Mr. Rogers' AP Physics C: Mechanics (With IB Physics Topics) Objectives

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Newton's Laws(4)
Friction(5) Mech Energy(7) Momentum Semester Exam
Latin

Latin/Greek Root Words

arch--------->ancient, example: archtype;         chrono------>time, example: chronology;             -dom----------->quantity/state, example: freedom               fer-------->carry, example: transfer;               gen--------->birth, example: generate;                 luc-------->light, example lucid;                 neo--------->new, example: neonatologist;                olig--------->few, example: oligarchy;              omni--------->all, omniscient;            sym--------->together, symbol;

(Physics connection)

Chapter 7 & 8: Mechanical Energy

AP Physics C Newtonian Mechanics Standards

C. Work, energy, power 20%  cumulative 58%

F. Oscillations and gravitation 
    1.Simple harmonic motion (dynamics and energy relationships) 
    2.Mass on a spring 
    3.Pendulum and other oscillations 

Practice Test Study Guide

Objectives

Essential Question: Can energy be defined?

The Nature of Work

  1. Define mechanical energy.

  • Position
  • Motion
  1. Correctly use the SI unit of energy. Joule = kg (m2 / s2)

  2. Define work 3 ways.

  • In words: mechanical energy transfer done by a force (F) acting through a displacement (S) in its same dimension
  • Mathematically: W F(s) ∙ ds,  
  • Graphically: work is the area under a force (F) vs. displacement (S) curve. Note: "S" is traditionally used to represent a generic displacement that could occur in the x, y, or z dimensions.
  1. State whether work and mechanical energy are vectors or scalars.

  2. State 2 requirements for work to be done by a force.

  • Motion
  • Non-zero force component in same dimension as motion
  1. Explain what a dot product (scalar product) is and how the concept relates to work.

  2. Calculate the net work done by a constant force acting through a displacement.

  3. Calculate dot products for the i, j, k, form of vectors.

  • Multiply the i part of the force times the i part of the displacement vector
  • Repeat the above for the j & k parts
  • Sum the 3 products from the above steps.
example:
force =  2i, 3j, - 4k
displacement =  1i, 3j, 2k
work =   2  +  9  - 8
=   3

Note: work itself cannot be expressed in i, j, k form because it is not a vector.      

  1. Explain why work cannot be done by a centripetal force? (The displacement is perpendicular to the force.) Relevance: This is why a satellite can remain in orbit for an indefinite period of time with almost no energy input.

Metacognition Problem Solving Principle: While work is a scalar, it does have a relationship to spatial dimensions. Note that the components of forces and displacements in the same dimension do work. components in a different dimensions do not. This relationship is most evident when multiplying the i j k form of the vectors.

Homefun: Questions 1-10 odd p 188; Problems 3, 5, 7 p. 189

Read: Insultingly Stupid Movie Physics
Chapter 3, Conservation of mass and Energy: Is Anything Sacred?, pp 33 - 51

Relevance: Mechanical energy is the most useful form. Its availability from a source other than muscle power has profoundly influenced every aspect of human existence.

 

 

Activities

Lesson 1

Key Concept: Work is the mechanical energy transfer done by a force acting through a displacement in its same dimension.

Purpose: Use work as a powerful problem solving tool.

Interactive Discussion: Objectives 1-8. Note that net positive work tends to increase kinetic energy and net negative decrease it.

Demo 7.1: Student holding a book. Is work being done?

In Class Problem Solving:   How much work is done by the superman force in each of the following:

  1. Superman pushing a trunk with and without friction.
  2. Superman lifting a trunk.
  3. Superman swinging a trunk (assume no air resistance).

Interactive Discussion: Objectives 9. Total work is the sum of the dot products in all the dimensions.

In Class Problem Solving:  

  1. Superman pushing a trunk with a variable force
  2. Superman lifting a trunk with a variable force

Interactive Discussion: Objectives 10, 11. Derive the spring potential energy equation.

Resources/Materials: 

Essential Question: How are kinetic energy and work related?

 The Nature of Kinetic Energy

  1. Define kinetic energy 2 ways
  • In words: the work needed to accelerate an object from rest to its current velocity. (The energy an object possesses due to its motion)
  • Mathematically: K 1/2 mv2
  1. Derive the equation for kinetic energy from the equation for work, Newton's second law, and the kinematic equations assuming constant force and acceleration.

  2. Explain the difference between positive and negative work.

  • Negative work: reduces kinetic energy. Done by a conservative force such as gravity converts kinetic energy into potential energy. Done by sliding friction converts kinetic energy into thermal energy (heat).
  • Positive work: increases kinetic energy
  1. Use the definition of kinetic energy and work in problem solving. 
  • Sliding Friction: negative work = heat
  • Gravity Force: positive work = kinetic energy

Homefun: Read 7.5, Problems 17, 29, 31 p. 189-190 Serway

 

Read: Insultingly Stupid Movie Physics
Chapter 11, High Energy Films: Nuclear Firecrackers, Falling people, and cars as weapons, pp 163- 179

 

 

Lesson 2

Key Concept: Kinetic energy and work are related

Purpose: Understand that work is mechanical energy transfer and that typically when work is done it either increases or decreases kinetic energy.

Interactive Discussion: Objectives.

In Class Problem Solving :  

  1. Derive the equation for kinetic energy and the kinematic equations
  2. Work done by gravity with box sliding down slope.
  3. Work done by friction with box sliding down a slope.

 

 

 

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)

Title Pendulum /energy Lab (groups of three)
Purpose Determine if a pendulum can be considered frictionless.
Overview The law of conservation of energy (1st law of Thermodynamics) is as close to absolute truth as anything in all of science. If a pendulum can be considered frictionless then the potential energy at the top of the swing will exactly match the kinetic energy at the bottom.
  • Set up a photogate to measure velocity at the bottom of a pendulum's swing
  • Release the pendulum from a variety of different heights and measure its velocity at the bottom of its swing.
Data, Calculations
  • Make a plot a kinetic energy at the bottom verses potential energy at the top.
  • Show a theoretical line on the plot. 
Questions, Conclusions
  1. Should the theoretical line be above or below the line of best fit for the above plot?
  2. Why does the photogate not measure instantaneous velocity and how does this error impact the above plot.
Resources/Materials: photogate, pendulum
Essential Question: Throughout history, how have springs enabled war? How have springs enable peaceful development?
The Nature of Spring Potential Energy
(The Linear Spring as an Energy Storage Device)
  1. Calculate the net work done by a variable force.

  2. Explain why the net work done in compressing an ideal spring is always zero.

  3. Derive the equation for the potential energy of a linear spring.

  4. Plot the spring potential energy vs. displacement for a linear spring and compare it to the force vs. displacement curve.

 
General Case: F = - dU/dx
(spring force @ x) = (slope @ a point)

 

Linear spring: F = -kx
 
General Case: U = - F(x) ∙ dx
(U @ x) = (area under curve from 0 to x)
or
(U at x) = (work to compress spring)
 

Linear spring: U = 1/2 kx2

  1. Find the spring constant with springs in parallel or series.

Homefun (formative/summative assessment): Read 7.4, Problems 47, 57  p.  192-193 Serway

Relevance: Springs are a ubiquitous mechanical component found in numerous applications including the suspension systems in vehicles and all kinds of mechanical devices. The bow and arrow is an example of a spring system in which energy is slowly input then quickly released.

 

Lesson 3

Key Concept: The equations for springs can be used to model many common situations involving the storage and release of energy.

Purpose: Use spring equations in problem solving.

Interactive Discussion: Objectives.

In Class Problem Solving:  14 - 17

  1. Horizontal spring launcher
  2. Catapult
  3. Spring bumper
  4. springs in parallel or series
Essential Question: What would driving a car be like if it had no suspension system?

Spring and Mass Systems

  1. Define simple harmonic motion.
  • periodic
  • restoring force magnitude linear with respect to displacement
  • restoring force direction always toward the equilibrium position

Notes:

  • If friction = 0, the displacement is symmetrical about the equilibrium position.
  • equilibrium position is location where total force = 0.
  • restoring force is actually the sum of all forces
  1. Give an example of motion that is periodic but not simple harmonic. The orbit of planets

  2. Draw the energy diagram for a spring in simple harmonic motion (p. 232), define the equilibrium position and describe location along the masses path of:

  • max velocity--at equilibrium position
  • max acceleration--at extremes
  • max restoring force--at extremes
  • max kinetic energy--at equilibrium position
  • max spring potential energy--at extremes

Note: the above does not change with the orientation of the spring. In other words, it does not matter if the spring is vertical, horizontal, or on a slope. If the spring is vertical, it does not matter if the mass is hung from the spring or placed on top of it.

  1. Explain why the mechanical energy in a ideal spring/mass system is constant. There's no friction

  2. Solve problems involving a spring mass system when the mass is not attached. (Assume the spring itself is massless.)

Homefun (formative/summative assessment):

Relevance: Modeling mechanisms as springs/mass systems is the first step in the analysis done by engineers to minimize vibration.

 

Lesson 4

Key Concept: Harmonic motion.

Purpose: Introduce and define harmonic motion.

Demo 7.2: The Mr. Rogers YoYo- object: give an example of simple harmonic motion and how it relates to resonance.

Interactive Discussion: Explain simple harmonic motion vs periodic motion.

In Class Problem Solving:  

  1. Find the maximum deflection a vertical spring can have without losing the mass, if the mass is not attached.
 

Formal Lab Investigation

Title Simple Harmonic Motion of a Spring and Mass System
Category Energy
Purpose Determine if the natural frequency of a spring and mass system can be predicted.
Models Linear spring force equation: F = k (x)

natural frequency of a mass & spring system: f = 1/(2p)(k / m)2

Overview Using a spring scale, measure the force required to deflect a spring various distances and plot force vs. displacement.

From the above, determine the spring constant.

Attach the spring to a ring stand so that it hangs vertically and attach a known weight to the end of the spring.

Lift the eight up and release it so that the system vibrates.

Measure the system's frequency.

Calculate the system's frequency from the natural frequency equation using the mass and spring constant.

Safety Issues Do not start the harmonic motion by pulling the mass downward and releasing it. This can launch the weight.
Resources/Materials: spring, known weights, stop watch, spring scale

 

Essential Question: For an athlete, is power the same thing as strength?

Power Basics

  1. Correctly use the SI unit of power. Watt is the unit of power.
  2. Define  power. 

In words: power is the rate of doing work or the rate of using energy.

Mathematically:

  P = W/Δt     
  P = dE/dt  
  1. Calculate the power requirements of a car driving up an incline at constant velocity.
  P = F (Δx/Δt)

P = Fv

Remember: W = F (Δx)

Homefun (formative/summative assessment): Read 7.8, Problems 29, 33, 35 p.221

Relevance: The Watt is a ubiquitous unit. Every electrical appliance has a power rating in watts listed on its side. Power is a greatly misused term but it is important to understand it for many reasons including to understand household energy usage.

 

Lesson 5

Key Concept: Power is work per unit of time.

Purpose: Use power equations in problem solving.

Interactive Discussion: Objectives

In Class Problem Solving (two person teams): Calculate the power required to drive up various slopes at 65 mph and 35 mph. Assume no friction or air resistance.

 

Essential Question: How dangerous are falls?
The Nature of Gravitational Potential Energy
And Conservative Forces Sec. 8.6
  1. Define gravitational potential energy 2 ways:

  • In words: the minimum work needed to move a mass from one position to another assuming gravity is the only possible resistance force. Note this depends only on the starting and ending positions. it is path independent.
  • Mathematically: Ug = mgh  (for a constant gravity field)
  1. Solve problems in which mechanical energy is conserved. In other words:

(Us0 + Ug0 + K0)  = (Us1 + Ug1 + K1)

Homefun (formative/summative assessment): Read 81 & 8.2, Problems 11, 15, 21 pp. 219-220 Serway

 

Lesson 6

Key Concept: Gravitational potential energy and conservative forces

Purpose: Solve problems in which mechanical energy is conserved.

Interactive Discussion: Objectives

In Class Problem Solving (assume no friction) :

  1. Bob slides down a slope
  2. Robin hood shoots an arrow straight up. (His bow is a spring.)
  3. Robin hood shoots an arrow at an angle.  (His bow is a spring.)
  4. Robin hood shoots an arrow over a cliff as he gallops on a horse.  (His bow is a spring.)
 

 

Essential Question: We have a law: conservation of energy. Do we have any similar law for force?
Conservative Forces and Potential Energy Diagrams
  1. Identify conservative forces (p. 218).

  • work done is path independent
  • work done moving thru a closed path = 0
  1. Name two types of conservative forces. Note that the equations in objective 17 (p. 232) can be applied to both types of forces even if the forces are not linear with displacement:
  • ideal spring force (no friction)
  • gravity force
  1. Be aware that potential energy can only be associated with conservative forces.

  2. Correctly use the following equation (p. 219):

Wc = Ui - Uf

Where Wc = work done by a conservative force.

  1. Solve problems using energy diagrams and the concept of stable and unstable equilibrium.

  • stable equilibrium: If an object is disturbed from its equilibrium position (B) by displacing it, it will return to the same position once it's released. Displaced to any position with a potential energy below AC, the system will be in stable equilibrium.
  • unstable equilibrium: If an object is disturbed from its equilibrium position (B) by displacing it, it will go to a new position once it's released. Displaced to any position with a potential energy above AC, the system will be in unstable equilibrium.

Homefun (formative/summative assessment): Read chap 8.3 - 8.6,

 

Lesson 4

Key Concept: Conservative forces and potential energy diagrams.

Purpose: Solve problems with potential energy diagrams.

In Class Problem Solving:  

  1. Potential energy vs. displacement problems
  2. rope over cliff problem
  3. Jurassic park bus problem
Essential Question: Efficiencies aside, how could an electric car require less energy to operate than a gasoline fueled car?

Using  Kinetic, Gravitational Potential Energy, Spring Potential Energy, and Work All Together With the First Law of Thermodynamics

  1. State the first law of thermodynamics.

  2. Solve problems with all the forms of mechanical energy including mechanical energy transfer.

  3. Be aware that sliding friction is not a conservative force and that when it does negative work it converts mechanical energy into heat.

  4. Solve energy problems in which mechanical energy is converted into heat. Relevance: This is what the brakes on your car do when you slow down.

Metacognition Problem Solving Principle: Energy problems are straightforward as long as you remember that all the energy in a system at the beginning of a problem has to still be there at the end, except for energy transferred into or out of the system using work. In equation form:

(energy at start) + (sum of work done by non-conservative forces acting on the system) = (energy at end)

or

(Us0 + Ug0 + K0) + (Wncf) = (Us1 + Ug1 + K1)

 Wncf = DK + DUs + DUg

Note that work can be either positive or negative. Remember negative work decreases kinetic energy and positive work increases it.

Homefun (formative/summative assessment): Problems

Lesson 7

Key Concept: Conservation of energy.

Purpose: Use all the energy equations to solve problems.

Interactive Discussion: Objectives

In Class Problem Solving (friction present) :

  1. Bob slides down a slope
  2. Robin hood shoots an arrow straight up. (His bow is a spring.)
  3. Robin hood shoots an arrow at an angle.  (His bow is a spring.)
  4. Robin hood shoots an arrow over a cliff as he gallops on a horse.  (His bow is a spring.)

 

 

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)

Title Measurement of Friction on an Air Track
Purpose Estimate the friction force on an air track
Overview Although air tracks come about as close to creating a zero friction environment as possible, they still have some. The results of any air track experiment could be improved by including friction in the mathematical models, but if the friction force is indeed very small, including it would have little effect on an air track experiment.

To estimate the friction force we will assume that it is constant and that there are no energy losses in the spring when a slider rebounds.

  1. Set up an air track at a known angle and place a slider at the top.
  2. Release the slider and let it rebound off the bottom.
  3. Record the height the slider rebounds to and calculate the change in height from the original position. Repeat the process several times and record your data.
Data, Calculations Given the above assumptions and data, estimate the friction force acting continuously on the slider. (Hint: the friction force does work and in the process converts mechanical energy to heat. Write an energy balance equation)

Construct a 95% confidence interval for your estimate of the friction force.

Questions, Conclusions
  1. Devise an experiment to measure the mechanical energy loss in the slider's spring.
  2. Devise an experiment to determine if the friction force on the track is indeed constant.
Resources/Materials: air track

 

Essential Question: Are we energy beings?

The Nature of the World's Most Famous Equation

  1. Explain all the variables in the equation E = mc2

E = energy

m = mass converted into energy

c = speed of light, approx 3.0 (108)

  1. Calculate the energy released if a quantity of mass is converted to energy. (one megaton of TNT = 4.184 X 1015 Joules of energy)

Relevance: E = mc2 is arguably the most famous mathematical equation not just in physics but simply the single most famous equation. it explains why nuclear bombs are so incredibly destructive.

Summative Assessment : Unit Exam objectives 1- 38

Lesson 9

Key Concept: Matter is condensed energy

Purpose: Use E = mc2.

Interactive Discussion: Objectives

In Class Problem Solving:

  1. Calculate the energy released by reacting 8 grams of anti-matter with matter.
 
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Insultingly Stupid Movie Physics is one of the most humorous, entertaining, and readable physics books available, yet is filled with all kinds of useful content and clear explanations for high school, 1st semester college physics students, and film buffs.

It explains all 3 of Newton's laws, the 1st and 2nd laws of thermodynamics, momentum, energy, gravity, circular motion and a host of other topics all through the lens of Hollywood movies using Star Trek and numerous other films.

If you want to learn how to think physics and have a lot of fun in the process, this is the book for you!

 

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