Unit2_LeeJ

Unit 2 Conservation Laws

=toc Section 1: Work, Energy, and Power=

Lesson 1: Basic Terminology and Concepts & Lesson 2: The Work Energy Theorem
Work Kinetic Energy Gravitational Potential Energy Elastic Potential Energy Law of Conservation of Energy
 * //__Class Notes__//**
 * Definition: caused by a force acting on axis of direction of motion
 * Symbol: W
 * Unit: Joules(J)
 * Equation: W = F * d * cos(φ)
 * W: work, F: force, d: distance, φ: an angle between force and direction of motion.
 * Force should exist
 * The direction of force should be same as direction in motion
 * There should be motion( Stopping an moving object is also work)
 * Cue: N, T, f along axis of motion
 * Definition: due to the motion of an object
 * Symbol: KE(K)
 * Unit: Joules(J)
 * Equation: (1/2)mv2
 * Any object that move has kinetic energy
 * Cue: object is moving
 * Definition: energy possessed by an object because it is above(or below) the zero level
 * Symbol: GPE(PEg, ug)
 * Unit: Joules(J)
 * Equation: mg*h or mg * y
 * m = mass, g = 9.8, h or y =vertical position of object
 * cue: location of an object is above or below zero position
 * Definition: energy possessed by an object due to compressed or stretch spring
 * Symbol: EPE,(PEs SPE, us, ue)
 * Unit: Joules(J)
 * Equation: (1/2)Rx2
 * R: spring force constant x: distance of stretching
 * Cue: stretched on compressed spring
 * Energy cannot be created or destroyed but change from one to another form
 * Initial energy + work= Final energy
 * Work is the only way to change energy but initial energy and final energy are always same.

Questions
 * //__Summary (Method 4)__//**
 * What is Work mean in physical world?
 * When force causes displacement of an object, the situation is called work is done
 * What are differences that 3 types of Energies have??
 * Potential energy is the energy of position that is stored in an object.
 * Kineric energy is the energy that occurs when an object is in motion
 * Mechanical energy is the energy that aquired by work done in an object
 * What is Power?
 * Power is the quantity of the force that causes work. Determine how fast the work done
 * What is difference between internal force and external force?
 * Internal forces is forces that exist at surface of the object and external do not deals with surface of an object
 * What ability is important to solve problems that includes work and energy?
 * Analysing the situation in the question and look for what are involved


 * Summary**

>
 * Work**
 * Work is only means forces that causes displacement of an object and also the direction of the object's displacement and force should in same direction. For example, when one hold the book and move around, that is not part of work. Force, displacement and the angle between them must known to calculate magnitude of work. The mathematical equation of work is W = F * d * cos(φ). φ means the angle between force and displacement. When a work is in negative number, it means the force and displacement have opposite direction and it is shown because when the angle between force and displacement is 180 degree, cos(180) is -1. In addition, the unit of work is J(Joule), which represents 1Newton * 1m.
 * [[image:cos.jpg width="329" height="198"]]
 * Energy**
 * There are three types of energy: potential energy, kinetic energy, and mechanical energy. Each energy represents and have different properties.
 * First, Potential energy represent the energy of position that stored in its object. When the object is away from its original position, the potential energy increases and when it goes closer to the energy, the potential energy decreases. In potential energy, there are two major examples that are usually issued, gravitational potential energy and elastic potential energy. Gravitational potential energy(GPE) is energy that stored in an object that deals with its height. It is caused by the attraction of gravity and GPE in creases when an object has greater mass and higher height. Due to GPE is directly proportional with height and mass, the mathematical equation to calculate GPE is GPE = m * g * h. The zero point of GPE is usually ground but it is the zero position when you measure the height of the object. Second potential energy that will issued in physics is Elastic Potential Energy(EPE). It represents the energy stored in elastic object, such as spring, which causes compress and stretch. EPE is related to how much elastic object is stretched of compressed therefore, the mathematical equation to find the EPE is EPE = (1/2) * k(spring constant) * x 2 (amount of compress or stretch).
 * Second, Kinetic energy represent the energy occurs when an object is in motion. Every objects with in motion has kinetic energy. the kinetic energy is directly proportional to the mass of an object and square of the velocity. The mathematical equation for kinetic energy is KE = (1/2) * v 2 * m. Also the unit of kinetic energy is Joule.
 * Third, Mechanical Energy represents the energy need to be work done. Simply, mechanical energy is the energy to do work. It can be either kinetic energy or potential energy because the mechanical energy always occurs when an object is in motion. The mathematical equation for total mechanical energy is ME = PGE + KE.
 * Power**
 * Power represent the quantity of force that need to be work done. It deals with time that takes and determine the quantity of work. The mathematical equation of power is Power = Work / time and the unit of power is watt which represent Joule/ time however, the power of machine is usually used horsepower to represent, which is about 750 Watts.
 * Internal Force vs External Force**
 * Forces are usually categorized in two groups, internal force and external force. Internal force represents the forces that occurs in surface of an object and contact such as tension, friction ...etc. External force represents the forces that occurs from distance such as gravitational force and spring force. When only net force is internal forces usually changes the total mechanical energy like decreasing and incresing, therefore it also called nonconsercation forces, however, when only net force is external force does not change the total mechanical energy therefore it also called conservation forces.
 * In the situation that includes external forces, the mathematical equation is Total mechanical energy + work done by external energy = Final total mechanical energy. In the equation, you have to be careful about +, - sign for work. Also you can express the equation to KE + PE + W = TME and apply kinetic energy equation and potential energy equation to solve the problems.
 * In the situation that involves internal forces, the mathematical equation is also KE + PE + W = KE + PE. However, in this types of question, the sum of KE and PE never changes.
 * In both type of questions, analysing ability is required.
 * Also it is easy to see Bar Chart of kinetic energy and potential energy. When potential energy and kinetic energy constantly inverse related and sum of energies are same, it's net force is internal force, other wise, net force is external force. In addition, when graph is going down, it represent decreasing in energy and when the graph is increasing, it represent increasing in energy.

__Objective:__ How does an air bag protect you during an accident? __Hypothesis:__ During an accident, an air bag will protect you by denting itself and reduce the force that will affect you. __Materials:__ List any materials used and draw a labeled diagram of your set-up.
 * //__LAB: AIR BAGS__//**

__Procedure:__
 * 1) Measure the length of your egg #1. Measure the mass of your egg. Record this information.
 * 2) Place an egg in a ziploc 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__ __Calculations:__ Show a sample for each, with equation(s), numbers plugged in, and answer with correct units.
 * 1) What is the initial gravitational potential energy?
 * initial GPE = egg mass * 9.8 * drop height
 * 1) How much work is done in each trial?
 * W = F * d * (cos angle), **W = GPE**
 * 1) How much force was used to stop the egg in each case?
 * W = GPE. mgh = F * d, **F = mgh / d**

__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?
 * egg represent th person, table represent the surface of the object that made accident with auto mobile and the flour represents the airbag.
 * 1) Define the terms: Gravitational Potential Energy, Kinetic Energy and Work.
 * GPE: potential energy that caused by gravity. It usaully deals with the height from zero point
 * KE: energy that stored when an object is in motion
 * Work: when force cause displacement.
 * 1) What factors determine an object's kinetic energy?
 * Mass and Velocity determine an object's kinetic energy.
 * 1) When work is done on an object, what is the effect on the object's kinetic energy?
 * Kinetic energy in creases when work is done on an object.
 * 1) How does the force needed to stop a moving object depend on the distance the force acts?
 * When it has greater force to stop, the distance the force act will increase
 * 1) What difference does a soft landing area make on a passenger during a collision?
 * When there is a soft landing area, a passenger would decrease his/her injuries and could prevent death.
 * 1) How does a cushion reduce the force needed to stop a passenger?
 * A cushion reduce the force needed to stop by absorb impact and will take all impacts caused by forces
 * 1) What does the law of conservation of energy have to do with this?
 * Even though flour took all impact of the egg, egg still has its own energy.

__Conclusion:__ The experiment proved that the airbag is effective to reduce the impact. Even though the airbag reduces the impact of an object, the total energy that an object has didn't change, which represent law of conservation of energy. The law of conservation of energy states that energy cannot be destroyed or created. An air bag can protect you during accident by doing negative work to decrease initial energy of an object. During the lab, when we let the egg fall to the ground, it crashed when it fall from only 50cm; however, when we let the egg fall onto the flour, it never crashed unless we missed the small bowl that holds flours although it falls from the ceiling that has height of 2.8 meter. The possible error source of the experiment is human error. Due to we are all human, we cannot be perfect and therefore when we measure how much the egg buries, it is unclear and hard to measure it with meterstick and human eye. Also when we let the egg fall, sometimes egg spins and drops with different form from original form. In this case, the quantity of egg buried would decreases or increases. To eliminate the experimental error, we had to make sure that the egg falls without spining and use small rural to get more accurate data for buried egg.

__//**Interesting animation about dampling**//__ [] This animation shows how dampling affect to simple harmonic motion and what dampling is.

=﻿Section 2: Momentum and Its Conservation=

Lesson1: The Impurse Momentum Change Theory & Lesson 2: The Law of Momentum Conservation
POWER Momentum
 * //__Class Notes__//**
 * Power is the rate of energy dissipation.
 * P = W /t
 * P = (F * d) / t = F * v à only when average or constant speed
 * Unit: Watts(W), horsepower
 * 1 Horsepower = 746 W
 * Quantity of motion
 * Directly proportional to mass and velocity
 * Equation: momentum = mass * velocity
 * Symbol: p
 * Unit: kg * m/s
 * m * Δv = change in momentum
 * F * Δt = Impulse change in momentum. J(N/s)
 * F * Δt = m * v

The 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
 * Sum of initial momentum = sum of final momentum
 * Can represented as m1v1i + m2v2i = m1v1f + m2v2f

Good Topic sentences
 * //__Summary(Method 5..don't know how to DRAW lines on the physics class room.....)__//**
 * Momentum can be defined as mass in motion
 * Momentum is directly related to mass and velocity
 * Momentum is vector quantity
 * Force times time is impulse.
 * The quantity m times change in velocity is change in momentum
 * Impulse = change in Momentum
 * The physics of collisions are governed by law of momentum
 * Collisions in object rebound with the same speed
 * Increase of collision time reduces the force and increase of mass changes velocity in same amount of value.
 * Impulse-momentum change theorem in real world
 * Rebound of collision is depeneded on velocity change.
 * Large Change in momentum represent large impulse
 * In collision, Newton's Third law applies and bullet object and target object has equal magnitude of force.
 * In isolated situation, initial total momentum and final total momentum of 2 objects that occured collision are equal
 * Which means, the momentum cannot be created of destroyed, but transffered or converted
 * [[image:law_of_conservation_of_momentum.jpg]]
 * This can be explained when collision occurs, the magnitude of Forces are same but opposite direction and it proves the time consumming is also same, which means impulse are same. If impulses are equal, then changes in momentum is also equal
 * Isolated system is the system that the F of the equation that represent the law of the conservation of Momentum is free from the external net force of 2 objects.
 * In the system that is not isolated and have resistance force such as friction and air resistance, the law of conservation of momentum is not correct.
 * With momentum table and simple algebra skills, you can solve problems invoves the law of the conservation of momentum easily.
 * [[image:momentum_table.jpg]]
 * In inelastic collision, the KE is not conserved
 * The law of conservatipn of momentum also works same in explosion situation.
 * [[image:ExplosionMomentum.jpg]]

__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? __Data and observations:__ and bullet cart moved back ward more and faster. || Mystery mass1 is approximately 800g. Because when we put .8 kg on the bullet cart, and push bullet carts with similar force of trial 1, carts moved same distance as trial 1. Therefore, the mass of mystery 1 is .8kg Mystery mass2 is approximately 1000g. Because when we put 1 kg on the bullet cart, and push bullet carts with similar force of trial 1, carts moved same distance as trial 1. Therefore, the mass of mystery 2 is 1kg __Questions:__
 * LAB : Momentum and Elastic Collisions**
 * Trial || Mass of Bullet Cart (kg) || Mass of Target Cart (kg) || Applied force (qualitative only) || Description and Observations (qualitative) ||
 * 1 || .5 || .5 || Gentle || Target cart moved forward when the bullet cart almost stopped ||
 * 2 || .5 || .5 || More than trial 1 || Target cart moved away faster than trial 1 and bullet cart moved back ward more and faster. ||
 * 3 || .5 || .5 || More than trial 2 || Target cart moved away faster than trial 2
 * 4 || 1 || 1 || Gentle like trial 1 || Target cart more than trial 1 with faster acceleration. ||
 * 5 || 2 || .5 || Gentle like trial 1 and 4 || Target cart moved away lot more than trial 4 when bullet cart is approximately stopped ||
 * 6 || 1 || 1.5 || Gentle like trial 1,4 and 5 || Target cart moved with less speed than other trials and bullet cart moved faster to backward ||
 * real: 700g % error = (ABS(actual - experimental) / actual) *100 = 14.29%
 * real: 1200g % error = (ABS(actual - experimental) / actual) *100 = 16.67%
 * 1) What is a real-life collision that the collisions in this investigation could represent?
 * In real life, collisions in this investigation represent a car accident such as when a small sports car hits a heavy truck.
 * 1) How well did observing collisions enable you to compare the masses of the carts in the last step?
 * It helped to determine the mass of mystery value, however, we are human and we couldn't use constant speed to get exact value.
 * 1) What happened after the collision as the masses changed?
 * With greater mass, the object had more resistant against moving when collision occurs and with same mass ratio, changes are always same.
 * 1) Define the term momentum.
 * Mass in motion
 * 1) Which object has greater momentum, a butterfly traveling at 16 km/h or an eagle traveling at the same speed?
 * Eagle
 * 1) How does the transfer of momentum occur?
 * Bullet Cart stops when it hit another cart and the another cart will move continuously
 * 1) Use momentum to describe what would happen if a skaterboarder was hit by a car.
 * Skaterboarder will move backward faster and more than car.

__Conclusion:__ As conclusion, the momentum is directly related to both mass and velocity. Therefore, with faster speed of bullet cart, target cart also moves faster and more and with greater mass of bullet cart, target cart also moves faster and more. In this experiment, there is too many errors because of unclear forces. They don't have any magnitudes and used human forces to the carts and therefore, we couldn't control our forces that affects to the cart's acceleration. This caused percent error when we are looking for mysterious mass of cart. By comparing and changing with masses on bullet cart, we could figured out the mass of mystery cart 1 and cart 2, which is 0.8 kg and 1.0kg. However, the actual value was 0.7kg and 1.2 kg and made 14.29% and 16.67% of percent errors respectively.

__Objective__: What physics principles do the traffic-accident investigators use to "reconstruct" the accident? __Hypothesis:__ Initial momentum and final momentum have equal magnitude. Also when the mass increases, velocity decrease and when the mass decreases, velocity increases to get same momemtum.
 * LAB : Momentum and Inelastic Collisions **

Data __Calculations:__ Show equation(s), numbers plugged in, and answer with correct units. Add columns in your data table to include these results. __Questions:__
 * 1) Find the initial momentum of the bullet cart for each trial.
 * p = m * v. p = 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.
 * p = m * v. p = 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.
 * p bullet + p target = 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.
 * p = m * v. p = 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?
 * Initial momenta and final momenta are approximately same for each trial.
 * 1) Which types of collisions are definitely inelastic? How do you know?
 * Inelastic collision: Total KE is not same, because when bullet cart touch and connected to target cart, the velocity decreases.
 * 1) Which types of collisions are definitely elastic? How do you know?
 * Elastic collisions: Total KE are same, because when bullet cart hit target, target cart moves same velocity as bullet cart did.
 * 1) 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.
 * When a cue ball hits the 15 balls in the middle of the pool table, all balls will separated with different velocity but the cue ball and the ball that directly hit the cue ball will not move from the position.

__Conclusion:__
 * Based on the law of conservation of momentum, the traffic-accident investigators were able to reconsturct an accident because the total momentum is always same. Also the conservation means there is no creating or destroying but tranffering . In the experiement, we discovered that initial momentum and final momentum are equal for each trial. However, there was slight difference between the initial momentum and final momentum. The possible source of error is human error that when the processor push the cart, the cart will not have enough speed or had too fast speed that the machine might made an error. Also the digits might cause a slight error because of the limit of digits. To improve the results, we can use the machine with more digits or put more effort on the controlling of your force.

//__Interesting applet about comparing elasitc and inelastic collision__// [] With this applet, you can compare the character of elastic and inelastic collision with different mass.