Unit2_AnzaiM

__**Lesson 17: July 8, 2011**__
toc there are three qualities: 1. Force on the object 2. the movement of the object must be the same as the direction of force 3.the object must move. || Symbol W || Units Joules J || F * d * cos(angle between force and direction of motion) || Normal Tension or Friction along axis of motion || Energy || energy possessed by an object because it is above or below the zero level. || GPE PEg Usubg || J || mgh or mgy || location is above or below zero position || or stretched spring. || EPE PEs || J || 1/2kx^2 k is spring force constant x is distance of stretching || stretched or compressed ||
 * Work || In order for work to be performed,
 * Kinetic Energy || is due to the motion of an object || KE || J || 1/2m*v^2 || Object is moving ||
 * Gravitational Potential
 * Elastic Potential Energy || is energy possessed by an object due to a compressed,

Law of conservation of Energy (LCE) Work In + Initial Energy = Final energy + Work out

** Lab: Energy and Air Bags **

__Objective:__ How does an air bag protect you during an accident?

__Materials:__ List any materials used and draw a labeled diagram of your set-up (alternatively, include a snapshot or video).

__Procedure:__ We will begin by testing at what height the egg falls.

__Hypothesis:__ The air bag protects people in an accident because it insulates the force by absorbing the speed you gain in an accident.

//Note: You may want to use the available technology to take "Before" and "After" pics to post in your data table to assist and elaborate on your written descriptions.//


 * 1) Measure the length of your egg #1. Measure the mass of your egg. Record this information.
 * 2) Place an egg in a ziplock bag, squeezing out all of the air in the bag before sealing.
 * 3) Hold a ruler up on the table vertically. Hold the egg vertically at the 2 cm mark. (Keep the excess bag on top.) Drop it.
 * 4) Hold the egg the same exact way at the 4-cm mark and repeat. Continue this process until the egg shell is slightly cracked.
 * 5) Continue until the egg is smashed and the yolk leaks out. Measure the amount of egg still undamaged. How much of the egg is smashed?
 * 6) Fill a bowl with flour and place the bowl inside of the box lid.
 * 7) Measure the length of your egg #2. Measure the mass of your egg. Record this information.
 * 8) Drop the egg from the smash height (Step 5). Measure the amount of egg sticking up out of the flour bed. How much of the egg is buried in the flour? Also, record your qualitative observations.
 * 9) Repeat this, increasing the height in 5-cm increments until the egg is cracked, and then smashed.

__Data and observations__: __Calculations:__ Show a sample for each, with equation(s), numbers plugged in, and answer with correct units.

What is the initial gravitational potential energy? GPE = 0.3003
 * GPE = mass(0.0613kg) * gravity(9.8) * height(0.5)

How much work is done in each trial?
 * W = force * distance * cos (angle (180))
 * W = GPE
 * W = mass(0.0613kg) * gravity(9.8) * height(0.5)

How much force was used to stop the egg in each case?
 * F = GPE / d
 * F = mgh / d
 * F = [mass(0.0613kg) * gravity(9.8) * height(0.5)] / distance buried (0.014)

__Questions:__


 * 1) This investigation is an analogy for a person in an automobile collision. What does the egg represent? What does the table represent? What does the flour represent? The egg represents the head of the driver, the table (ground) represents the dashboard of a car, and the flour represents the airbags.
 * 2) Define the terms: Gravitational Potential Energy, Kinetic Energy and Work. Gravitational potential energy is the potential or stored energy in objects whenever they are placed higher or lower then a given origin giving the object energy. Kinetic energy is energy that is stored in objects in motion.
 * 3) What factors determine an object's kinetic energy? Factors that determine the objects kinetic energy is its mass, and velocity.
 * 4) When work is done on an object, what is the effect on the object's kinetic energy? Usually when work is done, kinetic energy is transferred into forms of work such as tension.
 * 5) How does the force needed to stop a moving object depend on the distance the force acts? It depends on the distance that the object had taken to stop because it is an inverse relation with the amount of force required to accomplish the work. W / F = D * cos(angle)
 * 6) What difference does a soft landing area make on a passenger during a collision? It causes less force because there is more distance for work to occur.
 * 7) How does a cushion reduce the force needed to stop a passenger? There is greater distance which causes less force to be expended.
 * 8) What does the law of conservation of energy have to do with this? The law of conservation of energy has to do with this experiment because, the egg is directly effected by the kinetic energy due to the gravitational potential energy. When the egg comes to a halt the energy needs to be transferred because it cannot be destroyed. This is why we must use flour to reduce the amount of force applied on to the egg.

__Conclusion:__
 * Using the law of conservation of energy, explain how an air bag can protect you during an accident. Use specific observations from this investigation to support your answers to these questions.
 * The law of conservation of energy states that all energy can neither be destroyed or created but only transferred. So in order for the egg to not break in this experiment, the energy had to transfered to work with the least possible force involved.
 * Explain at least 1 cause of experimental error. Be sure you describe a specific reason.
 * 1 cause of experimental error was the way the egg fell, the measurements of the distance the egg had buried itself into the flour.
 * How would you improve the results of this lab? (In other words, what would you change about the materials or procedure to eliminate or reduce the experimental error you describe above?)
 * The use of the bag made it hard for the egg to fall straight down, also air always found a way into the bag which made it hard to measure it correctly.



**__Homework July 9, 2011:__**
__Method #4:__ SQR^3

Questions: 1. What is work? 2. How can we calculate work done by forces? 3. What is potential Energy? 4. What is kinetic Energy? 5. What kind of energy is mechanical energy? 6. How can we understand power?

Recite:

1. There are three things necessary to figure out work: force, displacement, and cause. Also in order for the force to do work, there has to be displacement of an object. Also along with positive work, there is negative work that causes negative displacement.

2. Mathematically, work can be expressed by the following equation. The angle of cos depends on the displacement and the force of the object. For example the angle of friction is 180.
 * force * displacement * cos**

3. Potential energy is the storage of energy because of the position of the object. There are two types of potential energy. Gravitational Potential Energy and Elastic Potential Energy. Gravitational potential energy is the energy stored in objects relative to the place of origin in terms of height. Gravitational potential energy can be expressed mathematically by: Mass * gravity * height Elastic Potential Energy is stored energy by elastic materials that stretch, or compress. Elastic Potential Energy can be expressed mathematically by: 1/2 * spring constant * amount of compression ^2

4. Kinetic energy is simply the energy dealing with motion. This form of energy can be horizontal or vertical. Kinetic energy is measured in joules and can be calculated by using this formula. m = mass, v = velocity

5. Mechanical energy is the energy that is supplied to an object to do work. Mechanical energy can be derived from objects or people. When objects are supplied with forces, or potential energy and is displaced from their original location or state, mechanical energy is used.

6. Power is the ability to do work under a certain amount of time. The more work, and the faster the work is done, it is considered to be more powerful. A common misconception from our everyday use of the word power makes us believe that speed does not have any counterpart with power, but in physics speed is one of the two components of power.

Power can be expressed in the mathematical formula:

__Joke:__ ** The following theorem can now be supported using some basic physics and two well known propositions, namely : **

** Knowledge is Power. **

** Time is Money. ** ** As every physicist knows, Power = Work/Time. **

** Therefore, Knowledge = Power = Work / Time = Work / Money, or **

** Money = Work / Knowledge **

** Thus for any given amount of work, as Knowledge approaches zero, Money goes to infinity (the executives). And conversely, as Knowledge gets larger, Money gets smaller (scientists and academics). QED **

This ones good :) __Lesson: 18__

Momentum = m * v momentum is lower case p units are kg m/s Force = ma Force = m(deltaVelocity/deltaTime) Force * deltaTime = mass * deltaVelocity Impulse = change in momentum Impulse unit is J N*S = kgm/s

__Law of Conservation of Momentum:__

Momentum cannot be created or destroyed but can be transferred. Total momentum of a system remains constant, as long as the system is isolated. (ignore friction during collision)

The sum of the initial momentum = the sum of the final momentum Mass initial * Velocity initial + m2 v2 = m1f * v1f + m2f + v2f

** LAB: Momentum and Elastic Collisions **

__Objective:__ A small sports car hits a heavy truck in a collision. What factors determine the outcome for the passengers of the two vehicles? Which driver will sustain worse injuries? Why?

__Materials:__ List any materials used and draw a labeled diagram of your set-up (alternatively, include a snapshot or video). __Hypothesis:__ The momentum of each car will determine what will happen to each passanger. The passanger in the small sports car will sustain worse injuries because it has less momentum due to the lack of mass. The truck will experience relatively little amount of damage from its greater mass. __Procedure:__
 * 1) Place a cart on the middle of the track with the spring to the right. On a piece of masking tape, label this the "Target cart." Place a second identical cart on the right end of the track. Mark this as the "Bullet cart".
 * 2) Push the bullet cart very gently towards the target cart so that they collide, with the spring between them.
 * 3) Repeat step 2 several times, giving the bullet cart a bigger push each time. Record your observations.
 * 4) Add 500-g to each cart and repeat the process. Record your observations and compare the results to the first set of collisions.
 * 5) Remove the mass from the target cart and repeat the above steps.
 * 6) Add the mass to the target cart and remove the mass from the bullet cart, and repeat.
 * 7) Get the "Mystery" cart from your teacher. Determine the relative mass of the cart by putting it through a sequence of collisions.

__Data and observations:__
 * Trial || Mass of Bullet Cart (kg) || Mass of Target Cart (kg) || Applied force (qualitative only) || Description and Observations (qualitative) ||
 * 1 || 1000 || 1000 || average || bullet cart remains almost stationary at collision and the target car moves with approximately the same force. ||
 * 2 || 0 || 1000 || average || the bullet cart moves back, but the target car has approximately the same speed ||
 * 3 || 1500 || 500 || average || both the target car and the bullet car moved in a forwards momentum ||
 * 4 || 1000 || 1000 || fast || The bullet car moves forward after the collision because it is faster then the speed. ||
 * 5 || 0 || 2000 || fast || The bullet car still moves backwards even when the speed is fast. ||
 * 6 ||  ||   ||   ||   ||

Mystery Weight 1: The weight is approximately 350-400 grams because our bullet cart moved a small amount when we used both the 400 gram weights and the 300 g weight.

Mystery Weight 2: The weight is approximately 600-700grams because our bullet cart moved a small amount when we used both the 700 gram weights and the 600g weight.

__Questions:__

What is a real-life collision that the collisions in this investigation could represent? This could answer what would happen in a real accident. The comparisons between the momentum and the weight of the carts. How well did observing collisions enable you to compare the masses of the carts in the last step? Even though this was a mere observational lab with little quantitative data involved, we were able to figure out what occurs when cars of different masses experience collisions. What happened after the collision as the masses changed? The differences of the bullet cart comparative to the stationary cart had created adverse effects. When the bullet train was equal to the weight of the target train, the bullet car stayed stationary after the collision. The bullet train was more then the target cart and continued moving forward even after the collision. Define the term momentum. Momentum is the impetus gained by a moving object Which object has greater momentum, a butterfly traveling at 16 km/h or an eagle traveling at the same speed? An eagle has greater momentum because it has more weight. How does the transfer of momentum occur? The transfer of momentum occurs through contact. Use momentum to describe what would happen if a skaterboarder was hit by a car. The skateboarder would move backward and the car would remain unchanged because of the results of the ellastic lab.

__Conclusion:__ · Based on the relative amounts of momentum, what is the outcome of a head-on collision between a heavy truck and a small sports car if both have the same speed? The sports car will be pushed backwards while the truck would continue moving forward. · Explain at least 1 cause of experimental error. Be sure you describe a specific reason. The amount of force at which the carts moved could have caused errors to the data. Also we didn't have any other abilities to observe the data except from our eyes. · How would you improve the results of this lab? (In other words, what would you change about the materials or procedure to eliminate or reduce the experimental error you describe above?) We would use a constant speed for the carts and measure the carts movements precisely.

** LAB: Momentum and Inelastic Collisions **

__Objective__: How does the initial momentum compare to the final momentum? __Hypothesis:__ They will reduce in momentum. __Procedure:__
 * 1) Place 2 photogates on a track, one at 50 cm and the other at 75 cm. Hook these into a Smart Timer and set the Smart Timer to Velocity.
 * 2) Place a cart so that its end is at 75 cm (right in front of the photogate), with the velcro facing 0-cm. Call this the "target cart." Place a second identical cart at the end of the track closest to 0-cm. Call this the "Bullet cart". Make sure that both carts have picket fences.
 * 3) Click "Start" on the Smart Timer, and then push the Bullet cart very gently towards the Target cart so that they collide and stick together. You may need to practice this a few times.
 * 4) Record the velocity right before (the Bullet Cart initially) and right after the collision (the two carts linked). Record these values in your data table.
 * 5) Vary the masses of the carts and repeat the process 5 times.

__Data and observations:__


 * Mass of Bullet Cart (kg) || Mass of Target Cart (kg) || Speed of Bulet Cart (m/s) || Combined Masses (kg) || Final Velocity of Both Carts (m/s) || Initial Momentum || Final Momentum ||
 * 0.5 || 0.5 || 0.083 || 1 || 0.04 || 0.0415 || 0.04 ||
 * 0.5 || 0.5 || 0.066 || 1 || 0.031 || 0.033 || 0.031 ||
 * 0.5 || 0.5 || 0.083 || 1 || 0.041 || 0.0415 || 0.041 ||
 * 0.5 || 0.5 || 0.072 || 1 || 0.034 || 0.036 || 0.034 ||
 * 0.5 || 0.5 || 0.083 || 1 || 0.04 || 0.0415 || 0.04 ||
 * 1 || 0.5 || 0.053 || 1.5 || 0.033 || 0.053 || 0.0495 ||
 * 1 || 0.5 || 0.045 || 1.5 || 0.029 || 0.045 || 0.0435 ||
 * 1 || 0.5 || 0.063 || 1.5 || 0.04 || 0.063 || 0.06 ||
 * 1 || 0.5 || 0.038 || 1.5 || 0.022 || 0.038 || 0.033 ||
 * 1 || 0.5 || 0.073 || 1.5 || 0.049 || 0.073 || 0.0735 ||
 * 0.5 || 1 || 0.12 || 1.5 || 0.033 || 0.06 || 0.0495 ||
 * 0.5 || 1 || 0.08 || 1.5 || 0.025 || 0.04 || 0.0375 ||
 * 0.5 || 1 || 0.125 || 1.5 || 0.041 || 0.0625 || 0.0615 ||
 * 0.5 || 1 || 0.091 || 1.5 || 0.029 || 0.0455 || 0.0435 ||
 * 0.5 || 1 || 0.125 || 1.5 || 0.04 || 0.0625 || 0.06 ||
 * 1.5 || 1 || 0.051 || 2.5 || 0.029 || 0.0765 || 0.0725 ||
 * 1.5 || 1 || 0.047 || 2.5 || 0.026 || 0.0705 || 0.065 ||
 * 1.5 || 1 || 0.092 || 2.5 || 0.055 || 0.138 || 0.1375 ||
 * 1.5 || 1 || 0.052 || 2.5 || 0.029 || 0.078 || 0.0725 ||
 * 1.5 || 1 || 0.05 || 2.5 || 0.028 || 0.075 || 0.07 ||

__Calculations:__ Show equation(s), numbers plugged in, and answer with correct units. Add columns in your data table to include these results. __Questions:__ > They are relatively similar, but the initial momentum seems to be slightly higher. Because the cue ball is the same weight as the first ball it strikes, the cue ball will remain stationary. Also the rest of the balls will move in an outward direction due to the law of conservation of momentum. The balls will move with the kinetic energy that the cue ball transfered after the strike.
 * 1) Find the initial momentum of the bullet cart for each trial.
 * initial momentum = m * v = mass of bullet * velocity of bullet sample(trial 1): 0.5kg * 0.08m/s = 0.0415 kg*m/s
 * 1) Find the initial momentum of the target cart for each trial.
 * initial momentum = m * v = mass of target * velocity of target sample(trial 1): 0.5kg * 0 m/s = 0 kg * m/s
 * 1) Find the sum of the initial momenta of the two carts for each trial.
 * initial momentum + final momentum = sum of momenta. sample(trial 1): 0.0415 + 0 = 0.0415kg*m/s
 * 1) Find the final momentum of the combined carts for each trial.
 * initial momentum = m * v = combined mass * final velocity. sample(trial 1): 1 * 0.04 = 0.04kg*m/s
 * 1) Find the percent difference between the initial momentum (calc 3) and the final momentum (calc 4).
 * % difference = (abs(calc 3 - calc 4) / ave(calc3 + calc4)) * 100. sample(trial 1): (0.0015 / 0/04075) * 100 = 3.68%
 * 1) How do the initial momenta compare to the final momenta? Allowing for minor variations due to uncertainties of measurement, are there any patterns?
 * 1) Which types of collisions are definitely inelastic? How do you know? The types of collisions that are inelastic are ones that stick together after the collisions. Also the kinetic energy is reduced in the collision converting into collision or work force.
 * 2) Which types of collisions are definitely elastic? How do you know? Elastic collisions conserve the kinetic energy and allow the target object to move away from the bullet object.
 * 3) Use the law of conservation of momentum to describe what happens when a cue ball hits the 15 balls in the middle of the pool table.

__Conclusion:__ > We can improve the lab results if we could get a precise start and recording of the carts.
 * Based on the law of conservation of momentum, how can the traffic-accident investigators use this to "reconstruct" an accident? What does it mean to "conserve" momentum? The traffic accident investigators can use the law of conservation of momentum to reconstruct the accident because there is no energy that becomes destroyed but is always transferred. When they mention conserve momentum, they mean that the energy will not be destroyed.
 * Explain at least 1 cause of experimental error. Be sure you describe a specific reason. 1 cause of experimental error is the position at which the timers recorded the data. There is also friction before the carts collided.
 * How would you improve the results of this lab? (In other words, what would you change about the materials or procedure to eliminate or reduce the experimental error you describe above?)

**__Homework: July 10, 2011__**
Method 5:

__Momentum:__ Momentum is a term that describes the force at which an object is moving, and can be shown mathematically as mass * velocity.

__Momentum and Impulse Connection:__ When we combine the two equations, newton's 2nd law F = mass * acceleration, and momentum mass * velocity, we can derive the impulse and change in momentum formula, this formula can tell us how the object with momentum will react after a collision. (Like in the Picture Below)


 * __Cool Applet for Conservation of Momentum:__**