TOP TEN FORMULAS AND EQUATIONS OF PHYSICS!

Top Ten Laws and Formulas of Physics

1.      Newton’s First Law

Newton’s first Law of Inertia states that an object in motion will stay in motion and an object at rest will stay at rest unless acted on by a net force. This concept is important because it is the basis for most physics concepts. An example of Newton’s first law would is used when you are in a car, and toss a coin up in the air. The coin will land in your hand and not behind you because the car, coin, and you are in motion and will continue to stay in motion until a net force acts upon you!

2.      Speed=distance/time

This concept is important to physics because it is the basis of many of the physics equations that we have learned throughout the year. Through this equation we are able to learn that Acceleration is equal to change in speed/time. With these equations, we were able to solve many physics problems. For example, if a car has gone 4 meters in 2 seconds, you can plug this information into the equation (speed=4/2) to find out that the car is going 2 meters a second.

3.      Distance traveled=1/2(acceleration x time²)

This equation, d=1/2 gt² was very important to learning about falling objects. Using the equations I had learned beforehand, I was now able to solve problems that asked me to find the distance that the falling ball had traveled. Know that I knew the basic physics equations, along with v=gt or velocity is equal to acceleration times time, I was able to solve most distance and time problems!

4.      Newton’s second law

      This law states that the acceleration of an object is directly proportional to the net force acting upon the object, and is in the direction of the net force which is inversely proportion to the mass of the object, or better known as Acceleration is proportional to net force/mass. This law was useful, because it was then that we began to learn about free fall. Using this equation I learned that in free fall, weight will be equal to resistance, so all objects no matter size of weight will fall at the same rate! While learning about this subject, we learned by example that a feather and a penny will fall at the same rate in free fall, because force of the object will be equal to the mass, so the acceleration will always be equal in free fall!

5.      Newton’s Third Law

Whenever one object exerts a force on another object the second object will exert an equal and opposite force on the first, or in a condensed version, every action has an equal and opposite reaction. This law is extremely important to physics because it is something that you don’t think about very often, but is needed for humans to live. Examples of newton’s third law would be if I was walking, I would push the floor backwards, and the floor would push me forwards, allowing me to walk, but the force would be equal and opposite. That is why, if I attempted to throw a piece of paper, it would not go very far because I can only exert a much force on the paper, as it can on me, and since it does not have very much mass, I cannot throw it very far!

6.      Work=fd Power=work/time

The formulas for work and power were very important to our class this year. While learning that work is equal to force times distance, we also learned that a Watt is how quickly work is done. This would later be beneficial to many of the equations that we would solve. By learning about power we could later apply this to how to power a light bulb through the equation I=V/R, but we would have not been able to find that out if it was not for the power and work equations. This concept showed me that in order to understand physics; you must understand all parts of the science.

7.      The change in Kinetic Energy is equal 1/2mv² and work

This formula is very important to our class because the change in KE is also equal to work. This equation allowed us to learn the answers for many questions such as how airbags keep us safe from getting hurt, to why there is padded grounding in gymnasiums. I learned that airbags keep us safe, because when you are in a car crash, you go from moving to not moving very quickly , and momentum is P=mv. The change in momentum is the same regardless of hitting the dashboard or the airbag. Because the change in momentum is constant, the J or impulse is constant also, so the airbag will increase the distance so that the force will be reduced in the equation J=f x the change in time, so the airbag will spread the force out over a longer period of time, making your chances of being hurt go down.

8.      Centripetal Force and Centrifugal Motion

While learning about these concepts, I learned that centripetal force is a center-directed force that causes an object to follow a curved path, while centrifugal force is the apparent outward force on a rotating body. I was able to connect these physics concepts by finding out the answer to why we move while in a turning car. I learned that centrifugal force doesn’t actually push you into the car door, but the real reason you hit the side of the car while turning is because NO force is acting upon you. Newton’s first law states that an object in motion will stay in motion unless a net force acts upon it, so in this case, since the car was moving in one direction and then changed, your body will continue to want to go in that direction but the car door will act as the net force that hits me and forced me to move towards the center of the circle that the car was making during its turn. Because of newton’s third law, I will push the door in, and the door will push me out, and so I will stay safely in the car.

9.      I=V/R

This formula states that current is equal to voltage divided by resistance. In order for current to flow there must be an electric potential difference. This is why it can be dangerous to plug an American appliance in into a European socket. European sockets have a much higher voltage, meaning there is a higher electric potential difference so there will be a lot of current running through the appliance. Our devices are not meant to have such a high amount of current running through them, so it may start a fire but because the European appliance expects a higher current, a lower current coming from an American appliance will not hurt the appliance or start an electrical fire.

10.   Opposite charges attract and like charges repel

We learned this concept while dealing with magnets. I learned that the charge of the

magnets always flows from south to north, and when opposite charges are near each other, they will be attracted, but if they are like charges, they will repel from each other. I learned that the reason your hair becomes frizzy after brushing it is because when you brush it, the brush will steal electrons from your hair, making your hair have a positive charge. Then the comb will become negative because of the stolen electron’s charge. We now know that like charges repel, and so your hair will stand up to get away from the other strands of hair.

Centrifugal Motion; The force that isn't actually a force!

Centrifugal Swingin' 

Category: Natural photo

              This picture demonstrates the physics that is incorporated when one swings on a swing. As you swing, your body will move with the swing, as the chains keep your body and the swing moving in a circular motion. Once you let go of the swing, there will no longer be a net force moving you in a circular motion, which was once the chains, and so your body will travel in a path tangential to the circle. On the other hand, as you can see, the swing will continue to move in the direction that it was before because no net force will act upon it. This notion is from Newton’s first law which states that an object in motion will stay in motion and an object at rest will stay at rest unless a net force acts upon it. This rule applies to both the swing and your body. In this case, the body will continue to move in the direction that is tangential to the circle until a net force acts upon it, which in this case will be gravity.

Magnets and more!

What I learnedThis section was a lot of fun! We started off by learning about magnets and electromagnets, and learned that a current carrying wire experiences a force when it is in a magnetic field. We also learned that change is very important to this section. In fact we learned that when a magnet moves through a wire, it changes the magnetic field thus inducing voltage and causing current. This is because in all objects, there are domains of atoms that spin, and when the domains are moving in the same direction, it creates a magnetic field, making the object a magnet. This shows that you can create and destroy magnets pretty easily by disrupting the direction of the domains by striking the magnetic object to align the domains. Going back, we started this section by learning about magnets. I learned that each magnet has a north and south pole, and that force always flows from south to north, so opposites will attract while like poles repel.  While still learning how magnetic fields work, we started the mini motor project! In this project we created our own mini motor, and learned how motors in general work. I learned that a motor works because a current carrying wire feels a for in a magnetic field. And in this case, the battery supplied energy for the current and the loop of wire and paperclips then carried the current to complete the circuit. The magnet supplied the magnetic field and so the wire loop felt a torue in the magnetic field when current ran through the wire when the side of the loop that was scraped of was vertical to the battery and magnet, thus the loop experienced a torque and turned, creating a mini motor! At this point we also learned how stoplights detect cars! In the ground there is a coil of wire in the pavement. So, when your car, which acts as a magnet runs over it the magnetic field, it will then change the magnetic field and induce voltage causing current. The flow of current then acts a signal for the light to change!  

 




 Connections to the real world…This section, I was able to connect many things to the everyday world! That’s what physics is about, isn’t it? One major thing that I learned was how security metal detectors work at the airport. I learned that they work, because throughout them, there is a coil of wire that carries a current in its own magnetic field, so when someone walks through the detector and is carrying metal, they change the magnetic field which induces voltage causing current to make a beeping noise to alert the TSA workers. Another thing that we actually took a field trip on that is a connection to the real world is how stoplights work, and it is actually very similar to how the metal detectors at the airport work. There are coils in the ground and your car acts as a magnet and changes the magnetic field in the coils, which therefore induces voltage and causes current acting as a signal for the light to change.

 


Problem solving skills….This section has not dealt with problem solving skills very much, but when working with transformers I was able to put my skills to work. By using the equations P=IV which means that for transformers the current of the primary times the voltage of the primary will equal the current of the secondary times the voltage of the secondary, so with this I am able to use the equation that states that the amount of voltage of the primary coil over the amount of turns in the primary coil is equal to the amount of voltage of the secondary of the turns of the secondary, so reverting back to Newton’s 3^rd law, every action has an equal and opposite reaction.

What I found difficult…This section, a concept that I felt was hard for me to grasp was how transformers work. I learned that transformers have coils of wire next to each other, where the primary has a lot of turns and the secondary has less turns, and the amount of turns is proportional to the voltage, so because there are less turns normally in the second than the primary, the voltage will be decreased, it that is your use for the transformer. The current running from the wall is alternative current, or ac which means that the voltage is constantly changing directions, and thereby changing the magnetic field and inducing voltage, creating current. The secondary’s magnetic field will change because of the change in the first’s magnetic field, and allow the transformer to work . It took some time for me to understand transformers, but after going over them with Ms. Lawrence, the subject was cleared up! Then, Going along with motors, it was difficult to see the differences between a generator and a motor. I then learned that a generators input was mechanical, while its output was electrical and made to work when the change in the magnetic field induced a voltage and caused a current, allowing the generator to work, but that a motors input was electrical, and it’s output was mechanical, and worked when the current carrying wire felt a force in a magnetic field. They really are two different things!

Motor Blog

Yesterday in class, we each learned how to create a working motor. We constructed the motor out of a battery, two paperclips, a coil of wire with the edges of the wire scraped off on the sides vertical to the battery and magnet. The reason that I did this was so that the wire loop could feel the torque caused by the magnetic field when current was running through it, and this occurred when only one side was scraped. I also learned that a current carrying wire feels a force in a magnetic field, and that contributes to the rotation of the coil in our project. The battery helped the motor by providing the flow of current into the paperclips, which acted as conductors. Then the coil of wire allowed the current to flow through the wire so that the force of the magnetic field was felt.  Finally, the magnet supplied the magnetic field so that the wire loop of coil would feel a torque when the current would flow through it, and turn. The rotation of the motor could be used to turn fan blades, blenders, car wheels, or really anything that rotates!

Click here to see my motor in action!

Ohm's Law, Circuits, Potential Energy difference and more!

Physics Review Blog

What I learned about….

In this section we started by learning about Charge. We learned that opposite charges attract and like charges repel. I then learned that electrons could be transferred in 2 different ways; direct contact and induction. To understand this way that charges work, we worked out some problems including why clothes stick together after being the dryer together. I found out that this happens because the clothes steal electrons from each other through friction, and some will be attracted to each other and stick. We then went on to learning about how lightning works, and induction. Induction happens when an object becomes charged without contact. Lightning is charged by induction and happens when clouds become negative through friction and polarizes them and they become polarized so that the negative clouds become attracted to the positive ground. Then the electrons attempts to find a path to the ground and once it is found, the energy will be released as thunder and lightning. Within this time, I learned about electricity and electric fields, which is the area in which a force can be felt. Electric potential is also the same thing as a volt. I then went on to learn about electric potential energy, which is stored to do work, and there must be a difference between the two to have current flow.

This encompasses ohm’s law, which states that I=V/R

Current and resistance are inversely proportional to each other.  In order to alter resistance, we learned some rules including           

-Increasing temperature increases resistance

-Increasing length increases resistance

-Altering the type of metal alters the resistance

-Increasing thickness decreases resistance

Then, we learned about circuits! During our lab we learned that when something is wired in series then, as bulbs are added on to the circuit, the length will add resistance and the bulbs will become dimmer, while if a circuit is wired in parallel, then the resistance will decrease and actually allow more energy to flow through the bulbs, and they will be brighter. We learned that homes and buildings are best wired in parallel because it protects the entire house from power going out because it isolates each circuit. Our lab encompassed some of what we had learned about circuits when we answered the question “Why does the circuit breaker in Lawrence often trip when the girls are getting ready for prom?” The answer to this question is the over use of the current will decrease from the resistance increasing making the current less able to flow because of the demand and so the circuit will become overwhelmed, and through the use of the fuse, the circuit will be shut off to prevent a fire.

What I found difficult…

This section, I feel as though we covered many different areas of physics, from basic electron behavior, to why lightning occurs, we had a broad section, but I learned a lot! One of the most challenging sections was when we learned about was polarization and induction. At first, these concepts did not make very much sense to me because I saw them as two very similar concepts. Then, after learning that Induction is when you bring a charged object near a conducting surface, the electrons inside the surface material will begin to move, and either be attracted or repelled by the object. Polarization is different because it is when one side of an atom becomes more negative or positive than the opposite side, causing charges to be attracted or repelled. Another question that was challenging to me was did the questions have to do with Electric voltage and the van de Graff generator. I learned that a van de Graff generator, although it has over 100,000 volts has low potential energy so a 120-volt outlet has a higher electric potential energy making the van de Graff machine less dangerous. Also we know that v=electric potential energy/charge, so you can have a high voltage object with low potential energy, which is what can flow through you and actually hurt you, so the Potential energy level is extremely important.

Problem Solving Skills…

My problem solving skills have definitely improved this section. When we learned the equations P=IV and I=V/R, I started having to identify the information given to me and plug it in to the equation in order to solve. I am now more confident in being able to solve equations, especially having to do with power and resistance because of this unit. During our labs, we experimented with light bulbs and circuits, which I found to improve my problem solving skills because getting each circuit to complete was similar to solving a puzzle, and when learning about series and parallel wires, the process got even more difficult, but I was able to work through all problems to find the working circuit.

Connections to everyday life…

This section I was able to connect many things that we learned to my every day life! One aspect was learning about circuits and how they work especially in homes, because before we learned about power and circuits I did not really know much about energy or direct and alternating currents. I learned that most houses are wired in AC and also they are wired in a parallel circuit, which means that the circuit can still be completed even if a bulb or outlet goes out while in series circuits, the entire circuit will break if one bulb goes out. Then we learned about fuses and why we have them! Fuses are used to regulate the current flowing through a circuit, and if the circuit becomes overwhelmed with current, the fuse will break and stop the circuit, potentially stopping an electric fire. 

Unit Reflection!

Chapter Reflection

What I learned….

This chapter we learned about many important concepts such as work, power, Kinetic Energy, Potential Energy, and the law of conservation of energy. First, we started off by learning about Work.

Work=force x distance

I learned that work is the effort exerted on something that will change its energy, and that no work is done on an object if it is carried parallel to the earth on a flat surface. A good example of a work problem is: If Tom carries a 10kg weight up a 10ft. high set of stairs, how much work is done?

Work=10(force)x10(distance)

=

100 Joules (work is measured in joules)

Next, we went on to learning about power!

Power=work/time (so essentially how long it takes you to get work done)

Now lets say it took Tom 5 seconds to get up the stairs. I would be able to solve by using the power equation

Power=100/5= 20 watts

After learning about power and work we began to learn about Kinetic Energy. During this I learned that the change in Kinetic energy is equal to the amount of work done.

KE=1/2mv²

Example Problem: How much work was done if a 10kg car was going 20 mph?

KE=1/2(10)20²

=2,000 joules

After learning about Kinetic energy I went on to learn about Mechanical Energy. During this section I learned that mechanical energy is the energy due to the position of something or the movement of something, and includes potential energy. I then learned that potential energy is stored energy held in readiness.

PE=mass x gravity x height

Then came the conservation of energy! The conservation of energy states that energy cannot be created or destroyed. It may be transformed from one form to another but the total amount of energy never changes. I a learned that energy in=energy out and work in=work out in this section. We then went on to learning about the work energy theorem which by using the equation for KE states that if for example a car is moving 2x the speed of another, it will take 4x as much work to stop, and if it is moving 4x the speed of another it will take 16x as much work to stop. After learning about the law of conservation of energy, we were shown an example of a pendulum swinging to demonstrate that an object cannot gain or lose energy. Each time the pendulum was swinging, it only reached the point that it was let go at, and didn’t go any further up because of energy’s conservation energy in=energy out.

What I found difficult…

This unit, I found that work and power were fairly easy concepts to grasp, but once we began to learn about kinetic and potential energy, I found the questions more demanding. Kinetic Energy, which equals ½ mv²  seemed easy enough to understand but once we began using the equations I felt more confused. Through practice though I was able to understand the concepts. Another concept I found difficult was the pulley system. It didn’t make sense to me at first how the system worked and how the force was cut in half when using 2 pulleys, but after going over the questions asked from the lab that we did involving Ms. Lawrence’s car, I felt as if the concept had been cleared up. This section I felt challenged by the class and mousetrap car, But through hard work I was able to understand the concepts.

Connections to the real world…

I feel as if every section in physics that we learn, I am able to find a stronger connection to in my everyday life. Perhaps this is because we build upon the lessons that we have already learned. This section I was able to connect the law of conservation of energy to, well, basically any object that uses energy. As we learned about the law of conservation of energy which states that energy cannot be destroyed or created, but only transformed. With this I was able to connect KE and PE to every day objects such as roller coasters! I learned that roller coasters are designed by using the law conservation of energy and by knowing that energy must equal energy out and the change in kinetic energy is equal to the change in potential energy, the coaster will not lose or gain energy, therefore the first hill is the largest so it will have the ability to get across the other hills, because the potential energy is the highest at the top of the hill, and lowest when in motion it will continue to maintain its energy and coast. I was also able to find connections to work and power when we first did the lab involving everyone running up the stairs, then walking, and then running with a weight.  I realized that the work is always the same no matter how fast you do it, but the power is the thing which actually changes. We then were able to calculate our horsepowers when running up the stairs which I though was pretty cool!

Problem Solving Skills…

Over this past section I believe my problem solving skills have improved. With the work and power problems finding the answers were fairly easy, but the kinetic and potential energy questions challenged me. Once learning that the change in KE=the change in PE and that work in=work out, solving the force problems got easier but were still arduous questions. Some of the problem solving questions that involve efficiency were also hard at times, but once I studied the material and took time to go over my notes to understand the concept better, I found that It was much easier to solve problems involving conservation of energy.

Final Mousetrap Blog

Final Mousetrap car report
a.     Newton’s first which states that and object in motion will stay in motion and an object at rest will stay at rest unless a net force acts upon it relates to the mousetrap car because It helped Natalia and I understand what the reasons for our law applies to the performance of my car because on our nonsuccess with the car due to friction. We learned that the car wanted to continue to move, but because certain things like the placement of the wheels got in the way, it was not able to go the 5-meter requirement. Newton’s second law, which states that acceleration is equal to net force over the mass of the object also relates to the car. During our journey, we realized that the car was not able to go very far because it did not have a big enough force exerted on it. Because a=fnet/m, we realized that we needed to add a greater net force in order for the mousetrap car to accelerate so we added a weight to the car. Once we added the weight, we noticed a significant improvement in the car’s speed and distance because it was given more acceleration. Newton’s third law also applied to our project. The third law states that every action has an equal and opposite reaction. I was able to connect this to the car’s situation because the energy that propelled the wheels was the energy that was derived from the mousetrap, and so the mousetrap's equal and opposite reaction was to accelerate. Another action and reaction pair that I noticed was when I pulled the actual trap backwards in order to wind the wheels up, the trap would push forwards. Going back to Newton’s first law, the trap wanted to stay at rest, but I was the net force that acted upon the trap, and so it was set into motion!
b.      The two types of friction present in the mousetrap car were the friction on the wheels against the ground and the friction within the axel and lever arm. On our car, friction was increased for stability on the wheels by using duck tape on the edges of the back wheels and rubber wheels on the front. In order to make sure the axel for the wheels would not rub the actual mousetrap we had to set them a significant distance apart, because if they were to touch, the car would apply friction to the axel and slow the rotation of the wheels down immensely. We also had to make sure that the wheels were able to turn easily on the laminate flooring, and so we chose to have rubber on the front wheels to provide traction and support, and duck tape on the edge of the back wheels to increase the overall stability of the car, which helped greatly!
c.      When deciding the number of wheels, we chose to have four because it would balance and stabilize the mousetrap, but we did not think the size of the wheels would be very important, but we were wrong. We started with two larger wheels at the back of the car and two smaller wheels at the front in order for the larger wheels to propel the smaller ones with more force, but still the wheels were only about 1-2 inches long, and relatively small. We began trying different ways to increase the speed in the middle of the mousetrap car process without realizing that the wheels might be the problem until the were end. Towards the end of our project, we decided to try CDs as our back two wheels because the more rotational inertia would mean the greater distance achieved in each rotation; which would ultimately make the car faster, and so the CDs with a cardboard support system were put on the mousetrap car, and did make the car measurably faster!
d.     The conservation of energy, which states that energy cannot be created or destroyed, but transformed from one form to another relates to how our car was powered. By having a long lever arm, we increased the amount of energy and torque within the lever, and as we pushed it further back, the PE was increased. Once we let go the PE transformed to KE and propelled the car forwards. Once we kept our lever arm the same, it was only a matter of properly winding the lever arm up and letting go carefully to power the car to go far distances, since the amount of energy in the car did not change. As the car was moving, it was using the spring’s energy and transforming it to kinetic energy, but while we were winding the car up, it was storing the energy as potential energy, for when the lever arm was let go.
e.     The length of the lever arm on the mousetrap car was an aspect of the car that changed frequently along with small changes with the car. We started with a relatively small lever arm, believing that the length would not matter for the 5m distance that was required, but as we progressed in the project, we realized that in order to go the distance, a much longer lever arm would be needed. Using kabob sticks, we connected the longer lever arm to the trap, but the more it was used, the weaker the wood became because the force of the lever arm was so strong. We made adjustments to the wooden stick and used a metal stick instead, which seemed to make the car go much faster. With the knowledge that torque=lever arm x force I knew that in order to make the car have more torque and eventually go faster, a larger lever arm was needed, and the force of the heavier metal stick propelled the car. The further back the car’s lever arm was pulled, the more force that was created, which made the power output of the mousetrap car greater.
f.      Rotational Inertia and Rotational Velocity and Tangential Velocity all related to the tires’ size and rotation. At the beginning, we used relatively small wheels that we got from the dollar store, but trial after trial, the car wouldn’t go very far, and I realized that if the rotational inertia was increased by having larger tires, and therefore having the wheels cover a larger distance per rotation, along with increasing the rate of rotation. To fix the wheel problem, we decided to use CDs as wheels and support them by putting cardboard around the wheels so that the wheels would be stabilized. Once the rotational inertia was increased with the larger tires, and it was covering a larger distance per rotation the car substantially increased in speed.
g.     We are not able to calculate the amount of work the spring does on the car because work=force x distance and in order to find this out we must know the force that the spring exerts on the car, which is impossible for us to find out without using special devices. Potential energy=mass x gravity x height, but the spring has a force of its own that we are not able to calculate. Because the change in KE=the change in PE, and we are not able to calculate the force, we are also not able to calculate how much KE and PE there is at one time while the spring does work. A=fnet/m, and although we know the mass, we still do not know the net force that the spring exerts on the rest of the car, and therefore we are not able to calculate the acceleration.
Reflection
a.     Over the course of the entire mousetrap project, our plans and car changed drastically. We started out planning on using much smaller wheels for our car, along with a lever arm that is about 3x as small as the lever that we ended up using. As we made adjustments, we learned what helped and did not help the car, such as larger wheels made the car cover a larger distance per rotation, and a larger lever arm increased the torque of the car, giving it the ability to go a longer distance. In order to succeed, we had to make the changes when we saw that our car was lacking speed and stability, and so we made the wheels much more stable with a support system made out of cardboard. I would say that we definitely learned from our mistakes.
b.     Starting out with smaller wheels definitely set us back, but when we decided to change the wheels for a larger set, even bigger problems we raised. We were not able to find stable wheels, and so we made them out of cardboard and paper cups. After trying the wheels out a few times, the car fell apart, and then we really needed to find more stable wheels that would not go lopsided while in motion. After finally finding 2 CDs as back wheels, we felt that we were prepared again to go forward in the competition once they had a secure support system of duck tape and cardboard sides.
c.      Seeing that we have yet to finish the car, in the future I would start out my making sure that my mousetrap had very stable wheels and a larger basis   for the car that uses more than just the trap in order to provide force and increase the work. Knowing what I know now, I would have also immediately increased the lever arm to hope that it would help propel the car more. Although the project was at times frustrating and challenging, it was fun way to incorporate everything that we have learned this year into a project!