Then it fell down to the table. Gravity pulled the ball to the table.

This was not a bouncy ball. It fell to the table with a thud when I let go of it.

Pushing and pulling the block of wood were contact forces because I had to touch the block to make it move. Gravity is a non-contact force because it works without touching the block or the ball.

The total mass of the two blocks was 89.69g and the added mass of the two blocks was 89.69g which is the same so I think masses can be combined or added together. Gravity creates weight and is a force so I think forces can be combined.