Energy is a word we hear often but what is it? Well in technical terms, energy is the ability for a physical system to produce changes in another physical system. There are a many types of energy as there are a variety of ways to produce changes. They include thermal, gravitational potential, chemical, elastic, and sound energy.
Thermal energy are changes in the temperature. Gravitational potential energy is energy stored in an object when it is above the surface of the Earth, which means that the object has the potential to do work or in this case fall down. Chemical energy is a form of potential energy and is stored in food, fuels, etc and could be released in different forms by breaking it down. Elastic potential energy is when force is applied to elastics since they will spring or bounce back and has the potential to return the energy. Sound energy is simply the energy used to produce sound or vibrations through whatever medium.
Wednesday, December 15, 2010
The Physics Behind Rollarcoasters
Rollarcoasters are large rides that we enjoy in places like Wonderland but what are the physics behind such a device. What keeps these large rides moving? Well, since a rollarcoaster are moving objects they must also obey Newton's three laws among other things. If one looks at a rollarcoaster they should notice that they all seem to begin with climbing a large hill. Well thats because rollarcoasters make use of something known as kinetic energy and potential energy. Potential energy is energy stored inside an object that could potentially be used to move the object. By moving the rollarcoaster up the hill, one is giving it a large amount of potential energy which is quickly transformed into kinetic energy or the movement when it starts coming down. A number of factors are then used to try and maintain as much of the energy as possible and to keep it on track.
Tuesday, December 14, 2010
The Secrets of a Monster Cannon
We are going to make a cannon soon for physics and my job is to discover what are the secrets behind a cannon that fires a projectile for a huge displacement. Obviously the first thing is the angle the barrel is above the ground. After much deliberate the best angle is 45 degrees since sin 45 times cos 45 gives the greatest result compared to other angles. Another factor is to make the paper cup cannon ball more pointy instead of blunt since unlike in our problems there is air resistance. A blunt cannon ball would suffer greater air resistance versus a pointed one. Finally we can have a tall, stable base since it won't due if the cannon falls over and a taller base means the projectile is in the air longer which means it will travel farther.
Equilibriums, Inclined, Pulleys, and Trains
Equilibrium
An equilibrium is when a system is not moving at all. Since this is true this must mean that all the forces are perfectly balanced and the sum of the forces on one side aren't greater than the forces acting against it. When dealing with these questions though it is always important to list ones assumptions.
Assumptions:
-there is no friction
-the results of the x and y components are 0
-F=ma
Inclined
In a inclined plane a new force is introduced which is friction. Friction can be split into static and kinetic friction for when the object is not moving and moving respectively. When solving these questions one must tilt their head to think in a new direction, since while the force of gravity is dragging the object down in the same direction, friction, the normal force, and perhaps acceleration are in a totally different direction. It is also interesting to note that the coefficient of friction is the tan of the degrees between the plane and the ground.
Assumptions
-positive axes in direction of acceleration
-normal force perpendicular to the plane
-no air resistance
-no movement in the y direction
Pulleys
A pulley is simply a system where a weight or an object is attached to a string which is on an axle and support the rope holding the pulley up or another weight connect to the same string. Tension is introduced in this system which is energy stored in the rope. Since the objects attached to the same rope, their tension is the same.
Assumptions:
-No friction or weight in the rope and pulley
-positive axes in the direction of acceleration
-no air resistance or wind
-acceleration is equal
-tension is equal
-two free body diagrams
Trains
Finally we are at trains. A train is simply a system where several objects are connect by rope and a force is acting on one end of it causing it to move. The other objects are dragged with it due to tension. A simple way to solve it is to draw it first as one big free body diagram with their combined mass since the tensions cancel each other out. This way one can quickly find the acceleration of the system and won't have to substitute one equation into another other and other again.
Assumptions
-acceleration is equal
-no air resistance
-same number of fbds as number of masses
-position axis in direction of acceleration
-weightless ropes/cables
An equilibrium is when a system is not moving at all. Since this is true this must mean that all the forces are perfectly balanced and the sum of the forces on one side aren't greater than the forces acting against it. When dealing with these questions though it is always important to list ones assumptions.
Assumptions:
-there is no friction
-the results of the x and y components are 0
-F=ma
Inclined
In a inclined plane a new force is introduced which is friction. Friction can be split into static and kinetic friction for when the object is not moving and moving respectively. When solving these questions one must tilt their head to think in a new direction, since while the force of gravity is dragging the object down in the same direction, friction, the normal force, and perhaps acceleration are in a totally different direction. It is also interesting to note that the coefficient of friction is the tan of the degrees between the plane and the ground.
Assumptions
-positive axes in direction of acceleration
-normal force perpendicular to the plane
-no air resistance
-no movement in the y direction
Pulleys
A pulley is simply a system where a weight or an object is attached to a string which is on an axle and support the rope holding the pulley up or another weight connect to the same string. Tension is introduced in this system which is energy stored in the rope. Since the objects attached to the same rope, their tension is the same.
Assumptions:
-No friction or weight in the rope and pulley
-positive axes in the direction of acceleration
-no air resistance or wind
-acceleration is equal
-tension is equal
-two free body diagrams
Trains
Finally we are at trains. A train is simply a system where several objects are connect by rope and a force is acting on one end of it causing it to move. The other objects are dragged with it due to tension. A simple way to solve it is to draw it first as one big free body diagram with their combined mass since the tensions cancel each other out. This way one can quickly find the acceleration of the system and won't have to substitute one equation into another other and other again.
Assumptions
-acceleration is equal
-no air resistance
-same number of fbds as number of masses
-position axis in direction of acceleration
-weightless ropes/cables
Newtons 3 Laws of Motion
Newtons three laws of motion revolutionized the way we think of the universe and they are as follows.
1. The Law of Inertia. Every object will maintain it's velocity unless an external force acts upon it.
This means that if I'm driving a car at a certain speed and I suddenly stop, I will fly out of the windshield unless I have my seat belt on since the brakes don't stop me from moving.
2. F=ma,
which means that while the mass is directly related to force and the acceleration is directly related to force, mass and acceleration are inversely related themselves.
3. For every force there is an equal and opposite reaction force.
I think this is rather obvious and explains why I can jump off the ground since I'm not giving a force to myself but to the ground which returns the force to me in the opposite direction pushing me up.
1. The Law of Inertia. Every object will maintain it's velocity unless an external force acts upon it.
This means that if I'm driving a car at a certain speed and I suddenly stop, I will fly out of the windshield unless I have my seat belt on since the brakes don't stop me from moving.
2. F=ma,
which means that while the mass is directly related to force and the acceleration is directly related to force, mass and acceleration are inversely related themselves.
3. For every force there is an equal and opposite reaction force.
I think this is rather obvious and explains why I can jump off the ground since I'm not giving a force to myself but to the ground which returns the force to me in the opposite direction pushing me up.
Projectile Motions
Naturally after learning about the big 5 equations we will move onto projectile motions. A simple type of projectile question would be if a fired a projectile at a certain initial velocity at a certain angle of elevation, how far would it travel. To solve these types of questions, first we must split it into two parts, the x and y components. The y component is used to figure out how long the projectile is in the air while the x component is to figure out the speed at which it travels horizontally. Naturally we will be assuming that this is occurring on earth and that there is no air resistance.
Y component
The initial vertical speed of the projectile can be defined as v sin(degrees). Since we are on earth, we can assume that the acceleration is -9.8 m/s^2 which is the gravity pulling it down and that eventually it will fall to a velocity of 0 m/s. At that point it will fall down using the same amount of time taken to get to that point. Thus the time the projectile is in the air can be expressed as t = 2(v2-v1/a) which will allow us find the time it is in the air.
X component
Unlike the y component, if we assume that there is no air resistance, there won't be any force acting against the projectile. Thus the horizontal speed of the projectile can be simply expressed as v cos(degrees).
With these two pieces of information, the distance that the projectile travels can simply be expressed as d = vt
Y component
The initial vertical speed of the projectile can be defined as v sin(degrees). Since we are on earth, we can assume that the acceleration is -9.8 m/s^2 which is the gravity pulling it down and that eventually it will fall to a velocity of 0 m/s. At that point it will fall down using the same amount of time taken to get to that point. Thus the time the projectile is in the air can be expressed as t = 2(v2-v1/a) which will allow us find the time it is in the air.
X component
Unlike the y component, if we assume that there is no air resistance, there won't be any force acting against the projectile. Thus the horizontal speed of the projectile can be simply expressed as v cos(degrees).
With these two pieces of information, the distance that the projectile travels can simply be expressed as d = vt
Deriving Big Five Equations 3 and 4 from a Graph
The equations number 3 and 4 of the big five are
d = v1t + 1/2at^2
d = v2t - 1/2at^2
But there question is that where did these equations come from. Certainly we can't just accept everything as it is. We known already that to find the displacement of a section of a d-t graph we simply find the area between the graph and the x-axis.
The the graph above the area below the first vertical line can be seen as a trapezoid. While we can find its area using a simple equation, it would be easier to break it down into a triangle and a square.
One way of finding out the total area is to find the area of the triangle and the square individually and add them together.
The area of the square is v1t since its initial velocity can be seen as the length and the time as the width. The area of the triangle is 1/2(v2-v1)t as the height is v2-v1 and t once again acts as the base. Adding then together, we get d=v1t + 1/2(v2-v1)t. If we subsitute v2-v1=at then we get d=v1t + 1/2at^2 which is the 3rd equation.
The other way to find the area is to see it as one large rectangle and then subtract the triangle from it. The area of the large rectangle is v2t and we can reuse the area of the triangle from before. After subtracting one from the other we get d=v2t - 1/2at^2 which is the fourth equation.
d = v1t + 1/2at^2
d = v2t - 1/2at^2
But there question is that where did these equations come from. Certainly we can't just accept everything as it is. We known already that to find the displacement of a section of a d-t graph we simply find the area between the graph and the x-axis.
One way of finding out the total area is to find the area of the triangle and the square individually and add them together.
The area of the square is v1t since its initial velocity can be seen as the length and the time as the width. The area of the triangle is 1/2(v2-v1)t as the height is v2-v1 and t once again acts as the base. Adding then together, we get d=v1t + 1/2(v2-v1)t. If we subsitute v2-v1=at then we get d=v1t + 1/2at^2 which is the 3rd equation.
The other way to find the area is to see it as one large rectangle and then subtract the triangle from it. The area of the large rectangle is v2t and we can reuse the area of the triangle from before. After subtracting one from the other we get d=v2t - 1/2at^2 which is the fourth equation.
Walking and Translating the Graphs
In physics we did a lab to help us understand how the different graphs worked. We were given a motion detector and several distance-time and velocity-time and were asked to walk them using the motion detector. While the distance-time graph were relatively simple to walk the velocity graph were slightly more difficult. For the graphs there are four main types to watch out for. Straight horizontal lines, straight angled lines going up or down, and curved lines that go up and down.
In displacement graphs straight lines are down by standing still since the distance isn't changing, straight angled lines are done by walking towards or back at a constant pace depending on the direction, and curved lines are down by walking at an increasing pace back or forwards.
For velocity graphs it becomes a bit more complicated. Straight lines are made by walking back or forwards at a constant pace since the velocity isn't changing over time. Straight lines that are on zero are a special case that occur when the person isn't moving. Finally, straight angled lines are done by moving back or forward at a steadily increasing pace.
In order to translating graphs from one type of another, it is important to identify the different parts and calculate them one at a time. Looking at displacement graphs its interesting to notice that the slope of the line is its velocity. Horizontal lines have no velocity while straight angled lines have a constant velocity. For curved lines one chooses two points near the beginning and the end and then draws straight lines that are almost touching the graph but not quite. One then calculates the slope of the lines then plots and connects them on the velocity graph to translate it.
Translating v-t to a-t graphs are easier since it is just like translating d-t graphs to v-t graphs except without the complication of curved lines. In order to transform a v-t back to a d-t graph is another matter. One must find the area between the line and the x-axis and then use it as the displacement. The same thing goes for translating an a-t graph to a v-t graph.
In displacement graphs straight lines are down by standing still since the distance isn't changing, straight angled lines are done by walking towards or back at a constant pace depending on the direction, and curved lines are down by walking at an increasing pace back or forwards.
For velocity graphs it becomes a bit more complicated. Straight lines are made by walking back or forwards at a constant pace since the velocity isn't changing over time. Straight lines that are on zero are a special case that occur when the person isn't moving. Finally, straight angled lines are done by moving back or forward at a steadily increasing pace.
In order to translating graphs from one type of another, it is important to identify the different parts and calculate them one at a time. Looking at displacement graphs its interesting to notice that the slope of the line is its velocity. Horizontal lines have no velocity while straight angled lines have a constant velocity. For curved lines one chooses two points near the beginning and the end and then draws straight lines that are almost touching the graph but not quite. One then calculates the slope of the lines then plots and connects them on the velocity graph to translate it.
Translating v-t to a-t graphs are easier since it is just like translating d-t graphs to v-t graphs except without the complication of curved lines. In order to transform a v-t back to a d-t graph is another matter. One must find the area between the line and the x-axis and then use it as the displacement. The same thing goes for translating an a-t graph to a v-t graph.
Adding Vectors
Vectors are basically forces with a direction. However it is important to know exactly what happens when several of these forces interact. To add two vectors, one will align the end of one with the start of the other then draw a line connecting them to form a triangle.
Then it is a simple matter of trigonometry to find the length of the missing side. One may use the Pythagorean theorem in the case of a right angled triangle or sin, cos, and tan in case it is not. Supposing A=10, B=15, and the angle between A and R is 30 degrees, then Sin 30 = 15 / R, R = 15 / 0.5, R = 30.
However, using this method while there are several vectors is long and unwieldy, especially when there is a limited amount of time like during a test or an exam. Thus the best way is to separate the vectors that don't point directly towards North, South, East, or West into two parts that do. Then we simply add the x components together and y components together to get the x and y forces for the final force. After that we find their sum and use tan to get the degrees of the force from the origin.
However, using this method while there are several vectors is long and unwieldy, especially when there is a limited amount of time like during a test or an exam. Thus the best way is to separate the vectors that don't point directly towards North, South, East, or West into two parts that do. Then we simply add the x components together and y components together to get the x and y forces for the final force. After that we find their sum and use tan to get the degrees of the force from the origin.
Wednesday, September 22, 2010
Right Hand Rules # 1 & 2
The right hand rule (or RHR) is a useful little rule for determining the direction of the magnetic field. The Right-hand rule #1 is used for a conventional current to determine the direction of current flow and magnetic field in a conductor. Depending on the information given, you either point your thumb in the direction of the current flow, or coil your fingers so that they point in the direction of the magnetic field. Using the rule, one can figure out which way current flows or which way the magnetic field turns.
For example, in the above diagram, if I only knew the current flowed upwards I would point my thumb up and grab the conductor. The direction my fingers coil is the direction the magnetic field is in.
RHR # 2 is used for coils. In a coiled conductor or solenoid, the thumb will always point to the north pole of the magnet and the fingers will point in the direction of current flow. Inside the coil, the thumb also represents the direction of the magnetic field.
The left hand rules are similar to the right hand rules, except they are used for electron currents, or when the charge flows from negative to positive.
Saturday, September 18, 2010
The Tallest Structure
Today in class we had a competition to build the tallest structure using 6 sheets of newspaper and a long strip of tape. My group decided to create a tripod as a base and use the rest of the newspaper to create a long and thin body. While we didn't win, we get some important insights. In order to create a tall structure one must first have a strong base. A solid shape like a triangle is required and it must be somewhat heavy to balance the structure. If a force where to act against one side of the triangle, there would be a leg to support it against the force. For height it's best to have it thin, with it gradually becoming thinner as the structure gets taller so the top won't be too heavy for the bottom to support. The winning group had a structure that was similar to a cone. It was large at the bottom and thin at the top. They used a long strip of paper at the end instead of a rolled up cone to lower the weight.
The center of gravity is the average location of the weight of the object. In a square-based pyramid for example, the center of gravity would be halfway up a line from the center of the square to the tip of the pyramid.
Thursday, September 16, 2010
Resistance - Ohm's Law
In any electric circuit, the amount of current that can flow depends on the potential difference of the power supply and the nature of the path connecting the loads and power supply. The more difficult the path, the harder it is for electrons to flow through. The measure of the opposition to the flow is known as resistance.
The formula for resistance is R = V / I , in which R is the resistance is in volts / ampere or ohms (Ω), V is the potential difference in volts (V), and I is the current in amperes (A).
This formula was developed by Georg Simon Ohm and the ratio V / I is known as Ohm's Law. Resistance is determined by several factors such as its thickness, length, cross-sectional area, the material, and it's temperature. The measure for the resistance of a substance is it;s resistivity. The gauge number of a wire refers to it's cross-sectional area. The larger the cross-sectional area, the smaller the gauge number.
There are two simple ways to connect conductors and loads. The first one is a series circuit, where the loads are connected one after another in a single path. The second is a parallel circuit, where the loads are side by side.
In a series circuit, the total current is equal to the current of each junction point. The total voltage is equal to the sum of all the potential losses and the total resistance is equal to the sum of all the resistors.
In a parallel, Vt=V1=V2=V3, It=I1+I2+I3, and Rt=1 / R1 + 1 / R2 + 1 - R3
The formula for resistance is R = V / I , in which R is the resistance is in volts / ampere or ohms (Ω), V is the potential difference in volts (V), and I is the current in amperes (A).
This formula was developed by Georg Simon Ohm and the ratio V / I is known as Ohm's Law. Resistance is determined by several factors such as its thickness, length, cross-sectional area, the material, and it's temperature. The measure for the resistance of a substance is it;s resistivity. The gauge number of a wire refers to it's cross-sectional area. The larger the cross-sectional area, the smaller the gauge number.
There are two simple ways to connect conductors and loads. The first one is a series circuit, where the loads are connected one after another in a single path. The second is a parallel circuit, where the loads are side by side.
In a series circuit, the total current is equal to the current of each junction point. The total voltage is equal to the sum of all the potential losses and the total resistance is equal to the sum of all the resistors.
In a parallel, Vt=V1=V2=V3, It=I1+I2+I3, and Rt=1 / R1 + 1 / R2 + 1 - R3
Monday, September 13, 2010
Voltage, Current, and More
In class today we filled in a table that summarized a concept we're already familiarized current, and introduced three new ones: voltage, resistance and watt. It is as follows..
Saturday, September 11, 2010
The Energy Ball
In class today we split into groups and received a small ping pong ball with two metal bands on the sides and twelve questions to answer. Through this activity we learned about series and parallel circuits. A series circuit is a circuit in which the loads are connected one after another in series. A parallel circuit is where the loads are connected parallel to each other.
1. Can you make the energy ball work? What do you think makes the ball flash and hum?
Well we managed to make the ball work by touching both bands with our fingers. I believe the ball flashes and hums because of the battery inside.
2. Why do you think you have to touch both metal contacts to make the ball work?
I think that by touching both metal contacts, my fingers act like wires and complete a circuit. This allows the electrons to flow and power the load.
3. Will the ball light up if you connect the contact with any material?
While the ball won't work with any material, it does with anything that is a good conductor of electricity. We managed to make it flash and hum by touching a metal contact with the steel part of a pen and touching the other metal contact with a finger holding the pen.
4. Which materials will make the energy ball work?
Like I stated above, good conductors such as copper and aluminum will make the energy ball work.
5. This ball does not work on certain individuals. What could cause this to happen?
The energy ball might not work for seniors because they lack water in the bodies. Due to their lack of water, they are missing metal in their body and don't conduct electricity as well. Thus the electrons won't flow through their bodies as well and the current won't be strong enough to power the ball.
6. Can you make the energy ball work with all the people in your group?
Yes, we could. By touching fingers and making a chain of people, we just allowed the electrons to flow through a bigger circuit.
7. What kind of circuit can you form with one energy ball?
We formed a series circuit, because the load is connect along a single path.
8.Given two balls can you create a circuit where both balls light up?
Yes we could. By inserting the second ball between two people we made a series circuit with two loads instead of one.
9. What do you think will happen if one person lets go and why?
If one person lets go then both balls will stop humming and the lights will dim. This is because the circuit is broken and the electrons stopped flowing.
10. Does it matter who lets go?
It doesn't matter who lets go because they were still part of the circuit.
11. Can you create a circuit where only one ball lights?
Yes we can. In a parallel circuit with each ball on opposite ends, we can break the circuit of one ball but the other will still be connected to a complete series circuit.
12. What is the minimum number of people required to complete this?
A minimum of four people is required to complete this parallel circuit.
1. Can you make the energy ball work? What do you think makes the ball flash and hum?
Well we managed to make the ball work by touching both bands with our fingers. I believe the ball flashes and hums because of the battery inside.
2. Why do you think you have to touch both metal contacts to make the ball work?
I think that by touching both metal contacts, my fingers act like wires and complete a circuit. This allows the electrons to flow and power the load.
3. Will the ball light up if you connect the contact with any material?
While the ball won't work with any material, it does with anything that is a good conductor of electricity. We managed to make it flash and hum by touching a metal contact with the steel part of a pen and touching the other metal contact with a finger holding the pen.
4. Which materials will make the energy ball work?
Like I stated above, good conductors such as copper and aluminum will make the energy ball work.
5. This ball does not work on certain individuals. What could cause this to happen?
The energy ball might not work for seniors because they lack water in the bodies. Due to their lack of water, they are missing metal in their body and don't conduct electricity as well. Thus the electrons won't flow through their bodies as well and the current won't be strong enough to power the ball.
6. Can you make the energy ball work with all the people in your group?
Yes, we could. By touching fingers and making a chain of people, we just allowed the electrons to flow through a bigger circuit.
7. What kind of circuit can you form with one energy ball?
We formed a series circuit, because the load is connect along a single path.
8.Given two balls can you create a circuit where both balls light up?
Yes we could. By inserting the second ball between two people we made a series circuit with two loads instead of one.
9. What do you think will happen if one person lets go and why?
If one person lets go then both balls will stop humming and the lights will dim. This is because the circuit is broken and the electrons stopped flowing.
10. Does it matter who lets go?
It doesn't matter who lets go because they were still part of the circuit.
11. Can you create a circuit where only one ball lights?
Yes we can. In a parallel circuit with each ball on opposite ends, we can break the circuit of one ball but the other will still be connected to a complete series circuit.
12. What is the minimum number of people required to complete this?
A minimum of four people is required to complete this parallel circuit.
Current Electricity
Current Electricity is the continuous flow of electrons. In an electric current, energized electrons flow the negative side of a power supply through a complete path or circuit to the positive side of a power supply while directed by a conductor. The model of positive charge flow is known as a conventional current. A load ( any device that uses energy) can be attached to the circuit to be powered.
To find the current in an electric circuit we must first find the total amount of charge that passes a certain point in the conductor and divide it by the time taken. The equation for this is I = Q / t where I represents the current in amperes (A), Q represents the charge in coulombs (C), and t represents the time in seconds. One ampere is the equivalent of one coulomb of charge passing a certain point in a conductor every second. A device which measures current or Ammeter can also be attached to the circuit in order to find the current.
Eg. How much current flows through a washing machine if 2500 c of charge passes through it in 500 s?
I = Q / t
I = 2500 c / 500 s
I = 5 c / s
Thus 5 A of current flows through the washing machine.
There are two types of currents. DC or direct current and Ac or alternating current. In a direct current , the electrons flows in single direction from the power supply through the conductor to a load and back to the power supply again. In an alternating current the electrons will periodically reverse directions.
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