Tangential and Rotational Velocity:
We started the unit by learning about tangential velocity and rotational velocity. My class found out that rotational velocity is about the number of rotations over a time. When talking about rotational inertia we discovered that if, for example, two kids are playing on a merry-go-round regardless of their position their rotational velocity is the same! So, does that mean their tangential velocity is the same? No! Tangential velocity depends on how far away the body is from the axis of rotation. If the body is far away from the axis of rotation it needs to cover a greater distance per rotation therefore it has a greater tangential velocity, the opposite is true for an object close to the axis of rotation.
tangential speed ~ radial distance x rotational speed
Rotational inertia:
Rotational inertia is the same as linear inertia but for rotating objects. Just like objects moving in a linear path, rotating objects do not want to stop doing what they are already doing. Rewriting Newton's first law we can say:
An object rotating about an axis tends to remain rotating around an axis unless interfered with by some external force and an object not rotating wants to remain that way unless an outside force is applied.
Rotational inertia depends on concentration of mass and how far is it from the axis of rotation. The furthest away the concentration of mass is from the center the greater it's rotational inertia is. I struggled to convince myself that the greater the rotational inertia the hardest it is to start rotating, I always wanted to say that it would start rotating sooner than an object with a small rotational inertia. The secret to understand this concept is always to remind yourself that the inertia is laziness and the lazier the object is the more reluctant it would be to start rotating!
The video above shows that because the hoop has it's concentration of mass away from the axis and the disk is solid (both have the same mass). The hoop has more rotational inertia and therefore is more reluctant to start rotating and therefore loses the race.
Torque:
After talking about rotational inertia we talked about torque which changes the rotation of things. It is important to know that torque is lever arm times the force (force = weight). The concept of torque is used to understand why some things are balanced and how to create a balanced system. The best example for this is a see-saw. If you have too people with different weights it is impossible to maintain the board balanced if they are both sited the same distance from the axis of rotation since for a system to be balanced there needs to be equal torques. To make the board balanced with different weights you need to increase the lever arm (lever arm = smallest distance from the axis of rotation) of the person with the least weight so that the torques equal. In practice the heaviest person of a see-saw needs to sit close to the center while the lightest one sits away from it
After a long year, and a lot of learning this is the ranking of my top ten real life examples for physics concepts.
1.Crumpled vs Flat sheet of paper: Both sheet's of paper are falling with air resistance, therefore they want to reach terminal velocity (f air = f - weight). There are two ways you can increase your f air: increasing surface area or increasing speed. The sheets of paper have the same weight, so they need the same f air to reach terminal velocity. The flat sheet of paper has more surface area, therefore it does not need to speed up to gain more f air. The crumpled piece of paper does not have the surface area needed to reach the f air needed, therefore it will speed up in order to reach increase the f air.
2. Balloon that sticks to the wall:
When someone rubs the balloon in someone's head the balloon picks up electrons from the hair and becomes negatively charged (by friction). After that, the balloon is placed against the wall. Because the wall is an insulator the electrons of the balloon will not be stolen by the wall, but the charges will rearrange in a way that the positive charges will move close to the negatively charged balloon, and the negative charges of the wall will move as far away from it as possible. This process of rearrangement of charges is called polarization.. You might be wondering why it sticks if there is also a force of repulsion between the like charges of the balloon and wall. Here is when Coulomb's law comes in handy! Coulomb's law says that distance is inversely proportional to force so since the opposite charges are closer together, the force of attraction is stronger than the force of repulsion, therefore the balloon sticks to the wall!
3. Roller Coasters:
Roller coasters work due to conservation of energy. The first hill is always the highest one so that it accumulates enough energy to go through all the elevations. As the car goes down, the PE goes down but KE goes up. If added together at any part of the ride, the KE and PE of the car will equal the PE that the car had on the first hill.
4. Balancing a see-saw:
If you have too people with different weights it is impossible to maintain the board balanced if they are both sited the same distance from the axis of rotation since for a system to be balanced there needs to be equal torques. To make the board balanced with different weights you need to increase the lever arm (lever arm = smallest distance from the axis of rotation, always perpendicular to force) of the person with the least weight so that the torques equal. In practice the heaviest person of a see-saw needs to sit close to the center while the lightest one sits away from it.
5. Fouette Turns
A ballerina turning is an example of conservation of angular momentum. The girl extends her leg and arms and that increases her rotational inertia (because her mass is farther away from the axis of rotation) and therefore decreases her rotational velocity since angular momentum is conserved.
6. Bouncing Ball vs. solid ball - Which can knock a block over?
The answer to that question is the bouncing ball! The reason why the bouncing ball knocks the block over is because there is not only one force acting on that block. Because of Newton's third law, we know that for every action there is an equal and opposite direction therefore ball pushes block, block pushes ball in both cases. The bouncing ball not only causes that force, the ball will bounce on the block adding another force that causes the block to fall over.
7. How to find out the height of a building
Go to the top of the building drop a ball from the top of it and record how long it took to reach the ground. Do this a few times plug in the average time for t in the how far equation (d = 1/2 gt2) and 9.8 for g! Do the math... and now you know how tall the building is!
8. Forgetting something on top of the car and driving away Have you ever stopped to observed that the object is at the same place it was before but on the ground? This concept is explained by Newton's first law! The object was at rest and therefore wanted to stay at rest, there was no outside force to stop it from doing so therefore the object continued in the same place but on the floor.
9. Best way to break a brick
In the equation J = f Δt , in order to prove that time determines the force necessary to achieve a certain
impulse, the impulse needs to be proven constant. To prove impulse is constant you need to state that
regardless of the time, the hand of the fighter is moving and comes to a stop therefore since the mass is
obviously the same and P = mv, the change in impulse is the same (ΔP = Pfinal - Pinitial). We stated before
that J = ΔP therefore J is constant! To continue to answer the question, you should now state that J is also
J = fΔt. Because of the last equation is possible to afirm that the smallest the time of contact the greater the force will be in order to achieve the constant J. Since to break a brick you need the greatest force possible, the time of contact should be as small as possible.
10. How a credit card works:
A credit card works because it contains magnets placed in a specific pattern. The credit card machine has coil of wires that cause a change in magnetic field when the card is swiped. This process is called electromagnetic induction. The change in magnetic field induces a voltage that creates a current that is used to signal your account information to the machine.
Tuesday, May 8, 2012
This is a contrived picture of a ballet step called an attitude turn. For this move the dancer needs to go from a position where she has her feet on the floor and knees bent to pushing up and lifting her leg in a 90 angle. In order to come up the dance pushes down into the ground, because of Newton's Third Law we know that for every action there is an equal and opposite reaction, that means that the floor also pushes the dancer up. Notice the arms of the dancer, one of her arms go up distributing her weight closer to the axis of rotation. That redistribution of weight reduces the rotational inertia and therefore increases rotational velocity, since the two are inversely proportional. The dancer's other arm is held beside her body and that helps her maintain her balance. The last thing the dancer wants is to have a torque in any direction, and since the leg needs to be held away from her body a torque is bound to occur, but the arms stand in a way to create a torque in the opposite way and therefore stops the dance from unbalancing as fast as she would have if her arms were simply by her side.
This Unit was all about magnetism and the benefits of this great discovery! On the chapter about electricity we learned that charged particles follow the Coulomb's Law - that means that the magnitude and the distance between two charges is the determinant of their attraction. When it comes to Magnetic Force the motion of the charged particle are also very important.
Every magnet has a south and a north pole, just like electrical charges, opposites poles attract and like poles repel. It's important to remember that if there is a south pole, there is a north pole and the other way around - one cannot exist without the other. For because north and south pole can't ever exist without each other if a magnet was broken, regardless of the number of times, all pieces would have a north and south pole and therefore they would remain being magnetic. The space around a magnet is called a magnetic field.
The earth itself has a magnetic field! This magnetic field explain why we only see the northern lights on the poles of the earth and not in the equator. Cosmic rays move towards the earth, and in the equator that movement is perpendicular to the earth's magnetic field, while in the pole it is parallel. When the rays move perpendicular there is a force of repulsion that causes the rays to be repelled by the magnetic field. When the rays move parallel there is no repulsion force, therefore the rays come in and are the lights we see!
The earth's magnetic field is also the reason why a compass works. The key to a compass is a magnetized needle that is free to move. The needle will line up with the magnetic field of the earth and point north and south. If you want to build a compass, this is how you can do it!
The picture above shows the direction of the field outside the magnet - it goes from north to south pole. Do not assume that the direction of the field is the same inside the magnet! Inside the magnet it moves from south to north pole. In order to understand why some things are magnetized and others are not, it is helpful to understand what domains are. Domains are a cluster of atoms spinning in the same direction. A bar of iron, for example, is composed of many domains. The difference between a magnetized and a nonmagnetic iron bar is that the first one has its domains aligned with each other. Have you ever used one of those magnetic paper clip holders, like the one bellow?
If yes, have you ever noticed that the paper clips do not only stick to the holder but to each other? That is because the paper clips have become magnetized, meaning that their domains are in line with the domains of the magnet in the paper clip holder. The paper clips now have a north and south pole as well and therefore are magnetized!
We also learned about electromagnets in this unit. Electromagnets are simply a current carrying coil of wire. They are really powerful and therefore are used, for example to lift up cars in a junk yard or to levitate trains!
After learning about electromagnets we learned about an important concept that is the reason why a motor works. That concept is: A current carrying wire feels a force in a magnetic field. The direction of the force can be easily determined by the right hand rule (picture in previous post). A motor works by this exact idea. There is a current carrying wire (current provided by the battery), a magnetic force due to the magnet and therefore there is a force that causes the copper loop to turn. For a more detailed explanation of motors, check out the previous post about building a simple motor.
The rest of the unit was based on electromagnetic induction! Electromagnetic induction happens when a magnet moves close to a wire (or the other way around) and therefore changes its magnetic field. The change in magnetic field results in the induction of voltage and therefore the creation of current. This concept is what explains the coils of wire on the floor in front of the traffic lights and the function of transformers. When cars drive by the wires on the floor, it acts as a magnet and therefore changes the magnetic field and induces a voltage. That induced voltage creates a current that signals the light to change.
A generator has a magnet and a coil of wire that receive the input of some type of mechanical force, the magnet creates a magnetic field that is changed when the coil of wire moves towards it. The change in magnetic field induces a voltage that creates a current.
A transformer changes the voltage from a primary source to a secondary. The voltage is changed by using the idea of power (P = IV) and the number of turns on each side of the transformer. The number of turns (loops) in the transformer is the determinant of the output voltage. If the secondary has more turns than the primary the transformer steps up the voltage, if it has less it will step down the voltage. A transformer works on the principle that a current carrying wire feels a force in a magnetic field. With AC current there is a change in the magnetic field that induces voltage and creates current. Because of the difference in number of loops the ratio of current vs. voltage can be changed to fit the needs of an appliance. A laptop, for example, needs less current than the one coming from our outlets therefore it has a transformer that changes that voltage before it harms the computer. We learned about two equations related to transformers:
number of turns/voltage = number of turns / voltage
IV primary = IV secondary
The first equation can let you find out how many loops of wire a transformer needs to have in order to step up/ step down a voltage. The second equation serves to find the amount of current or voltage on the transformer.
Reflection:
One of the hardest things of this unit was to remember the difference between a generator and a transformer. My teacher made the table bellow that was really helpful in understanding the difference between the two.
Besides that, the unit was simple. The idea of a compass confused me at first but after our review I understood that the needle of the compass lines up with the earth's magnetic field, or a stronger field - like on ships or big metal things that have not been moved.
What do you need to build a motor, and the function of it:
It is amazing to find out that to build a simple motor you only need: paper clips, a battery, copper wire and a magnet. With a motor like the one we built in class you could build things like a blander, a fan or anything else that relies on a spinning axle.
The copper wire is used to create a loop that is held above a magnet. A current flows through the paper clips on each side of the battery to the copper wire, which completes the circuit.
The magnet creates a magnetic field that works to works with the current to form the force that will cause the copper wire to spin.
The Picture above gives a visual representation for the reason why the copper wire is forced to spin. Like we said before the battery provides a current that is conducted by the paper clips to the copper loop. That current moves through one side of the loop and back through the other. The magnet is placed on top of the battery (under the loop) and creates a magnetic field that points up. If we use the rule that is exemplified by the hand above we can find out which way the force, resulting from the current and the magnetic field (A current carrying wire feels a force in a magnetic field), will push. That is the way we can determine where to scrape the armature. This step, which does not seem too important, is a main component in the function of the motor. By using the finger rule we decided to scrape when one side of the loop is vertical to the battery, because that is when the force would push the loop in a way that it would cause it to turn. Here is a link of my motor! http://www.youtube.com/watch?v=ZmY9sdaeWWI
This unit was all about energy electricity! We learned how lightnings work, how are houses are wired, why energy flows, what voltage is and much more! One of the first things we established and that helped us through the entire unit was that opposite charges attract each other, and like charges repel. Charges can never be destroyed, only transferred and electrons (negative charges) can move better than protons (positive charges) because they are not bound to the nucleus as the protons are. After learning the relationship of charges we establish what we call Coulomb's Law represented by the equation:
F = (K q1q2) /d²
Coulomb's law means that the closer something is to another, the greater the force between them is - Distance is inversely proportional to force.
Electric fields was a concept that I did not understand in the beginning of this unit. I latter found out that it was simply the area where a force can be felt. The complicated pictures with arrows only symbolized where a positive test charge would move. The equations for electric field are:
E = F/q
and
E = (K q1q2)/d²
Another concept learned was the difference between a insulator and a conductor. Conductor's electrons are free to move and an insulator's electrons are closely bound to particular atoms.
Now we can put together Coulomb's law, the relationship of charges and the concept of insulator and conductor we can explain why a balloon can stick to a wall for example.
Here is why the boy can stick the balloon to the wall after rubbing it to his sister's hair. When he rubs the balloon in the baby's head the balloon picks up electrons from the hair and becomes negatively charged (by friction). After that, he puts the balloon on the wall. Because the wall is an insulator the electrons of the balloon will not be stolen by the wall, but the charges will rearrange in a way that the positive charges will move close to the negatively charged balloon, and the negative charges of the wall will move as far away from it as possible. This process of rearrangement of charges is called polarization. The illustration bellow shows what the charges of the balloon and the wall look before and after polarization. You might be wondering why it sticks if there is also a force of repulsion between the like charges of the balloon and wall. Here is when Coulomb's law comes in handy! Coulomb's law says that distance is inversely proportional to force so since the opposite charges are closer together, the force of attraction is stronger than the force of repulsion, therefore the balloon sticks to the wall!
The same idea that explains a balloon sticking to the wall can explain why the comb of the video bellow can attract the water. The comb is negatively charged and the water is neutral. The charges of the water become polarized and because of Coulomb's the attractive force wins once again!
There are many ways of charging an object, one of them we already mentioned before and that is friction. When something rubs against another electrons tend to be transfered therefore charging it through friction (like the balloon that picked up electrons from the hair). Another way of charging an object is byinduction; induction happens when something is charges without touch.An example of induction is the formation of lightings. Lightning is caused by a combination of facts. All starts when clouds rubb against each other and the bottom of the clouds become negatively charged by friction. The negative charges of the clouds attract the positive charges of the ground by induction, because opposite charges attract. Like charges repel, therefore the negative charges of the ground will go deep into the ground. The attraction of the electrons of the clouds and the protons of the ground is so great that the charges create a path so that they can travel from cloud to ground and ground to clouds. This exchange of charges emmits the light we see and call lightning.
We can't avoid having lightning strikes, but how can you protect your house from them? Lightning rods can protect your house of the damish lightnings can cause. For an unknown reason, positive charges build up on sharp points and that is exactly what lighting rods have. The rod will be placed on your roof and because of the positive charges that build up on it when there is a lightning the electrons from the clouds will be attracted to those charges. When the lightining strikes the rod the charges will flow through a metal wire that will ground the charges protecting your house from it.
From the begging of the unit we learned that for charge to flow there needs to be a complete circuit, and later on we learned that for current to flow there also needs to be an electric potential difference. The voltages from one place to the othere needs to be different.
A capacitor is what makes the potential difference to create a circuit. It builds up electric potential difference by having two oppositely charged plates (they are attracted to each other). This is the mechanics behind a defibrillator and the flash on a camera. In a defibrillator the electric potential difference is build between the plates, and the circuit is complete when they touch the patient's body. The energy flows through the person and the defibrillator needs to charge, so that the electric potential difference can be built up again.
When talking about how current flows we learned that voltage doesn't move through a circuit but "pushes" current through. We also learned about resistance it is basically how much an appliance oposes the passage of current through a circuit. Resistance is not the only determinant of resistance, here are some other factors:
Length (the longest the more resistance)
Width (The wider the less resistance)
Temperature (The hotter the more resistance)
Material
After learning this deffinitions we found out that:
Current = Voltage / Resistance
With the equation above is easy to analyse the affect of resistance in current. Now you can explain why light bulbs blow right after they are turned on because you know the effect of a cold temperature to resistance and the effect of resistance to current.
Power = Current x Voltage
This equation relates to watts. You will probably come across a light bulb that has a label saying how many watts it uses. Withe the equation above you can find how much current passes through the circuit for each light bulb therefore you can find how bright they are.
We talked a lot about this equation when we tried to figure it out why a van de Graaff generator, that has a high voltage, doesn't hurt you, but an outlet that has a much lower voltage does. We stablished that what hurts you is not volte but energy. We used the equation above to plug in the voltage and charge in order to find how much energy the outlet, and the generator had. We found that the generator has a small energy and the outlet has a big one therefore it is safe to touch the generator but not the outlet.
The last thing we learned about was parallel and series circuits. In the image above you can see an example of series circuit (left) and a parallel circuit (right). The main difference between the circuits is the effect of switching one of the appliances off. In the series circuit all appliances would go off if one got of'; in parallel the other appliances would keep on working. Because of that, our houses are wired in parallel. We also discovered in a lab that a parallel circuit has more "lanes" and therefore the resistance is lower and since I = V/R the current is greater. Series has more "stoplights" therefore the resistance is higher and current is lower. We said earlier in the post that current is directly proportional to the brightness/efficiency of an appliance, therefore the bulbs in parallel would be brighter than the ones in series. Another important thing to remember is the role of fuses in a circuit. Fuses are wired in series and they are sensitive to the amount of current in that circuit, if the current gets to high so that it becomes dangerous, the filament of the fuse will break causing the current to stop flowing. That might be extremely annoying if it happens in your house, but is saving you from a possible fire. But why would the current go up? In a parallel current the more appliances you plug in the system the higher the current will get! In a series circuit on the other hand, the total current remains the same and the individual goes down.
Reflection:
What I found the most difficult in this unit was connecting one concept with the other. Because the unit was long, it was hard to remember equations and to what they related to. The idea of voltage, electric potential energy, and electric potential sometimes seemed to be the same exact thing. The way I overcame this problems was by making many mistakes in homework assignments and quizzes, and looking back to my notes after that and finding out what I did wrong. Coming in for help and asking questions also was a great tool to finally understand this sometimes confusing topics.
Newton’s First Law states that an object at rest wants to stay at rest and an object in motion wants to stay in motion unless an outside force acts on it. Newton’s first law can be observed in a mousetrap car because is evident that the car does not want to move until an outside force acts on it, and then it takes another outside force to make it stop moving, the force of friction. Newton’s second Law states that a = Fnet/m. That Law is also noticeable in the cars because none of the cars of our class were heavy. All of the students made their cars light and that works because the more massive your car is the smaller the acceleration will be. Newton’s third Law states that for every action there is an equal and opposite reaction. As the mousetrap car moved across the floor, gravity was pushing it down and the car was pushing the floor up also, car pushes floor backward, floor pushes car forward. My partner and I decided to use four wheels to keep the car balanced; its center of mass needs to be under its base. We first chose to use small wheels but after many failed trials we decided to switch them to large wheels. Large wheels worked better because they have less rotational inertia so they are easier to start and they are a lot more stable. They have less rotational inertia because their mass is more evenly distributed. Friction between the wheels and the floor is necessary to propel the car forward but air resistance or the lever arm dragging on the floor is something you want to avoid. Conservation of energy means that the energy in is equal to the energy out. On the mousetrap car the extended lever adds Potential Energy to the car. When the mousetrap car is moving the lever arm moves down losing potential energy and gaining Kinetic Energy that through the string attached to the axle of the car is used to turn it and move the car. We first started using a short lever arm and at the end we decided to use a lever arm a lot longer than the first one. A longer lever pulls more string and that makes the axle spin better. The farther the string is pulled the more energy is given to the axles.Rotational inertia and velocity are a factor when it comes to the wheels of the car. You do not want the wheels to be like a loop because that would make the concentration of mass be in the outer part of the wheel increasing the rotational inertia. The more rotational inertial something has, the more resistant to a change in motion it will be. Tangential velocity has to do with the radial distance and rotational velocity, the larger the wheel the more tangential velocity it will have. The rotational velocity also needs to be as great as possible, that means the axle needs to spin fast! With the combination of a big wheel and an axle that spins fast, the wheels should have a great tangential velocity.
Reflection: Our design changed a lot from the begging of the project to the end. The size of the wheels were the main change. We started with small wheels that did not even make the car move at all. After that we change to large wheels on the back and small wheels on the front. We found that in order for the string to spin the axle, it had to be taped to the axle and that a larger lever arm is more effective than a short one. The changes were made because our original design was not causing the car to move. Another big problem we’ve encountered was making the wheels stables enough. By using only tape and cardboard wheels it is difficult to make the wheels stay in place. The solution we found to this problem was to tape the wheels to the axle on the outside and inside of them. If I had to do this project again I would start with large wheels a large lever and a more stable base. I would also spend more time planing which materials to use so it would save me time on the construction.
Work:
The first thing we talked about in this unit was about work! Work is the effort put n something that changes its energy. The equation for work is;
work = fd
It is really important to remember that the force and distance of the equation above have to be parallel! That mean that if someone is walking around (on a flat surface) carying a tray he is not doing any work on it. The distance the person is going is perpendicular to the force that is pushing the tray up. Now imagine that someone is walking up the stairs, the distance now is parallel to the force, that in this case is the weight of the person. Remember that if you were to calculate the work done by the person climbing up the stairs you wold use the distance from the very top straight down, not the diagonal extension of the stairs! What matters in the stairs scenario is how far up from the ground you are, not how much distance you walked. Remember that if you are pushing against a wall, you are not doing work on the wall since its not moving, but you are doing work within yourself inside your body.
Power:
Power is a rate of how fast work is being done! The equations for power is
Power = work/time
Imagine that there is a race up the stairs and both participants have the same weight (force is constant), which of the competitors would have more power? The one that won the race! The winer of the race would have more power because he would have done the same amount of work (since the distance and force are constant) in a shorter amount of time!
Potential Energy:
Pontial Energy is the energy of possition, is the energy stored in "readiness", the energy that has the potential of doing work. Because Potential Energy is the energy of possition, ther higher something is from the ground the more PE it has! The Equation for Potential Energy is:
PE = mgh
Kinetic Energy:
Kinetic Energy is the energy of movement! The faster something is moving the more kinetic energy it has. The equation for Kinetic Energy is
KE = 1/2mv2
Another important thing to remember about KE is that the change in kinetic energy is equal to work. Therefore...
change in KE = fd
Work = 1/2 mv2
Conservation of Energy:
Conservation of Energy's simple deffinition is enegy in is equal to energy out! Based on that deffinition we can talk about the relationship between the kinetic energy and potential energy. Let's say that there is a person jumping from a rock to the sea, when the person is on the top of the rock and about to jump he has PE. When he jumps from the rock he loses height and therefore loses PE (PE = mgh), but since we have established that energy in is equal to energy out, the energy can't be lost right? Right, the energy is being transformed from PE to KE. Now the person does not have as much height but it is a greater velocity therefore no energy is lost, it is only transfered.
The same idea applies to roller coasters, the same hill is always the highest one so that it accumulates enough energy to go through all the elevations. As the car goes down, the PE goes down but KE goes up. If added together at any part of the ride, the KE and PE of the car will equal the PE that the car had on the first hill.
Machines:
Machines can be understood by using the concept of conservation of energy. We said earlier that energy in = energy out and that change in KE = work. That means that the work in also equals the work out! A machine works by increasing the distance you put in in order to decrease the force (work = fd). To decrease the force you have to exert, you will have to pull for a longer distance and the distance that the object will move will be smaller that the one you pulled. Regardless of how the distances turn out to be the work in wil always equal the work out.
Efficiency:
In real life no machine works with 100% efficiency. There is always some energy that is transformed in something else, like in heat due to friction. The efficiency of a machine can be meassure by dividing the energy output by the energy input.
Reflection:
The first part of this unit was easy to understand. The concept of work seemed easy enough to understand. On the quizzes about work tough... I fell for every single one of the questions that asked how much work someone walking with their books is doing. No work, the answer is no work! I found it hard not to be ready to plug in numbers that were given to me before analising if there was any work being done at all. When question asked for me to say what would happened to the work if the velocity was doubled I also got a little confused but after going over on of those questions with my teacher I now know what to do! The questions about the change in kinetic energy, when the velocity went from a number to another also tricked me. I made the mistake of calculating the difference in velocity first and using that number in the kinetic energy formular, while I learned that I should have calculated the kinetic energy of each individually, and then found the difference. This energy was easy in theory but complicated in practice but after looking back to some quizzes I found out what mistakes I made and now know what not to do!
Once again the construction of the car did not go as smoothly as we imagined... We drilled a whole and added the four eye-hooks and then tried to cut the axle out of the wood stick we bought. We planed on connecting everything with the zip ties, but that was the part that did not work as predicted. We all of the four wheels on the axle and placed one zip tie of each side of all the wheels. The wheels did not move out of place but they did not spin faster either. Mrs. Lawrence than suggested that we used tape instead of the zip ties, and that idea in fact was a lot more effective. My partner and I also observed that the wheels were not aligned, and that might also be the reason for the them to be unstable. We took everything apart and made sure that the axle were of the same length, and started to put the same amount of tape on each end of the wood stick so that the wheels are the same distance from the car. That was when our time was done!
The first day of construction of the car did not go as me and my partner expected... We began by trying to get the wheels off the toy car we bought. The wheels did not seem to want to come out at all, and soon we found out that it was because the car was a remote controlled so it did not have an axle! That was a big disappointment because we planed on using the axle from the toy car on our mouse trap car. We were finally able to take the wheel off and decided to use the wood stick, we had bought for extending the lever of the mouse trap, as the axle. We drilled a whole on the four wheels so that they fit through the wood stick, and on the mouse trap so we could insert the eye hooks on the second construction day. Our first day of construction was not as easy as I expected it to be, but we ended up figuring out how to make it work! Looking forward for the second day of construction!
My partner and I had no idea how to build a mousetrap car so we looked up some videos on the internet and found this tutorial that was really helpful on understanding what we had to do. One interesting thing about the mousetrap car on the video is that the frame is the mousetrap! My partner and I thought that might be a really good idea to not use a frame so the car would be lighter. We plan to follow the video but make a few adjustments. We are going to start with the eye-hooks and the wheels from toy car seemed to work pretty effectively. Extending the lever was also something we saw be done on every video about mousetraps so we plan to do that too. The one thing we did not like about the way the car from the video bellow was built was that the wheels could move from left to right and that can cause the car to curve. To solve this problem we thought that we could maybe use zip ties on each side to keep the wheel from shifting without stopping them to turn. So our plan step by step is:
1. Buy eye-hooks, rubber bands, wood stick, two toy cars (with different sizes of wheels) and zip ties;
2. Unlock the mousetrap;
3. Lengthen the lever with the wood stick and attached with three zip ties;
4. Make a whole on the sides of the mousetrap with a pin and place the eye-hooks on the wholes;
5. Take the wheels out of the toy cars and put the larger wheels though the eye-hooks on the back side of the car and the small one in front;
6. Fix the wheels with a zip tie on each side of the wheels so that it wont move side to side and put the rubber bands around each tire;
7. Attach the string;
8. Win the race!!!
Tangential and Rotational Velocity:
We started the unit by learning about tangential velocity and rotational velocity. My class found out that rotational velocity is about the number of rotations over a time. When talking about rotational inertia we discovered that if, for example, two kids are playing on a merry-go-round regardless of their position their rotational velocity is the same! So, does that mean their tangential velocity is the same? No! Tangential velocity depends on how far away the body is from the axis of rotation. If the body is far away from the axis of rotation it needs to cover a greater distance per rotation therefore it has a greater tangential velocity, the opposite is true for an object close to the axis of rotation.
tangential speed ~ radial distance x rotational speed
Rotational inertia:
Rotational inertia is the same as linear inertia but for rotating objects. Just like objects moving in a linear path, rotating objects do not want to stop doing what they are already doing. Rewriting Newton's first law we can say:
An object rotating about an axis tends to remain rotating around an axis unless interfered with by some external force and an object not rotating wants to remain that way unless an outside force is applied.
Rotational inertia depends on concentration of mass and how far is it from the axis of rotation. The furthest away the concentration of mass is from the center the greater it's rotational inertia is. I struggled to convince myself that the greater the rotational inertia the hardest it is to start rotating, I always wanted to say that it would start rotating sooner than an object with a small rotational inertia. The secret to understand this concept is always to remind yourself that the inertia is laziness and the lazier the object is the more reluctant it would be to start rotating!
The video above shows that because the hoop has it's concentration of mass away from the axis and the disk is solid (both have the same mass). The hoop has more rotational inertia and therefore is more reluctant to start rotating and therefore loses the race.
After talking about rotational inertia we talked about torque which changes the rotation of things. It is important to know that torque is lever arm times the force (force = weight). The concept of torque is used to understand why some things are balanced and how to create a balanced system. The best example for this is a see-saw. If you have too people with different weights it is impossible to maintain the board balanced if they are both sited the same distance from the axis of rotation since for a system to be balanced there needs to be equal torques. To make the board balanced with different weights you need to increase the lever arm (lever arm = smallest distance from the axis of rotation, always perpendicular to force) of the person with the least weight so that the torques equal. In practice the heaviest person of a see-saw needs to sit close to the center while the lightest one sits away from it as the Figure 1 shows.
Center of Mass/Weight and Stability:
Center of mass is the average position of all the mass that makes up the object. If the object is symmetrical the center of mass is at the geometrical center. Center of mass is called center of gravity when weight is involved. To balance an object one needs to hold it on the center of mass and that will support the entire object and thus it will be balanced. Stability has everything to do with center of gravity. If the center of balance of an object is directly above it's base it will have balance if it is not it is unbalanced. The concept of center of mass and stability explains why you lean forward when carrying a heavy backpack, you want to keep your center of mass over your feet so you can keep your balance. The boy in the picture above is not leaning forward and that is why he feels unbalanced. If he can shift his center of mass so that is over his feet maybe he can make in time for class!
Centripetal Force and Centrifugal "Force":
Centripetal force is a force directed towards the center. If you have a can and a sting that your swing above your head you can notice the effect of centrifugal force. Even though you may think that there is a force pulling the can out there is only the force of tension of the string pulling it to the center. When talking about centripetal force we used the spin cycle of the of a washing machine as an example. The fact that the clothes are drier after the spin cycle is explained because the water and clothes have the same tangential velocity the water can go through the wholes in the side because there is no external force stopping them from continuing moving in the straight line they want to keep following since it has inertia. The sides of the washing machine provide a force of friction on the clothes that for that reason are pushed inward (centripetal force). It is possible to think that there is a centrifugal force on the clothes on the washing machine since they stay up against the washing machine walls but centrifugal force does not exist! The clothes seemed to be pushed outward because of the combination of the velocity of the clothes that is tangential to the circle with the friction force from the walls of the washing machine.
Conservation of Angular Momentum:
Just like linear momentum angular momentum is also conserved. The fact that angular momentum is conserved allows us to establish a relationship between it's two component: rotational inertia and rotational velocity. Angular momentum is rotational velocity times rotational inertia, since angular momentum is conserved they have a inversely proportional relation. The inversely proportional relation means, in other words, that if rotational inertia increases rotational velocity will decrease and the other way around. The ballerina on the video bellow is an example of conservation of angular momentum. The girl extends her leg and arms and that increases her rotational inertia (because her mass is farther away from the axis of rotation) and therefore decreases her rotational velocity since angular momentum is conserved. The ballerina probably has no idea but the fact that she decreases her velocity after every turn allows her to be able to put her foot flat on the ground and regain balance to do another pirouette.
Reflection:
This unit was probably one of the trickiest on the sense that all the concepts seemed to overlap. When trying to answer homework questions it was sometimes difficult to understand which concept to use. After some practice it became easier to distinct what concept the question was actually asking about. I struggled understanding how the train wheels work, what helped me to understand this was reading about on the book again. After reading about it I figured out that it was all about different tangential velocities and that they cause the train to self correct along it's way.
The objective of this lab was to use a meter stick and a 100g lead weight to find the mass of the meter stick. My original plan was to find the lever arm of the meter stick with the weight and than calculate the torque by using the equation torque = lever arm x force. My plan did not work because I did not know that the force that had to be used for this equation was only the force of the lead weight and not the force of the lead weight plus the force of the meter stick as I previously thought. When me and my partner started to try different approaches to finding out the mass of the meter stick we both agree that the torque of the meter stick would equal the torque of the lead weight. (torque1 = torque 2 / force x lever arm = force x lever arm) since the meter stick was balancing. From that point we started to try finding the numbers that had to be plug in to find the weight of the meter stick. We knew that force in this case would equal the weight of the meter stick and the other force would equal the weight of the lead weight. We balanced the meter stick with the lead weight on the edge and found that the lever arm for the that side was 29 cm and assumed that the lever arm for the meter stick alone would be from the axis of rotation to the end of the stick (51 cm). Thinking we finally got the right result we wrote down the equation:
This was not the right result! After struggling some more we noticed that the force could not be in grams therefore the force had to be converted to newtons. We used the formula w = mg and found out that the force was 0.98 Newtons. That was not our only mistake on the equation above. Miss Lawrence explained that the lever arm for the the meter stick was not 51 because that was not the measure from the center of mass of the meter stick to the axis of rotation. To find the correct lever arm we balanced the stick without the weight and than measured the distance between the distance from the axis of rotation of the system to the center of mass of the stick and we got 21.2 cm. Now that we had all the correct number we plug them all in the previous equation:
When I got to this result and converted from weight to mass (w = mg) and got 0.136 I though I got the wrong answer again since a meter stick could not be 0.136 grams. Ms. Lawrence than pointed out that my answer was not in grams but in Kg so it was actually 136g which makes a lot more sense.
