Momentum Test Results

Test corrections: explain what you did incorrectly for a problem and show your new answer. Use extra paper if needed.

ON ALL FUTURE TESTS, ANSWERS WITHOUT UNITS WILL BE MARKED INCORRECT.

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Re-assess due: Nov 25th. Complete this work:�Worksheets 3, 4, review and rocket science.

Momentum Reflection

What helped you learn?

What was challenging?

What did you enjoy?

Any notes/feedback?

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For energy:

Option 1: summative lab AND test (separate standard)

Option 2: just summative test, no graded lab

Energy Schedule

11-10

11-11

11-17

11-21

11-24

11-25

Thanksgiving Break

Test: HS-PS3-1 Calculate changes/transformations of energy in systems

12-1

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12-3

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11-14

12-5

Physics of Collisions

Big question: How do we design and build vehicles to reduce injuries from collisions?

Energy - Notes Day

One of the most fundamental aspects of Physics and the universe is the concept of energy. What gives you ‘energy’?

Physics is described as the study of matter and energy

Energy is the ability to do work. It is measured in Joules.�Work = Force*distance (Newton*meters)

Energy allows matter to change its motion or arrangement.

Like momentum, energy is a conserved quantity in a closed system. The universe has a finite and constant total energy (at least given what we know and observe).

Power is a measurement of how much energy is transferred per second. Watts are the units for power, or Joules/second.

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Video

From the video, which kinds of energy are due to motion, and what are due to position/arrangement?

Energy Pie Charts

One representation of energy is a pie chart. In any given second, what kind of energy do you as a human have? Make a pie chart to represent your energy types.

Kinds of energy: Ek (kinetic), Eg (gravity), Eel (elastic), Ee (electric), Eth (thermal), nuclear, sound, light

What is the largest percentage? Smallest?

Basic Energy Biomechanics - click here to read more

Global energy storage systems

Unit of electrical energy - kilowatt-hour

An important unit to be aware of is the kilowatt-hour, abbreviated kWh. A home uses around 1,000 kWh every month.

This is an 1,000 watt item, running for one hour. It is equivalent to 1,000 joules/second *3600 seconds/hour = 3.6*10^6 joules, or 3.6 MJ (megajoules).

Energy Scale

1 Joule = 1 Newton-meter = �1 kgm^2/s^2

Check out this table to get an idea of how much energy 1 joule is.

Or, check out this one.

Right down some reference values for perspective.

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1. List objects in the system. Usually, include earth. Indicate +/- y direction. �2. Sketch the bar graphs in position A (before) and position B (after). Include anything outside the system that adds or subtracts energy (does work). �3. Write equation and solve. Situation: Egg during drop, prior to crash

E_initial +/- E_{transferred to/from system} = E_final

Egg right before and after crash

How do we calculate the impact force? Let’s derive Ek, Eg, and work.

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Deriving our first energy equation - Kinetic Energy

One definition of kinetic energy is the integral of momentum with respect to velocity (mass not changing). AKA, area under the graph below. Assume the object starts at rest, and its mass doesn’t change. Draw the trendline. Write an equation for the area of the graph, in terms of final velocity vf and mass m.

Momentum�p = mv

(kgm/s)

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Velocity (m/s)

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Ek = 1/2 mv^2

P is directly proportional �to v. �Area = ½*base*height�Base is vf-0 -> vf. �Height is pf -> m*vf

Area = ½ vf*m*vf

Kinetic Energy = ½mv^2

�Velocity usually referring to final/current velocity.

Momentum�p = mv

(kgm/s)

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Velocity (m/s)

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Alternate Derivation Strategy

All energy types/transfers require a force to be applied through a distance. Ek = some force*x

Using F=mv/t, find t in terms of v and x, substitute and solve. Other helpful equations: �x = v/t t=x/ave v ave. v = (vf-vi)/2

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To see another derivation of this equation, click here

Deriving our gravitational energy equation

If energy can be expressed as a force*distance, what equation might represent the energy of an object’s position relative to earth and gravitational force?

E_g = some force * distance =

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Energy flow in egg drop:

Gravitational energy –> Kinetic Energy -> Thermal/sound energy/strain energy

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Egg right before and after crash

This would have made our egg drop calculations much easier!

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Let’s calculate the energy and final velocity from egg drop

Assumptions: g = 9.8m/s^2 Height = 4 meters�Egg mass = .05 kg

Mgh = 1/2mv^2 = Fd�By approximating the crash distance, we can calculate the average impact force.

Estimate crash distance, solve for average crash force.

1. List objects in the system. Usually, include earth. Indicate +/- y direction. �2. Sketch the bar graphs in position A (before) and position B (after). Include anything outside the system that adds or subtracts energy (does work). �3. Write equation and solve for missing variable(s)

E_initial +/- E_{transferred to/from system} = E_final

Objective: Deriving Elastic Energy Model

So far we have 3 representations for energy:

Work = energy transfer = fd �Kinetic energy, E_k= .5mv^2 gravitational energy, E_g= mgh

How do we model elastic energy, E_el? �What might determine the energy contained in a spring?��Application: Predict the launch velocity of a spring-loaded cart.

Elastic Energy Relevant Info

Energy can be thought of as a force acting through a distance: work = Force * displacement, (joules or Newton*meters)�

E_el = some force acting some distance =

k = spring constant = Newtons/meter

Hooke’s law: Force_spring = -kx

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Deriving Elastic Energy Equation

Slope? �Area? �Intercept?�Should we ignore it?

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General form elastic energy equation: �Use k and x in your definition.�Use your E_el equation to predict the cart’s launch velocity. E_el = .5mv^2

Spring Force (N)

Spring Displacement (m)

Fenbert’s Data

Slope: ��Area:��Intercept:�Should we ignore it?

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General form elastic energy equation: �Use k and x in your definition.�Use your E_el equation to predict the cart’s launch velocity. E_el = .5mv^2

Fenbert’s Data

Slope: k = 287N/m�Area: E_el (N*m)�Intercept: Load Force of 3.17N�Should we ignore it?�No! The spring was compressed �before testing started.

General form elastic energy equation: .5bh → .5F*x → .5kxx → .5kx^2�Elastic energy on graph: .032m*.5(3.17+12.35) = .248 Joules �Predicted v = sqrt(2*.248J/.499kg)= 0.997 m/s �Actual v ~ 0.90 m/s�Fenbert’s % error: (.9-.997)/.997*100 = -9.7%�

Average slope: 0.89 m/s Ave peak v: 0.87m/s

Elastic Energy Lab Reports - In pairs, after sharing data

Analysis: �- What is the relationship between force and displacement? �- How do we represent that with a math model? Substitute y and x with real variables. �- What does the slope represent in the graph? What are its units? �- What is the vertical intercept, and if significant, what does it represent?�- What does your area represent? How can you create an equation for your graph area, using the symbols Es, k and x. �- Complete a percent-error calculation for your predicted velocity vs actual velocity. % error = (measured velocity - predicted velocity)/predicted value x 100.

Conclusion - Based on your math models, what is the general form equation linking spring force and displacement? What generalized math model did you develop for spring energy? AKA Does your data support that the elastic energy of a spring can be modeled by Es = .5kx^2. Include the appropriate proportionality description (linear, directly proportional, inverse etc) and any future recommendations for testing based on mistakes during the lab or improvements that could be made.

1. List objects in the system. Usually, include earth. Indicate +/- y direction. �2. Sketch the bar graphs in position A (before) and position B (after). Include anything outside the system that adds or subtracts energy (does work). �3. Write equation and solve. Situation: Spring cart is launched.

E_el = E_k: .5kx^2 + F₀x = .5mv^2

% error = (actual v-predicted v/predicted v)*100

Cart launch velocity challenge

Given a spring-loaded cart, predict its launch velocity. Which group can make the most accurate prediction!? �Fenbert’s % error was: 4% actual 0.83 m/s predicted 0.8 m/s

1. Determine the spring constant k.
2. Calculate Elastic Energy when fully compressed.
3. Calculate velocity, assuming all elastic energy is converted to kinetic energy.

Eel = Ek .5kx^2 = .5mv^2 �% error = (experiment-theoretical)/theoretical*100

% error = (actual v-predicted v/predicted v)*100

Happy Friday!

Mr. Fenbert went for a run yesterday. Describe where energy was stored, and what it did. For an interesting read about energy and running, click here.

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Future Labs

By the end of the year, my goal is that you all can independently design an experiment based on variables of interest, to get accurate results.

What could have caused poor results/data?

What can you do differently for the next lab?

In the future, what can I do to help you collect consistent, accurate data, WITHOUT showing you exactly what to measure and how?

Energy Schedule

11-10

11-11

11-17

11-21

11-24

11-25

Thanksgiving Break

Test: HS-PS3-1 Calculate changes/transformations of energy in systems�Lab: HS- PS3-2 Develop models for motion and positional energys

12-1

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12-3

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11-14

12-5

Do you notice anything surprising about this chart?

Sugar has a lot of energy!

Energy Transfer Problem

Energy Transfer Problem

Assuming minimal friction/thermal energy:

At the arrow’s peak, all Elastic energy of the bow will be transferred to Gravitational energy.

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Eel of bow = Eg of arrow —> 1/2kx^2 = mgh

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.5*300N/m*.8m^2 = .05kg*9.8m/s^2 * height

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96J = .05kg*9.8m/s^2*height

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96J/(.05kg*9.8m/s^2) = height = 196 meters

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Energy Transfer Problem

What is the arrows velocity shortly after launch?

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Energy Transfer Problem

What is the arrows velocity shortly after launch?

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Assuming minimal friction/thermal energy:

Shortly after release, all of the bows elastic energy will be transferred to the arrow’s kinetic energy.

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Eel bow = Ek arrow —> 1/2kx^2 = 1/2mv^2

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96J (from previous calculations = ½*mass*v^2

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96J = ½ *.05kg*v^2

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Square root(96J/1/2*.05kg)= v = 62m/s

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How far will the penguin slide? Last energy equation!

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How far will the penguin slide? GUESS

How far will the penguin slide?

Eg = Ek = Eth -> Eth = Ff*d -> Ff = uk*m*g

Eg = Ff*d mgh = uk*m*g*d -> d = h/uk d = 4m/.2 = 20 meters

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Energy equations

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E_k = ½mv² E_g = mgh E_el = ½kx²

E_th = F_fr x E_trans= Fx P = E_trans/ t

E_initial +/- E_{transferred to/from system} = E_final

_{Energy is measured in J (joules), which is a newton-meter. �Power is measured in W (watts), or Joules/second. �K is the spring constant, in Newtons/meter}

Unit Check - A Joule is a kgm^2/s^2, or a newton-meter.

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E_k = ½mv² E_g = mgh E_el = ½kx²

Show that all three equations have units of joules, or Newton-meters, or kgm^2/s^2.

Energy storage and bar charts

Today, we are focused on identifying forms of energy storage and representing that with bar graphs.

Groups will be assigned problems to present. Create your bar graph of assigned problems to help you share your work with the class.

Happy Monday!

What gives you energy? �What is something that brought you joy over break?

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Metaphor Time

We have learned two equations before break:

Force*time = change in momentum�Force*distance = work

These are two fundamental equations for our collisions project.

What meaning beyond physics might these equations represent?

Energy Efficiency = Useful energy in system at end/energy in system at start.

Car efficiency = 30J Ekinetic/100J Echemical = .3 or 30% efficient

Note on thermal

For some context, to raise 1 kg of water by 1 degree celsius, it takes ~4000 Joules of energy.

Internal Combustion Engine vs Electric and Watts

Electric vehicles are around 4 times more efficient at converting energy to motion ie a majority of the electrical energy goes to kinetic energy of the rotating tires and moving vehicle (~90%).

A typical car engine power is about 100,000 Watts, or 100,000 joules per second.

Energy equations

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E_k = ½mv² E_g = mgh E_el = ½kx²

E_th = F_fr x E_trans= Fx P = E_trans/ t

E_initial +/- E_{transferred to/from system} = E_final

_{Energy is measured in J (joules), which is a newton-meter. �Power is measured in W (watts), or Joules/second. �K is the spring constant, in Newtons/meter}

Energy vs Torque

What variables would you use to describe the mechanical advantage I get from using a lever/hammer/wrench?

Energy vs Torque

Torque has the same units as energy - Newton*meter, but they are not the same!

Energy is a force acting �through a distance.

Torque is a force acting �at a distance.

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Does anyone remember what a dot product/ cross product is?

Dot Product vs Cross Product - Energy vs Torque

Both have units of Newton-meters, but are different!

Work = Fdcos𝛳�Dot product of F and d�F parallel to d

Torque = Fdsin𝛳�Cross product of F and d�F perpendicular to d

Energy equations - Continue practice with wk 5�Energy transfer and power

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E_k = ½mv² E_g = mgh E_el = ½kx²

E_th = F_fr x E_trans= Fx P = E_trans/ t��Energy and/or work measured in joules, equivalent to a Newton-meter or kgm^2/s^2�Power is measured in joules per second, or the Watt

E_initial +/- E_{transferred to/from system} = E_final

Quiz day - All questions/parts worth ½ point. 3 total points.

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E_k = ½mv² E_g = mgh E_el = ½kx²

E_th = F_fr x E_transfer= Fx P = E_transfer/ t��Energy and/or work measured in joules, equivalent to a Newton-meter or kgm^2/s^2�Power is measured in joules per second, or the Watt

E_initial +/- E_{transferred to/from system} = E_final

Quiz Answers - Each question/part worth ½ points. 3 points total.�1. Ball with v0 = 3m/s. Without friction, how high will it roll?

2. Dart gun vertically launches 25g dart 50cm high. What was the energy stored in the spring?

1. You are operating a bicycle generator like the one at right. Suppose that 10% of the energy from a fun-sized snickers bar (74 Calories) is transferred to electrical energy. For how many minutes could this energy power a 60W light bulb? 1 Calorie= 4186J

2. Accelerate from 0-28m/s in 6s in a 1300kg car.

B. Equation:�

C. Power of car?

Rube Goldberg Inspiration

Before break, have some fun building a Rube Goldberg machine. Do the energy transfer calculations for your steps!

Energy Schedule

11-10

11-11

11-17

11-21

11-24

11-25

Thanksgiving Break

Test: HS-PS3-1 Calculate changes/transformations of energy in systems

12-1

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12-3

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11-14

12-5

The machine consists of two blocks, shown below. The pulley friction and string mass are negligible. The blocks are released from rest, and m2 > m1. Assume that h=0 at the floor. Which graph best represents the gravitational energy U and kinetic energy K of the system as a function of the height of block m1?

Link for demo

Draw an energy chart for the loop.

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Bonus: What is the ratio Eg/Ek at point 1?

Happy Test Day! This is a Summative test for our Energy unit.

Quantitative means include numerical answers. Do not ignore friction/thermal energy unless told!

ANSWERS MUST INCLUDE CORRECT UNITS.

E_k = ½mv² E_g = mgh E_el = ½kx²

E_th = F_fr x E_trans= Fx P = E_trans/ t

E_initial +/- E_{transferred to/from system} = E_final

Energy Test Results

Test corrections: explain what you did incorrectly for a problem and show your new answer. Use extra paper if needed.

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Re-assess due December 19th.

Complete Worksheet 3, 4, 5 and Review.

Collisions Project Concept - Injury

We will watch a 20 minute video, which highlights ways people can get injured in crashes. Take notes, and be prepared to explain these ideas in your project.

Halfway there…

Semester Reflection/Project Wrap Up

With a piece of paper respond to the following questions:

1. How did the semester go? Anything working/not working for you?
2. Is there a particular subject/field you’d like to learn about during S2?�As time allows, our plan will be Electric Fields, electric circuits, magnetism, nuclear physics, modern physics (relativity, quantum).
3. My classroom values are to be curious, reflective, engaged, empathetic and dedicated. How did you demonstrate those values this semester? What could you and/or our community improve on?

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Happy Monday

Who do you associate most with for how semester 1 went?

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Who would you like to be during semester 2?

Energy Test Class Data

Happy Monday - Energy Test

Get materials, notes, calculators out before class starts. I’d like to give everyone as much in-class time as possible!

Problem 9 should read: You and your friend push a 1500kg car along a level road, acceleration it from rest. The pushers transfer 6000 J of energy into the system: 2000J of which ends up in the Ethermal account due to friction.

Energy Transfer Project - Rube Goldberg Device

Our last standard of the year will be: Design, build and refine a device that works within given constraints to convert one form of energy into another form of energy. ��AKA, Rube Goldberg Machines!

Today, we will watch some videos for inspiration, look at the rubric, and brainstorm ideas. Your primary constraint is resources available in the room.

If you think something would be really cool to have, Mr. Fenbert will attempt to shop this week for general supplies.

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To Do

For Project:

1. Determine group roles. Sign contract.
2. Brainstorm materials you want, and let me know.
3. Materials in this room are fair game. Just let me know what you find/grab from somewhere.
4. Continue the quantitative energy problems, due tue.

Happy Tuesday

How effective are humans at transferring energy into useful forms?

How efficient is a standard combustion engine?

Link to interesting read on human efficiency

Project Day - Assembly (long advisory) schedule today/tomorrow

You’ll have the next three days to build, refine, and measure your Rube Goldberg Device.

Monday will be dedicated to creating your shared presentation slides, and presentations will happen Tuesday/Wednesday.

If you want feedback on your slides and grade, turn them in early!

Today’s Goal: have your mechanisms built/tested. Find spring constant of your elastic object. Start measuring and calculating energy for one of your steps.

Project Day - Assembly (long advisory) schedule today/tomorrow

You’ll have the next three days to build, refine, and measure your Rube Goldberg Device.

Monday will be dedicated to creating your shared presentation slides, and presentations will happen Tuesday/Wednesday.

If you want feedback on your slides and grade, turn them in early!

Today’s Goal: Have your device completed. Start measuring needed values (mass, velocity, height, spring constant).

Project Day - Presentations/Calculations

1. Picture (or video) of your device. Live demo could work to.
2. Bar charts for each energy transfer (energy converting to another form, or transferring between objects.
3. Calculate kinetic, gravitational, and elastic energy in the system for steps.
4. Choose two transfers to calculate efficiency. Ex: How much Gravitational Energy —> Kinetic in a step. Efficiency = Final energy/initial energy

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Make measurements for velocity, mass, height, spring constant, deflection needed to approximate joules and energy transfers in your device.

Project Day - Presentations/Calculations

• Picture (or video) of your device. Live demo could work to.
• Bar charts for each energy transfer (energy converting to another form, or transferring between objects.
• Calculate kinetic, gravitational, and elastic energy in the system for steps.
• Choose two transfers to calculate efficiency. Ex: How much Gravitational Energy —> Kinetic in a step. Efficiency = Final energy/initial energy

Make measurements for velocity, mass, height, spring constant, change in length, needed to approximate joules and energy transfers in your device.

Upload your groups presentation to canvas, so that I can easily share it for you on Wednesday! A link to your shared google slides works fine.