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 14 %  cumulative 58%

F. Oscillations and gravitation 9%, cumulative 61%
    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.

  2. Define work 3 ways.

  • In words: mechanical energy transfer done by a force acting through a displacement in its same dimension
  • Mathematically: W =∫F(s) ∙ ds,  
  • Graphically: work is the area under a force vs. displacement curve.

  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.
  4. Explain why work cannot be done by a centripetal force?

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 209; Problems 1, 3, 5, 6 p. 209-210 Serway

 

 

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.
  3. Use the definition of kinetic energy and work in problem solving. 

Homefun: Read 7.5, Problems 25 p. 211 Serway

 

Lesson 2

Key Concept: Kinetic energy and work are related

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

Interactive Discussion: Objectives.

In Class Problem Solving teams of 2:   Derive the equation for kinetic energy and the kinematic equations

 

 

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 a 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.
  F = - dU/dx (the spring force at x) = (the slope at a point on the U vs x curve)
  U = ∫F(x) ∙ dx
(U at a given value of x) = (the area under the F vs x curve from 0 to x)
or
(U at a given value of x) = (the work required to compress the spring)
  1. Find the spring constant with springs in parallel or series.

Homefun: Read 7.4, Problems 19  p.  211 Serway

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

  1. Give an example of motion that is periodic but not simple harmonic.

  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 and min velocity
  • max and min acceleration
  • max and min restoring force
  • max and min kinetic energy
  • max and min spring potential energy

  1. Explain why the mechanical energy in a ideal spring/mass system is constant.

  2. Solve problems involving a spring mass system when the mass is not attached.

Homefun: Problems 11, 13, 15 p. 210  Serway

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.

  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:Read 7.8, Problems 39, 41 p. 212 Serway

 

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 in a gravity field.
  • Mathematically: Ug = mgh  (for a constant gravity field)

  1. Solve problems in which mechanical energy is conserved. In other words, there is no work done or mathematically:

(Us1 + Ug1 + K1)  = (Us1 + Ug1 + K1)

Homefun:Read 81 & 8.2, Problems 1, 3 p. 240 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.

Homefun: Read chap 8.3 - 8.6, Questions 44, 45, 46 p. 245   Serway

 

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
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.
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: Problems 33, 49, 51, 63  Serway

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)

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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