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K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 1 of 12 K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

instantaneous velocity 2. Average acceleration,  and instantaneous  acceleration 3. Uniformly accelerated  linear motion 4. Free-fall motion 5. 1D Uniform Acceleration  Problems

2. Recognize whether or not a physical situation  involves constant velocity or constant  acceleration STEM_GP12KIN-Ib-13 3. Interpret displacement and velocity,  respectively, as areas under velocity vs. time  and acceleration vs. time curves STEM_GP12KIN-Ib-14 4. Interpret velocity and acceleration, respectively,  as slopes of position vs. time and velocity vs.  time curves STEM_GP12KIN-Ib-15 5. Construct velocity vs. time and acceleration vs.  time graphs, respectively, corresponding to a  given position vs. time-graph and velocity vs.  time graph and vice versa STEM_GP12KIN-Ib-16 6. Solve for unknown quantities in equations  involving one-dimensional uniformly accelerated  motion STEM_GP12KIN-Ib-17 7. Use the fact that the magnitude of acceleration  due to gravity on the Earth’s surface is nearly  constant and approximately 9.8 m/s2 in free-fall  problems STEM_GP12KIN-Ib-18 8. Solve problems involving one-dimensional  motion with constant acceleration in contexts  such as, but not limited to, the “tail-gating  phenomenon”, pursuit, rocket launch, and free fall problems STEM_GP12KIN-Ib-19 Kinematics: Motion in 2- Dimensions and 3- Dimensions Relative motion 1. Position, distance,  displacement, speed,  average velocity,  instantaneous velocity,  average acceleration,  and instantaneous  acceleration in 2- and  3- dimensions 2. Projectile motion 1. Describe motion using the concept of relative  velocities in 1D and 2D STEM_GP12KIN-Ic-20 2. Extend the definition of position, velocity, and  acceleration to 2D and 3D using vector  representation STEM_GP12KIN-Ic-21 3. Deduce the consequences of the independence  of vertical and horizontal components of  projectile motion STEM_GP12KIN-Ic-22 4. Calculate range, time of flight, and maximum  heights of projectiles STEM_GP12KIN-Ic-23

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K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 2 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

3. Circular motion 4. Relative motion

5. Differentiate uniform and non-uniform circular  motion STEM_GP12KIN-Ic-24 6. Infer quantities associated with circular motion  such as tangential velocity, centripetal  acceleration, tangential acceleration, radius of  curvature STEM_GP12KIN-Ic-25 7. Solve problems involving two dimensional  motion in contexts such as, but not limited to  ledge jumping, movie stunts, basketball, safe  locations during firework displays, and Ferris  wheels STEM_GP12KIN-Ic-26 8. Plan and execute an experiment involving  projectile motion: Identifying error sources,  minimizing their influence, and estimating the  influence of the identified error sources on final  results STEM_GP12KIN-Id-27 Newton’s Laws of Motion  and Applications 1. Newton’s Law’s of  Motion 2. Inertial Reference  Frames 3. Action at a distance  forces 4. Mass and Weight 5. Types of contact forces:  tension, normal force,  kinetic and static  friction, fluid resistance 6. Action-Reaction Pairs 7. Free-Body Diagrams 8. Applications of  Newton’s Laws to  single-body and  multibody dynamics 9. Fluid resistance 10. Experiment on forces 11. Problem solving using 1. Define inertial frames of reference STEM_GP12N-Id-28 2. Differentiate contact and noncontact forces STEM_GP12N-Id-29 3. Distinguish mass and weight STEM_GP12N-Id-30 4. Identify action-reaction pairs STEM_GP12N-Id-31 5. Draw free-body diagrams STEM_GP12N-Id-32 6. Apply Newton’s 1st law to obtain quantitative  and qualitative conclusions about the contact  and noncontact forces acting on a body in  equilibrium (1 lecture) STEM_GP12N-Ie-33 7. Differentiate the properties of static friction and  kinetic friction STEM_GP12N-Ie-34 8. Compare the magnitude of sought quantities  such as frictional force, normal force, threshold  angles for sliding, acceleration, etc. STEM_GP12N-Ie-35 9. Apply Newton’s 2nd law and kinematics to  obtain quantitative and qualitative conclusions  about the velocity and acceleration of one or  more bodies, and the contact and noncontact  forces acting on one or more bodies STEM_GP12N-Ie-36 10. Analyze the effect of fluid resistance on moving STEM_GP12N-Ie-37

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K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 3 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

Newton’s Laws

object

11. Solve problems using Newton’s Laws of motion  in contexts such as, but not limited to, ropes  and pulleys, the design of mobile sculptures,  transport of loads on conveyor belts, force  needed to move stalled vehicles, determination  of safe driving speeds on banked curved roads STEM_GP12N-Ie-38 12. Plan and execute an experiment involving  forces (e.g., force table, friction board, terminal  velocity) and identifying discrepancies between  theoretical expectations and experimental  results when appropriate STEM_GP12N-If-39 Work, Energy, and Energy  Conservation 1. Dot or Scalar Product 2. Work done by a force 3. Work-energy relation 4. Kinetic energy 5. Power 6. Conservative and  nonconservative forces 7. Gravitational potential  energy 8. Elastic potential energy 9. Equilibria and potential  energy diagrams 10. Energy Conservation,  Work, and Power  Problems 1. Calculate the dot or scalar product of vectors STEM_GP12WE-If-40 2. Determine the work done by a force (not  necessarily constant) acting on a system STEM_GP12WE-If-41 3. Define work as a scalar or dot product of force  and displacement STEM_GP12WE-If-42 4. Interpret the work done by a force in one dimension as an area under a Force vs. Position  curve STEM_GP12WE-If-43 5. Relate the work done by a constant force to the  change in kinetic energy of a system STEM_GP12WE-Ig-44 6. Apply the work-energy theorem to obtain  quantitative and qualitative conclusions  regarding the work done, initial and final  velocities, mass and kinetic energy of a system. STEM_GP12WE-Ig-45 7. Represent the work-energy theorem graphically STEM_GP12WE-Ig-46 8. Relate power to work, energy, force, and  velocity STEM_GP12WE-Ig-47 9. Relate the gravitational potential energy of a  system or object to the configuration of the  system STEM_GP12WE-Ig-48 10. Relate the elastic potential energy of a system  or object to the configuration of the system STEM_GP12WE-Ig-49 11. Explain the properties and the effects of  conservative forces STEM_GP12WE-Ig-50 12. Identify conservative and nonconservative STEM_GP12WE-Ig-51

Don't forget about the age old question of Why Lithium shows bizarre behaviour over the other elements of the same group?

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 4 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

forces

13. Express the conservation of energy verbally and  mathematically STEM_GP12WE-Ig-52 14. Use potential energy diagrams to infer force; stable, unstable, and neutral equilibria; and  turning points STEM_GP12WE-Ig-53 15. Determine whether or not energy conservation  is applicable in a given example before and after  description of a physical system STEM_GP12WE-Ig-54 16. Solve problems involving work, energy, and  power in contexts such as, but not limited to,  bungee jumping, design of roller-coasters,  number of people required to build structures  such as the Great Pyramids and the rice  terraces; power and energy requirements of  human activities such as sleeping vs. sitting vs.  standing, running vs. walking. (Conversion of  joules to calories should be emphasized at this  point.) STEM_GP12WE-Ih-i 55 Center of Mass, Momentum,  Impulse, and Collisions 1. Center of mass 2. Momentum 3. Impulse 4. Impulse-momentum  relation 5. Law of conservation of  momentum 6. Collisions 7. Center of Mass,  Impulse, Momentum,  and Collision Problems 8. Energy and momentum  experiments 1. Differentiate center of mass and geometric  center STEM_GP12MMIC-Ih 56 2. Relate the motion of center of mass of a system  to the momentum and net external force acting  on the system STEM_GP12MMIC-Ih 57 3. Relate the momentum, impulse, force, and time  of contact in a system STEM_GP12MMIC-Ih 58 4. Explain the necessary conditions for  conservation of linear momentum to be valid. STEM_GP12MMIC-Ih 59 5. Compare and contrast elastic and inelastic  collisions STEM_GP12MMIC-Ii 60 6. Apply the concept of restitution coefficient in  collisions STEM_GP12MMIC-Ii 61 7. Predict motion of constituent particles for  different types of collisions (e.g., elastic,  inelastic) STEM_GP12MMIC-Ii 62

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K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 5 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

8. Solve problems involving center of mass,  impulse, and momentum in contexts such as,  but not limited to, rocket motion, vehicle  collisions, and ping-pong. (Emphasize also the  concept of whiplash and the sliding, rolling, and  mechanical deformations in vehicle collisions.) STEM_GP12MMIC-Ii 63 9. Perform an experiment involving energy and  momentum conservation and analyze the data  identifying discrepancies between theoretical  expectations and experimental results when  appropriate STEM_GP12MMIC-Ii 64 Integration of Data Analysis  and Point Mechanics  Concepts Refer to weeks 1 to 9 (Assessment of the performance standard) (1 week) Rotational equilibrium and  rotational dynamics 1. Moment of inertia 2. Angular position,  angular velocity,  angular acceleration 3. Torque 4. Torque-angular  acceleration relation 5. Static equilibrium 6. Rotational kinematics 7. Work done by a torque 8. Rotational kinetic  energy 9. Angular momentum 10. Static equilibrium  experiments 11. Rotational motion  problems Solve multi-concept,  rich context problems using  concepts from  rotational motion,  fluids, oscillations,  gravity, and  thermodynamics 1. Calculate the moment of inertia about a given  axis of single-object and multiple-object  systems (1 lecture with exercises) STEM_GP12RED-IIa-1 2. Exploit analogies between pure translational  motion and pure rotational motion to infer  rotational motion equations (e.g., rotational  kinematic equations, rotational kinetic energy,  torque-angular acceleration relation) STEM_GP12RED-IIa-2 3. Calculate magnitude and direction of torque  using the definition of torque as a cross product STEM_GP12RED-IIa-3 4. Describe rotational quantities using vectors STEM_GP12RED-IIa-4 5. Determine whether a system is in static  equilibrium or not STEM_GP12RED-IIa-5 6. Apply the rotational kinematic relations for  systems with constant angular accelerations STEM_GP12RED-IIa-6 7. Apply rotational kinetic energy formulae STEM_GP12RED-IIa-7 8. Solve static equilibrium problems in contexts  such as, but not limited to, see-saws, mobiles,  cable-hinge-strut system, leaning ladders, and  weighing a heavy suitcase using a small  bathroom scale STEM_GP12RED-IIa-8 9. Determine angular momentum of different  systems STEM_GP12RED-IIa-9

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 6 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

10. Apply the torque-angular momentum relation STEM_GP12RED-IIa 10 11. Recognize whether angular momentum is  conserved or not over various time intervals in a  given system STEM_GP12RED-IIa 11 12. Perform an experiment involving static  equilibrium and analyze the data—identifying  discrepancies between theoretical expectations  and experimental results when appropriate STEM_GP12RED-IIa 12 13. Solve rotational kinematics and dynamics  problems, in contexts such as, but not limited to,  flywheels as energy storage devices, and spinning hard drives STEM_GP12RED-IIa 13 Gravity 1. Newton’s Law of  Universal Gravitation 2. Gravitational field 3. Gravitational potential  energy 4. Escape velocity 5. Orbits 1. Use Newton’s law of gravitation to infer  gravitational force, weight, and acceleration due  to gravity STEM_GP12G-IIb-16 2. Determine the net gravitational force on a mass  given a system of point masses STEM_GP12Red-IIb 17 3. Discuss the physical significance of gravitational  field STEM_GP12Red-IIb 18 4. Apply the concept of gravitational potential  energy in physics problems STEM_GP12Red-IIb 19 5. Calculate quantities related to planetary or  satellite motion STEM_GP12Red-IIb 20 6. Kepler’s laws of  planetary motion 6. Apply Kepler’s 3rd Law of planetary motion STEM_GP12G-IIc-21 7. For circular orbits, relate Kepler’s third law of  planetary motion to Newton’s law of gravitation  and centripetal acceleration STEM_GP12G-IIc-22 8. Solve gravity-related problems in contexts such  as, but not limited to, inferring the mass of the  Earth, inferring the mass of Jupiter from the  motion of its moons, and calculating escape  speeds from the Earth and from the solar system STEM_GP12G-IIc-23 Periodic Motion 1. Periodic Motion 2. Simple harmonic  motion: spring-mass 1. Relate the amplitude, frequency, angular  frequency, period, displacement, velocity, and  acceleration of oscillating systems STEM_GP12PM-IIc-24

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 7 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

system, simple  pendulum, physical  pendulum

2. Recognize the necessary conditions for an object  to undergo simple harmonic motion STEM_GP12PM-IIc-25 3. Analyze the motion of an oscillating system  using energy and Newton’s 2nd law approaches STEM_GP12PM-IIc-26 4. Calculate the period and the frequency of spring  mass, simple pendulum, and physical pendulum STEM_GP12PM-IIc-27 3. Damped and Driven  oscillation 4. Periodic Motion  experiment 5. Differentiate underdamped, overdamped, and  critically damped motion STEM_GP12PM-IId-28 6. Describe the conditions for resonance STEM_GP12PM-IId-29 7. Perform an experiment involving periodic motion  and analyze the data—identifying discrepancies  between theoretical expectations and  experimental results when appropriate STEM_GP12PM-IId-30

5. Mechanical waves 8. Define mechanical wave, longitudinal wave,  transverse wave, periodic wave, and sinusoidal  wave STEM_GP12PM-IId-31 9. From a given sinusoidal wave function infer the  (speed, wavelength, frequency, period,  direction, and wave number STEM_GP12PM-IId-32 10. Calculate the propagation speed, power  transmitted by waves on a string with given  tension, mass, and length (1 lecture) STEM_GP12PM-IId-33 Mechanical Waves and  Sound 1. Sound  2. Wave Intensity 3. Interference and beats 4. Standing waves 5. Doppler effect 1. Apply the inverse-square relation between the  intensity of waves and the distance from the  source STEM_GP12MWS-IIe 34 2. Describe qualitatively and quantitatively the  superposition of waves STEM_GP12MWS-IIe 35 3. Apply the condition for standing waves on a  string STEM_GP12MWS-IIe 36 4. Relate the frequency (source dependent) and  wavelength of sound with the motion of the  source and the listener STEM_GP12MWS-IIe 37 5. Solve problems involving sound and mechanical  waves in contexts such as, but not limited to,  echolocation, musical instruments, ambulance  sounds STEM_GP12MWS-IIe 38

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 8 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

6. Perform an experiment investigating the  properties of sound waves and analyze the  data appropriately—identifying deviations from  theoretical expectations when appropriate STEM_GP12MWS-IIe 39 Fluid Mechanics 1. Specific gravity 2. Pressure 3. Pressure vs. Depth  Relation 4. Pascal’s principle 5. Buoyancy and  Archimedes’ Principle 6. Continuity equation 7. Bernoulli’s principle 1. Relate density, specific gravity, mass, and  volume to each other STEM_GP12FM-IIf-40 2. Relate pressure to area and force STEM_GP12FM-IIf-41 3. Relate pressure to fluid density and depth STEM_GP12FM-IIf-42 4. Apply Pascal’s principle in analyzing fluids in  various systems STEM_GP12FM-IIf-43 5. Apply the concept of buoyancy and Archimedes’  principle STEM_GP12FM-IIf-44 6. Explain the limitations of and the assumptions  underlying Bernoulli’s principle and the  continuity equation STEM_GP12FM-IIf-45 7. Apply Bernoulli’s principle and continuity  equation, whenever appropriate, to infer  relations involving pressure, elevation, speed,  and flux STEM_GP12FM-IIf-46 8. Solve problems involving fluids in contexts such  as, but not limited to, floating and sinking,  swimming, Magdeburg hemispheres, boat  design, hydraulic devices, and balloon flight STEM_GP12FM-IIf-47 9. Perform an experiment involving either Continuity and Bernoulli’s equation or buoyancy,  and analyze the data appropriately—identifying  discrepancies between theoretical expectations  and experimental results when appropriate STEM_GP12FM-IIf-48 Temperature and Heat 1. Zeroth law of  thermodynamics and  Temperature  measurement  2. Thermal expansion  3. Heat and heat capacity  4. Calorimetry

1. Explain the connection between the Zeroth Law  of Thermodynamics, temperature, thermal  equilibrium, and temperature scales STEM_GP12TH-IIg-49 2. Convert temperatures and temperature  differences in the following scales: Fahrenheit,  Celsius, Kelvin STEM_GP12TH-IIg-50 3. Define coefficient of thermal expansion and  coefficient of volume expansion STEM_GP12TH-IIg-51

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 9 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

4. Calculate volume or length changes of solids due  to changes in temperature STEM_GP12TH-IIg-52 5. Solve problems involving temperature, thermal  expansion, heat capacity,heat transfer, and  thermal equilibrium in contexts such as, but not  limited to, the design of bridges and train rails using steel, relative severity of steam burns and  water burns, thermal insulation, sizes of stars,  and surface temperatures of planets STEM_GP12TH-IIg-53 6. Perform an experiment investigating factors  affecting thermal energy transfer and analyze  the data—identifying deviations from theoretical  expectations when appropriate (such as thermal  expansion and modes of heat transfer) STEM_GP12TH-IIg-54 7. Carry out measurements using thermometers STEM_GP12TH-IIg-55 5. Mechanisms of heat  transfer 8. Solve problems using the Stefan-Boltzmann law  and the heat current formula for radiation and  conduction (1 lecture) STEM_GP12TH-IIh-56 Ideal Gases and the Laws of  Thermodynamics 1. Ideal gas law 2. Internal energy of an  ideal gas  3. Heat capacity of an  ideal gas  4. Thermodynamic  systems  5. Work done during  volume changes 6. 1st law of  thermodynamics  Thermodynamic  processes: adiabatic,  isothermal, isobaric,  isochoric 1. Enumerate the properties of an ideal gas STEM_GP12GLT-IIh 57 2. Solve problems involving ideal gas equations in  contexts such as, but not limited to, the design  of metal containers for compressed gases STEM_GP12GLT-IIh 58 3. Distinguish among system, wall, and  surroundings STEM_GP12GLT-IIh 59 4. Interpret PV diagrams of a thermodynamic  process STEM_GP12GLT-IIh 60 5. Compute the work done by a gas using dW=PdV  (1 lecture) STEM_GP12GLT-IIh 61 6. State the relationship between changes internal  energy, work done, and thermal energy supplied  through the First Law of Thermodynamics STEM_GP12GLT-IIh 62

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 10 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT CONTENT CONTENT STANDARD PERFORMANCE  STANDARD LEARNING COMPETENCIES CODE

7. Differentiate the following thermodynamic  processes and show them on a PV diagram:  isochoric, isobaric, isothermal, adiabatic, and  cyclic STEM_GP12GLT-IIh 63 8. Use the First Law of Thermodynamics in  combination with the known properties of  adiabatic, isothermal, isobaric, and isochoric  processes STEM_GP12GLT-IIh 64 9. Solve problems involving the application of the  First Law of Thermodynamics in contexts such  as, but not limited to, the boiling of water,  cooling a room with an air conditioner, diesel  engines, and gases in containers with pistons STEM_GP12GLT-IIh 65 7. Heat engines  8. Engine cycles 9. Entropy  10. 2nd law of  Thermodynamics  11. Reversible and  irreversible processes 12. Carnot cycle  13. Entropy 10. Calculate the efficiency of a heat engine STEM_GP12GLT-IIi-67 11. Describe reversible and irreversible processes STEM_GP12GLT-IIi-68 12. Explain how entropy is a measure of disorder STEM_GP12GLT-IIi-69 13. State the 2nd Law of Thermodynamics STEM_GP12GLT-IIi-70 14. Calculate entropy changes for various processes  e.g., isothermal process, free expansion,  constant pressure process, etc. STEM_GP12GLT-IIi-71 15. Describe the Carnot cycle (enumerate the  processes involved in the cycle and illustrate the  cycle on a PV diagram) STEM_GP12GLT-IIi-72 16. State Carnot’s theorem and use it to calculate  the maximum possible efficiency of a heat  engine STEM_GP12GLT-IIi-73 17. Solve problems involving the application of the  Second Law of Thermodynamics in context such  as, but not limited to, heat engines, heat pumps,  internal combustion engines, refrigerators, and  fuel economy STEM_GP12GLT-IIi-74 Integration of Rotational  motion, Fluids, Oscillations,  Gravity and Thermodynamic  Concepts Refer to weeks 1 to 9 (Assessment of the performance standard) (1 week)

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 11 of 12K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT Code Book Legend Sample: STEM_GP12GLT-IIi-73 LEGEND SAMPLE First Entry Learning Area and  Strand/ Subject or  Specialization Science, Technology,  Engineering and Mathematics General Physics STEM_GP12GLT Grade Level Grade 12 Uppercase  Letter/s Domain/Content/ Component/ Topic Ideal Gases and Laws of Thermodynamics

- Roman Numeral *Zero if no specific  quarter Quarter Second Quarter II Lowercase  Letter/s *Put a hyphen (-) in  between letters to  indicate more than a  specific week Week Week 9 i

- Arabic Number Competency State Carnot’s theorem and  use it to calculate the  maximum possible efficiency  of a heat engine 73

DOMAIN/ COMPONENT CODE Units and Measurement EU Vectors V Kinematics KIN Newton’s Laws N Work and Energy WE Center of Mass, Momentum, Impulse and Collisions MMIC Rotational Equilibrium and Rotational Dynamics RED Gravity G Periodic Motion PM Mechanical Waves and Sounds MWS Fluid Mechanics FM Temperature and Heat TH Ideal Gases and Laws of Thermodynamics GLT

K to 12 Senior High School STEM Specialized Subject – General Physics 1 December 2013 Page 12 of 12 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   TOPIC / LESSON NAME GP1 – 01: Units, Physical Quantities, Measurement, Errors and Uncertainties,  Graphical Presentation, and Linear Fitting of Data CONTENT STANDARDS 1. The effect of instruments on measurements  2. Uncertainties and deviations in measurement  3. Sources and types of error  4. Accuracy versus precision  5. Uncertainty of derived quantities  6. Error bars  7. Graphical analysis: linear fitting and transformation of functional dependence to linear form PERFORMANCE STANDARDS Solve, using experimental and theoretical approaches, multiconcept, rich-context problems  involving measurement, vectors, motions in 1D, 2D, and 3D, Newton’s Laws, work, energy,  center of mass, momentum, impulse, and collisions LEARNING COMPETENCIES 1. Solve measurement problems involving conversion of units, expression of  measurements in scientific notation (STEM_GP12EU-Ia-1)  2. Differentiate accuracy from precision (STEM_GP12EU-Ia-2)  3. Differentiate random errors from systematic errors (STEM_GP12EU-Ia-3)  4. Use the least count concept to estimate errors associated with single  measurements (STEM_GP12EU-Ia-4)  5. Estimate errors from multiple measurements of a physical quantity using variance  (STEM_GP12EU-Ia-5)  6. Estimate the uncertainty of a derived quantity from the estimated values and  uncertainties of directly measured quantities (STEM_GP12EU-Ia-6)  7. Estimate intercepts and slopes—and their uncertainties—in experimental data with  linear dependence using the “eyeball method” and/or linear regression formula  (STEM_GP12EU-Ia-7) SPECIFIC LEARNING OUTCOMES

TIME ALLOTMENT 180 minutes

Lesson Outline: GP1-01-1  GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data  1. Physical Quantities Introduction/Motivation (10 minutes): Talk about the discipline of physics, and the discipline required to  understand physics.  Instruction / Delivery (30 minutes): Units, Conversion of Units, Rounding-Off Numbers  Evaluation (20 minutes)  2. Measurement Uncertainities Motivation (15 minutes): Discuss the role of measurement and experimentation in physics; Illustrate issues  surrounding measurement through measurement activities involving pairs (e.g. bidy size and pulse rate  measurements)  Instruction/Delivery (30 minutes): Scientific notation and significant figures; Reporting measurements with  uncertainty; Significant figures; Scientific Notation ; Propagation of error; Statistical treatment of uncertainties  Enrichment (15 minutes ): Error propagation using differentials  3. Data Presentation and Report Writing Guidelines  Instruction/Delivery (60 minutes): Graphing; Advantages of converting relations to linear form; “Eye-ball” method  of determining the slope and y-intercept from data; Least squares method of determining the slope and y-intercept  from data; Purpose of a Lab Report; Parts of a Lab Report MATERIALS ruler, meter stick, tape measure, weighing scale, timer (or watch) RESOURCES University Physics by Young and Freedman (12th edition)  Physics by Resnick, Halliday, and Krane (4th edition)

PROCEDURE MEETING LEARNERS’ Part 1: Physical quantities

Introduction/Motivation (10 minutes)  1. Introduce the discipline of Physics:  - Invite students to give the first idea that come to their minds whenever

GP1-01-2  GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   they hear “Physics”  - Let some students explain why they have such impressions of the field.  - Emphasize that just as any other scholarly field, Physics helped in  shaping the modern world.  2. Steer the discussion towards the notable contributions of Physics to humanity:  - The laws of motion(providing fundamental definitions and concepts to  describe motion and derive the origins of interactions between objects in  the universe)  - Understanding of light, matter, and physical processes  - Quantum mechanics (towards inventions leading to the components in a  cell phone)  3. Physics is science. Physics is fun. It is an exciting adventure in the quest to find  out patterns in nature and find means of understanding phenomena through  careful deductions based on experimental verification. Explain that in order to  study physics, one requires a sense of discipline. That is, one needs to plan how  to study by:  - Understanding how one learns. Explain that everyone is capable of  learning Physics especially if one takes advantage of one’s unique way of  learning. (Those who learn by listening are good in sitting down and  taking notes during lectures; those who learn more by engaging others  and questioning can take advantage of discussion sessions in class or  group study outside classes.)  - Finding time to study. Explain that learning requires time. Easy concepts  require less time to learn compared to more difficult ones. Therefore, one  has to invest more time in topics one finds more difficult. (Do students  study Physics every day? Does one need to prepare before attending a  class? What are the difficult sections one find?)

Instruction / Delivery (30 minutes)

GP1-01-3 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   1. Units  Explain that Physics is an experimental science. Physicists perform  experiments to test hypotheses. Conclusions in experiment are derived from  measurements. And physicists use numbers to describe measurements.  Such a number is called a physical quantity. However, a physical quantity  would make sense to everyone when compared to a reference standard. For  example, when one says, that his or her height is 1.5 meters, this means that  one’s height is 1.5 times a meter stick (or a tape measure that is one meter  long). The meter stick is here considered to be the reference standard. Thus,  stating that one’s height is 1.5 is not as informative.  Since 1960 the system of units used by scientists and engineers is the  “metric system”, which is officially known as the “International System” or SI  units (abbreviation for its French term, Système International).  To make sure that scientists from different parts of the world understand the  same thing when referring to a measurement, standards have been defined  for measurements of length, time, and mass.  Length – 1 meter is defined as the distance travelled by light in a vacuum in  1/299,792,458 second. Based on the definition that the speed of light is  exactly 299,792,458 m/s.  Time – 1 second is defined as 9,192,631,770 cycles of the microwave  radiation due to the transition between the two lowest energy states of the  cesium atom. This is measured from an atomic clock using this transition.  Mass – 1 kg is defined to be the mass of a cylinder of platinum-iridium alloy  at the International Bureau of weights and measures (Sèvres, France).

GP1-01-4 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   Figure 1. Length across the scales (adapted from University Physics by  Young and Freedman, 12th ed.).  2. Conversion of units  Discuss that a few countries use the British system of units (e.g., the United  States). However, the conversion between the British system of units and SI  units have been defined exactly as follows:  Length: 1 inch = 2.54 cm  Force: 1 pound = 4.448221615260 newtons  The second is exactly the same in both the British and the SI system of units.  How many inches are there in 3 meters?  How much time would it take for light to travel 10,000 feet?  How many inches would light travel in 10 fs? (Refer to Table 1 for the unit  prefix related to factors of 10).  How many newtons of force do you need to lift a 34 pound bag? (Intuitively,  just assume that you need exactly the same amount of force as the weight of

GP1-01-5 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data  the bag).  3. Rounding off numbers  Ask the students why one needs to round off numbers. Possible answers  may include reference to estimating a measurement, simplifying a report of a  measurement, etc.  Discuss the rules of rounding off numbers:  a. Know which last digit to keep  b. This last digit remains the same if the next digit is less than 5.  c. Increase this last digit if the next digit is 5 or more.  A rich farmer has 87 goats—round the number of goats to the nearest 10.  Round off to the nearest 10:  314234, 343, 5567, 245, 7891  Round off to the nearest tenths:  3.1416, 745.1324, 8.345, 67.47 prefix symbol factor atto a 10-18 femto f 10-15 pico p 10-12 nano n 10-9 micro μ 10-6 milli m 10-3

GP1-01-6

GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   centi c 10-2 deci d 10-1 deka da 101 hecto h 102 kilo k 103 mega M 106 giga G 109 tera T 1012 peta P 1015 exa E 1018 Table 1. Système International (SI) prefixes.

Evaluation (20 minutes)  Conversion of units:  A snail moves 1cm every 20 seconds. What is this in in/s? Decide how to report the  answer (that is, let the students round off their answers according to their  preference).  0.1 cm 1 in in ⋅ = 0.01968503937007874015748031496063 20 s 54.2 cm s 0.1 cm 2 2 = = ⋅ = = ⋅ 05.0 / 0.5 10 / .0 020 / 0.2 10 / cm s cm s in s in s 20 s In the first line, 1.0cm/20s was multiplied by the ratio of 1in to 2.54 cm (which is  equal to one). By strategically putting the unit of cm in the denominator, we are able

GP1-01-7 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   to remove this unit and retain inches. However, based on the calculator, the  conversion involves several digits.  In the second line, we divided 1.0 by 20 and retained two digits and rewrote in terms  of a factor 102. The final answer is then rounded off to retain 2 figures.  In performing the conversion, we did two things. We identified the number of  significant figures and then rounded off the final answer to retain this number of  figures. For convenience, the final answer is re-written in scientific notation.  *The number of significant figures refer to all digits to the left of the decimal point  (except zeroes after the last non-zero digit) and all digits to the right of the decimal  point (including all zeroes).  *Scientific notation is also called the “powers-of-ten notation”. This allows one to  write only the significant figures multiplied to 10 with the appropriate power. As a  shorthand notation, we therefore use only one digit before the decimal point with the  rest of the significant figures written after the decimal point.  How many significant figures do the following numbers have?  10 .1 2343 10 ⋅ 035 23.004 23.000 4 2.3 10 ⋅ Perform the following conversions using the correct number of significant figures in  scientific notation:

GP1-01-8 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   A jeepney tried to overtake a car. The jeepney moves at 75km/hour, convert this to  the British system (feet per second)?  It takes about 8.0 minutes for light to travel from the sun to the earth. How far is the  sun from the earth (in meters, in feet)?  Let students perform the calculations in groups (2-4 people per group). Let  volunteers show their answer on the board.

Part 2: Measurement uncertainties

Motivation for this section (15 minutes)  1. Measurement and experimentation is fundamental to Physics. To test  whether the recognized patterns are consistent, Physicists perform  experiments, leading to new ways of understanding observable phenomena  in nature.  2. Thus, measurement is a primary skill for all scientists. To illustrate issues  surrounding this skill, the following measurement activities can be performed  by volunteer pairs:  a. Body size: weight, height, waistline  From a volunteer pair, ask one to measure the suggested dimensions of  the other person with three trials using a weighing scale and a tape  measure.  Ask the class to express opinions on what the effect of the measurement  tool might have on the true value of a measured physical quantity. What  about the skill of the one measuring?  b. Pulse rate (http://www.webmd.com/heart-disease/pulse-measurement)  Measure the pulse rate 5 times on a single person. Is the measurement

GP1-01-9 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   repeatable?

Instruction / Delivery (30 minutes)  1. Scientific notation and significant figures  Discuss that in reporting a measurement value, one often performs several  trials and calculates the average of the measurements to report a  representative value. The repeated measurements have a range of values  due to several possible sources. For instance, with the use of a tape  measure, a length measurement may vary due to the fact that the tape  measure is not stretched straight in the same manner in all trials.  So what is the height of a table?— A volunteer uses a tape measure to  estimate the height of the teacher’s table. Should this be reported in  millimeters? Centimeters? Meters? Kilometers?  The choice of units can be settled by agreement. However, there are times  when the unit chosen is considered most applicable when the choice allows  easy access to a mental estimate. Thus, a pencil is measured in centimeters  and roads are measured in kilometers.  How high is mount Apo? How many Filipinos are there in the world? How  many children are born every hour in the world?  2. Discuss the following:  a. When the length of a table is 1.51 ± 0.02 m, this means that the true value  is unlikely to be less than 1.49 m or more than 1.53 m. This is how we  report the accuracy of a measurement. The maximum and minimum  provides upper and lower bounds to the true value. The shorthand  notation is reported as 1.51(2) m. The number enclosed in parentheses

GP1-01-10 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   indicates the uncertainty in the final digits of the number.  b. The measurement can also be presented or expressed in terms of the  maximum likely fractional or percent error. Thus, 52 s ± 10% means  that the maximum time is not more than 52 s plus 10% of 52 s (which is  57 s, when we round off 5.2 s to 5 s). Here, the fractional error is (5 s)/52  s.  c. Discuss that the uncertainty can then be expressed by the number of  meaningful digits included in the reported measurement. For instance, in  measuring the area of a rectangle, one may proceed by measuring the  length of its two sides and the area is calculated by the product of these  measurements.  Side 1 = 5.25 cm  Side 2 = 3.15 cm  Note that since the meterstick gives you a precision down to a single  millimeter, there is uncertainty in the measurement within a millimeter.  The side that is a little above 5.2 cm or a little below 5.3 cm is then  reported as 5.25 ± 0.05 cm. However, for this example only we will use  5.25 cm.  Area = 3.25 cm x 2.15 cm = 6.9875 cm2 or 6.99 cm2  Since the precision of the meterstick is only down to a millimeter, the  uncertainty is assumed to be half a millimeter. The area cannot be  reported with a precision lower than half a millimeter and is then rounded  off to the nearest 100th.  d. Review of significant figures  Convert 45.1 cubic cm to cubic inches. Note that since the original  number has 3 figures, the conversion to cubic inches should retain this

GP1-01-11 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   number of figures:  3 1 45 1. in   ⋅ 3 cm 54.2 cm 3 1 45 1. in 3 3 = ⋅ = cm 2.75217085 ... 16.387064 in 3 cm 3 3 45.1 2.75 cm in = Show other examples.  3. Review of scientific notation  Convert 234km to mm:  1000 234 m km 100 cm ⋅ ⋅ 1 km 1 m = 23400000 cm 7 234 2.34 10 km cm = ⋅ 4. Reporting a measurement value  A measurement is limited by the tools used to derive the number to be  reported in the correct units as illustrated in the example above (on  determining the area of a rectangle).  Now, consider a table with the following sides:

GP1-01-12 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   25.23±0.02 cm and 35.13±0.02 cm or  25.23(2) cm and 35.13(2) cm  2 23.25 13.35 886.3299 cm cm cm ⋅ = 2 2 2 886 3. 863.8 10 cm cm = ⋅ What about the resulting measurement error in determining the area?  Note: The associated error in a measurement is not to be attributed to human  error. Here, we use the term to refer to the associated uncertainty in  obtaining a representative value for the measurement due to undetermined  factors. A bias in a measurement can be associated to systematic errors that  could be due to several factors consistently contributing a predictable  direction for the overall error. We will deal with random uncertainties that do  not contribute towards a predictable bias in a measurement.    5. Propagation of error  A measurement x or y is reported as:  x x ± ∆   y y ± ∆  The above indicates that the best estimate of the true value for x is  found between x – Δx and x + Δx (the same goes for y).  How does one report the resulting number when arithmetic operations are  performed between measurements?  Addition or subtraction: the resulting error is simply the sum of the corresponding  errors.

GP1-01-13 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   x x ± ∆ y y ± ∆ z x y = ± ∆ = ∆ + ∆ z x y Multiplication or division: the resulting error is the sum of the fractional errors  multiplied by the original measurement  x x ± ∆ x x ± ∆ y y ± ∆ y y ± ∆ x .  z = z x y = ⋅ y ∆ = ∆ z x ∆ y ∆ = ∆ z x ∆ y + + z x y z x y  ∆  ∆ ∆ = x y  ∆  ∆ ∆ = x y z z + z z + x y x y The estimate for the compounded error is conservatively calculated. Hence, the  resultant error is taken as the sum of the corresponding errors or fractional errors.  Thus, repeated operation results in a corresponding increase in error.

GP1-01-14 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   Power-law dependence:  x x ± ∆ ∆ = → ∆ = x n z x z nz x z nx z n x = → ∆ = ∆ For a conservative estimate, the maximum possible error is assumed. However, a  less conservative error estimate is possible:  For addition or subtraction:  () () () () 2 2 2 2 ∆z = ∆x + ∆y +...+ ∆p + ∆q For multiplication or division:  2 2 2 2  ∆  +   ∆ ∆ = qq + +  ...   ∆ +   ∆ x y p z z x y p 6. Statistical treatment  The arithmetic average of the repeated measurements of a physical quantity  is the best representative value of this quantity provided the errors involved is  random. Systematic errors cannot be treated statistically.

GP1-01-15 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   1 N ∑x m i x = N i = 1 mean:  1 N ∑( ) 2 sd − − = i m x x standard deviation:  N 1 i = 1 For measurements with associated random uncertainties, the reported value  is: mean plus-or-minus standard deviation. Provided many measurements  will exhibit a normal distribution, 50% of these measurements would fall  within plus-or-minus 0.6745(sd) of the mean. Alternatively, 32% of the  measurements would lie outside the mean plus-or-minus twice the standard  deviation.  The standard error can be taken as the standard deviation of the means.  Upon repeated measurement of the mean for different sets of random  samples taken from a population, the standard error is estimated as:  sd sdmean = standard error N

Enrichment: (__ minutes)

GP1-01-16 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   df ∆ f ≈ dx ∆ x   df f x ∆ ≈ ∆ = o dx xx Figure 2. Function of one variable and its error Δf. Given a function f(x), the local  slope at xo is calculated as the first derivative at xo.  Example: ( ) y x = sin x x x = ± ∆ o d   ∆ ≈ ∆ [ ] y x sin( ) x dx xx = o ∆ ≈ ∆ y x x cos( ) o

GP1-01-17 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   Similarly, ( ) y x = sin ( ) y y x x ± ∆ = ± ∆ sin o y y x x x x ± ∆ = ∆ ± ∆ sin( ) cos( ) cos( )sin( ) o o y y x x x ± ∆ ≈ ± ∆ sin( ) cos( ) o o ∆ << x 0.1 cos( ) 0.1 ∆ ≈ x sin( ) ∆ ≈ ∆ x x ∴∆ ≈ ∆ y x x cos( ) o

Part 3: Graphing

Instruction / Delivery (60 minutes)  1. Graphing relations between physical quantities. 1 d d at = o + 2 2

GP1-01-18 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   Figure 3. Distance related to the square of time (for motions with constant  acceleration). The acceleration a can be calculated from the slope of the line. And  the intercept at the vertical axis do is determined from the graph.  The simplest relation between physical quantities is linear. A smart choice of  physical quantities (or a mathematical manipulation) allows one to simplify the study  of the relation between these quantities. Figure 3 shows that the relation between  the displacement magnitude d and the square of the time exhibits a linear relation  (implicitly having a constant acceleration; and having no initial velocity). Another  example is the simple pendulum, where the frequency of oscillation fo is proportional  to the square-root of the acceleration due to gravity divided by the length of the  pendulum L. The relation between the frequency of oscillation and the root of the  multiplicative inverse of the pendulum length can be explored by repeated  measurements or by varying the length L. And from the slope, the acceleration due  to gravity can be determined.  g f 1 = o 2 L π 1 1   = L f g o 2 π 2. The previous examples showed that the equation of the line can be  determined from two parameters, its slope and the constant y-intercept  (figure 4). The line can be determined from a set of points by plotting and  finding the slope and the y-intercept by finding the best fitting straight line.

GP1-01-19 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   Figure 4. Fitting a line relating y to x, with slope m and y-intercept b. By visual  inspection, the red line has the best fit through all the points compared to the other  trials (dashed lines).  3. The slope and the y-intercept can be determined analytically. The  assumption here is that the best fitting line has the least distance from all the  points at once. Legendre stated the criterion for the best fitting curve to a set  of points. The best fitting curve is the one which has the least sum of  deviations from the given set of data points (the Method of Least Squares).  More precisely, the curve with the least sum of squared deviations from a set  of points has the best fit. From this principle the slope and the y-intercept are  determined as follows:

GP1-01-20 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   y mx b = +    − N N N ∑ ∑ ∑ ( ) N yx x y ii i i i = = = 1 1 1 i i m = 2   − N N ∑ ∑ 2 N x x i i i = = 1 i 1        − N N N N ∑ ∑ ∑ ∑ 2 x y x yx i i i ii  i = = = = 1 1 1 1 i i i b = 2   − N N ∑ ∑ 2 N x x i i i = = 1 i 1 The standard deviation of the slope sm and the y-intercept sb are as follows:  ∑ 2 x n i s s − = 2 2 s s ∑ − ∑ =i i b yn x x ∑ ∑( ) m yn x x ( )2 2 i i 4. The lab report  Explain that in performing experiments one has to consider that the findings  found can be verified by other scientists. Thus, documenting one’s  experiments through a Laboratory report is an essential skill to a future  physicist. Below lists the sections normally found in a Lab report (which is  roughly less than or equal to four pages):

GP1-01-21 GENERAL PHYSICS 1  QUARTER 1  Units, Physical Quantities, Measurement, Errors and Uncertainties, Graphical Presentation, & Linear Fitting of  Data   Introduction - a concise description of the entire experiment (purpose, relevance,  methods, significant results and conclusions).  Objectives  - a concise and summarized list of what needs to be accomplished in the  experiment.  Background  - an account of the experiment intended to familiarize the reader with the  theory, related research that are relevant to the experiment itself.  Methods  - a description of what was performed, which may include a list of  equipment and materials used in order to pursue the objectives of the  experiment.  Results  - a presentation of relevant measurements convincing the reader that the  objectives have been performed and accomplished.  Discussion of Result  - the interpretation of results directing the reader back to the objectives Conclusions  - could be part of the previous section but is not intended solely as a  summary of results. This section could highlight the novelty of the  experiment in relation to other studies performed before.

GP1-01-22 GENERAL PHYSICS 1  QUARTER 1  Vectors   TOPIC / LESSON NAME GP1 – 02: Vectors CONTENT STANDARDS 1. Vectors and vector addition  2. Components of vectors  3. Unit vectors PERFORMANCE STANDARDS Solve, using experimental and theoretical approaches, multi-concept, rich-context problems  involving measurement, vectors, motions in 1D, 2D, and 3D, Newton’s Laws, work, energy,  center of mass, momentum, impulse, and collisions LEARNING COMPETENCIES 1. Differentiate vector and scalar quantities (STEM_GP12EU-Ia-8)  2. Perform addition of vectors (STEM_GP12EU-Ia-9)  3. Rewrite a vector in component form (STEM_GP12EU-Ia-10)  4. Calculate directions and magnitudes of vectors (STEM_GP12EU-Ia-11) SPECIFIC LEARNING OUTCOMES

TIME ALLOTMENT 60 minutes

Lesson Outline:  1. Introduction / Review: (5 minutes) Quick review of previous lesson involving physical quantities, right-triangle  relations (SOH-CAH-TOA), and parallelograms; Vectors vs. Scalars  2. Motivation: (5 minutes) Choose one from: scenarios involving paddling on a flowing river, tension game, random  walk  3. Instruction / Delivery: (25 minutes)  Geometric representation of vectors  The unit vector  Vector components  4. Enrichment: (10 to 15 minutes)  5. Evaluation: (10 or 15 minutes) MATERIALS For students: Graphing papers, protractor, ruler,  For teacher: 2 pieces of nylon cord (about 0.5m long for the teacher only), 1 meter  stick or tape measure RESOURCES University Physics by Young and Freedman (12th edition)

GP1-02-1  GENERAL PHYSICS 1  QUARTER 1  Vectors

Physics by Resnick, Halliday, and Krane (4th edition)

PROCEDURE MEETING LEARNERS’ Introduction/Review (5 minutes)  1. Do a quick review of the previous lesson involving physical quantities, SOH CAH-TOA, basic properties of parallelograms  2. Give examples which of these quantities are scalars or vectors then ask the  students to give examples of vectors and scalars.  Vectors are physical quantities that has both magnitude and direction Scalars are physical quantities that can be represented by a single number

Motivation (5 minutes)  Option 1: Discuss with students scenarios involving paddling upstream,  downstream, or across a flowing river. Allow the students to strategize how should  one paddle across the river to traverse the least possible distance?  Option 2: String tension game (perform with careful supervision)  - ask for two volunteers  - one student would hold a nylon cord at length across two hands  - the second student loops his nylon cord onto the other student’s cord  - the second student pulls slowly on the cord; if the loop is closer to the other  student’s hand, ask the class how the student would feel the pull on each  hand, and why  Option 3: Total displacement in a random walk - ask for six volunteers  - blindfold the first volunteer about a meter away from the board, let the  volunteer turn 2-3 times to give a little spatial disorientation, then ask this

GP1-02-2 GENERAL PHYSICS 1  QUARTER 1  Vectors   student to walk towards the board and draw a dot on the board. Do the  same for the next volunteer then draw an arrow connecting the two  subsequent dots with the previous one as starting point and the current dot  with the arrow head. Do the same for the rest of the volunteers.  - after the exercise, indicate the vector of displacement (red arrow) by  connecting the first position with the last position. This vector is the sum of  all the drawn vectors by connecting the endpoint to the starting point of the  next.    Figure 1. Summing vectors by sequential connecting of  dots based on the random walk exercise.

Instruction / Delivery (25 minutes)  Part 1: Geometric representation of vectors  1. If option 3 above was performed, use the resulting diagram to introduce  displacement as a vector. Otherwise, illustrate on the board the magnitude and direction of a vector using displacement (with a starting point and an  ending point, where the arrow head is at the ending point).

GP1-02-3 GENERAL PHYSICS 1  QUARTER 1  Vectors   Figure 2. Geometric sum of vectors example. The sum is  independent of the actual path but is subtended between  the starting and ending points of the displacement steps.  2. Illustrate the addition of vectors using perpendicular displacements as  shown below (where the red vector is the sum):

GP1-02-4 GENERAL PHYSICS 1  QUARTER 1  Vectors    Figure 3. Vector addition illustrated in a right triangle  configuration.  3. Explain how to calculate the magnitude of vector C by using the Pythagorian  theorem and its components as the magnitude of vector A and the  magnitude of vector B.  4. Explain how to calculate the components of vector C in general, from its  magnitude multiplied with the cosine of its angle from vector A (theta) and  the cosine of its angle from vector B (phi).  5. Use the parallelogram method to illustrate the sum of two vectors. Give  more examples for students to work with on the board.

GP1-02-5 GENERAL PHYSICS 1  QUARTER 1  Vectors     Figure 4. Vector addition using the parallelogram  method.  6. Illustrate vector subtraction by adding a vector to the negative direction of  another vector. Compare the direction of the difference and the sum of  vectors A and B. Indicate that vectors of the same magnitude but opposite  directions are anti-parallel vectors.  Figure 5. Subtraction of Vectors. Geometrically vector  subtraction is done by adding the vector minuend to the

GP1-02-6 GENERAL PHYSICS 1  QUARTER 1  Vectors   anti-parallel vector of the subtrahend. Note: the  subtrahend is the quantity subtracted from the minuend.  7. Discuss when vectors are parallel and when they are equal. Part 2: The unit vector  1. Explain that the direction of a vector can be represented by a unit vector that  is parallel to that vector.  2. Using the algebraic representation of a vector, calculate the components of  the unit vector parallel to that vector.  Figure 6. Unit vector.  Aˆ 3. Indicate how to write a unit vector by using a caret or a hat:  Part 3: Vector components 1. Discuss that vectors can be written by using its components multiplied by  unit vectors along the horizontal (x) and the vertical (y) axes.  r A i j ˆ ˆ = Ax + Ay 2. Discuss vectors and their addition using the quadrant plane to illustrate how  the signs of the components vary depending on the location on the quadrant

GP1-02-7 GENERAL PHYSICS 1  QUARTER 1  Vectors   plane as sections in the 2-dimensional Cartesian coordinate system.  3. Extend discussion to include vectors in 3 dimensions.  r A ˆi ˆj kˆ = Ax + Ay + Az 4. Discuss how to sum (or subtract vectors) algebraically using the vector  components.  r ˆ ˆ ˆ A i j k = + + A A A x y z r ˆ ˆ ˆ B i j k = + + B B B x y z r r r ˆ ˆ ˆ C A B ( )i ( )j ( )k = ± = ± + ± + ± A B A B A B x x y y z z Tips –In paddling across the running river, you may introduce an initial angle or  velocity or let the students discuss their relation. An intuition on tension and length  relation can be discussed if necessary. Vectors can be drawn separately before  making their origins coincident in illustrating geometric addition.

Enrichment (10 or 15 minutes)  1. Illustrate on the board how the magnitude of the components of a uniformly  rotating unit vector change with time. Note that this magnitude varies as the  cosine and sine of the rotation angle (the angular velocity magnitude  multiplied with time).  2. Calculate the components of a rotated unit vector and introduce the rotation  matrix. This can be extended to vectors with arbitrary magnitude. Draw a  vector that is ө degrees from the horizontal. This vector is then rotated by Ф degrees. Calculate the components of the new vector that is ө + Ф degrees  from the horizontal by using trigonometric identities as shown below.  The two equations can then be re-written using matrix notation where the

GP1-02-8 GENERAL PHYSICS 1  QUARTER 1  Vectors   2x2 (two rows by two columns) matrix is called the rotation matrix.  For now, it can simply be agreed that this way of writing simultaneous  equations is convenient. That is, a way to separate vector components (into  a column) and the 2x2 matrix that operates on this column of numbers to  yield a rotated vector, also written as a column of components.  The other column matrices are the rotated unit vector (ө + Ф degrees from  the horizontal) and the original vector (ө degrees from the horizontal) with  the indicated components. This can be generalized by multiplying both sides  with the same arbitrary length. Thus, the components of the rotated vector  (on 2D) can be calculated using the rotation matrix.

GP1-02-9 GENERAL PHYSICS 1  QUARTER 1  Vectors

GP1-02-10 GENERAL PHYSICS 1  QUARTER 1  Vectors   Figure 7. Rotating a vector using a matrix multiplication.

Evaluation (10 or 15 minutes)  Seatwork exercises using materials (include some questions related to the  motivation; no calculators allowed)  Sample exercise 1: involving calculation of vector magnitudes  Sample exercise 2: involving addition of vectors using components  Sample exercise 3: involving determination of vector components using triangles

GP1-02-11 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   TOPIC / LESSON NAME GP1 – 03: Displacement, time, average velocity, instantaneous velocity CONTENT STANDARDS Position, time, distance, displacement, speed, average velocity, instantaneous velocity PERFORMANCE STANDARDS Solve, using experimental and theoretical approaches, multiconcept, rich-context problems  involving measurement, vectors, motions in 1D, 2D, and 3D, Newton’s Laws, work, energy,  center of mass, momentum, impulse, and collisions LEARNING COMPETENCIES 1. Convert a verbal description of a physical situation involving uniform acceleration in  one dimension into a mathematical description (STEM_GP12KIN-Ib-12)  2. Differentiate average velocity from instantaneous velocity  3. Introduce acceleration  4. Recognize whether or not a physical situation involves constant velocity or constant  acceleration (STEM_GP12KIN-Ib-13)  5. Interpret displacement and velocity , respectively, as areas under velocity vs. time  and acceleration vs. time curves (STEM_GP12KIN-Ib-14) SPECIFIC LEARNING OUTCOMES

TIME ALLOTMENT 60 minutes

Lesson Outline:  1. Introduction / Review/Motivation: (15 minutes) Quick review of vectors and definition of displacement; use of  vectors to quantify motion with velocity and acceleration; walking activity; class discussion of speed vs velocity  2. Instruction / Delivery: (25 minutes)  Calculation of average velocities using positions on a number line  Average velocity as a slope of a line connecting two points on a postion vs. time graph  Instantaneous velocity as a derivative and as the slope of a tangent line  Inferring velocities from posion vs. time graphs  Displacement in terms of time-elapsed and average velocity  Displacement as an area under a velocity vs. time curve  Displacement as an integral  Introduce average/acceleration as change in velocity divided by elapsed time  3. Practice/Evaluation: (20 minutes) Seatwork GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line MATERIALS timer (or watch), meter stick (or tape measure) RESOURCES University Physics by Young and Freedman (12th edition)  Physics by Resnick, Halliday, and Krane (4th edition)

PROCEDURE MEETING LEARNERS’ Introduction/Review/Motivation (15 minutes)  1. Do a quick review of the previous lesson in vectors  with some emphasis on the definition of  displacement.  2. In describing how objects move introduce how the use of distance and time leads to the more precise  use by physicists of vectors to quantify motion with  velocity and acceleration (here, defined only as  requiring change in velocity)  3. Ask for two volunteers. Instruct one to walk in a  straight line but fast from one end of the classroom  to another as the other records the duration time  (using his or her watch or timer). The covered  distance is measured using the meter stick (or tape measure). Repeat the activity but this time let the volunteers switch tasks and ask the other volunteer to walk as fast as the first volunteer from the same  ends of the classroom. Is the second volunteer able to walk as fast as the first? Another pair of volunteers  might do better than the first pair.  4. Ask the class what the difference is between speed  and velocity.

GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line

Instruction / Delivery (25 minutes)  1. Discuss how to calculate the average velocity using  positions on a number line, with recorded arrival time  and covered distance (p1, p2, …, p5). For instance  at p1, x1 = 3m, t1 = 2s, etc.  p1 p2 p3 p4 p5 11m 3m 8m 3m 5m 20m 50s 30s 2s 10s 300sThe average velocity is calculated as the ratio  between the displacement and the time interval  during the displacement. Thus, the average velocity between p1 and p2 can be calculated as:  !"# = ∆& ∆' = &( − &* '( − '*= 5 - − 3 - 10 1 − 2 1 = 0.25 -/1 What is the average velocity from position p2 to p5?  Note that the choice for a positive direction is not  necessarily referring to a displacement from left to  right. However, when the choice of the positive  direction is arbitrarily taken, the other direction is

GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line towards the negative.  2. Emphasize that the average velocity between the  given coordinates above vary (e.g., between p1 to p2  and p1 to p4). The displacement along the  coordinate x can be graphed as a function of time t.  x ( ) 2 2 x , t ∆x ( ) 11 x , t ∆tt Figure 1. Average velocity.  Discuss that the average velocity from a coordinate x1 to x2 is taken as if the motion is a straight line  between said positions at the given time duration.  Hence, the average velocity is geometrically the  slope between these positions.  Aside: is the average velocity the same as the  average speed?  3. Now, discuss the notion of instantaneous velocity v as the slope of the tangential line at a given point  (figure 2). Mathematically, this is the derivative of x with respect to t.

GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line ∆( ∆) = +(+) = , lim ∆%→' Figure 2. Tangential lines.  4. Discuss between which time points in figure 3 (left)  illustrate motion with constant or non-constant  velocity, negative or positive constant velocity.  Figure 3 (right) shows instantaneous velocities as  slopes at specific time points. Discuss how the  values of the instantaneous velocity varies as you  move from v1 to v6.  x t 0 t 1t 2 t 3 t 4 tFigure 3. x-t graphs.  5. Show how one can derive the displacement based

GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line on the expression for the average velocity:  !"# = ∆& ∆'→ ∆& = !"#∆' Note that when the velocity is constant (Figure 4), so  is the average velocity between any two separate  time points. Thus, the total displacement magnitude is the rectangular area under the velocity vs. time graph (subtended by the change in time).  v av v ∆tt 1t 2 t Figure 4. Constant velocity.  6. Show that for a time varying velocity, the total displacement can be calculated in a similar manner  by summing the rectangular areas defined by small  intervals in time and the local average velocity. The  local average velocity is then approximately the  value of the velocity at a given number of time  intervals. Say, there are n time intervals between  time t1 and t2, the total displacement x is summed as  follows:

GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line & & ! = #∆!% = #)%∆* %'( %'(   Figure 5. Sum of discrete areas  under the velocity versus time  graph.  7. Discuss that as the time interval becomes  infinitesimally small, the summation becomes an  integral. Thus, the total displacement is the area  under the curve of the velocity as a function of time  between the time points in question.

GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line / ,- ! = #\$%∆' = ( \$)'*+' ,. %01 8. Introduce acceleration as the change in velocity between a given time interval (in preparation for the  next lesson).

Practice/Evaluation (20 minutes)  Seatwork exercises  Sample exercise 1: involving calculation of average velocities given initial and final position and time.  Sample exercise 2: Given x as a function of time, calculate  the instantaneous velocity at a specific time.  Sample exercise 3: Calculate the total displacement between a time interval, given the velocity as a function of  time.

GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   TOPIC / LESSON NAME GP1 – 04: Average and instantaneous acceleration CONTENT STANDARDS Average acceleration, and instantaneous acceleration PERFORMANCE STANDARDS Solve, using experimental and theoretical approaches, multiconcept, rich-context problems  involving measurement, vectors, motions in 1D, 2D, and 3D, Newton’s Laws, work, energy,  center of mass, momentum, impulse, and collisions LEARNING COMPETENCIES 1. Convert a verbal description of a physical situation involving uniform acceleration in  one dimension into a mathematical description (STEM_GP12KIN-Ib-12)  2. Recognize whether or not a physical situation involves constant velocity or constant  acceleration (STEM_GP12KIN-Ib-13)  3. Interpret velocity and acceleration, respectively, as slopes of position vs. time and  velocity vs. time curves (STEM_GP12KIN-Ib-15)  4. Construct velocity vs. time and acceleration vs. time graphs, respectively,  corresponding to a given position vs. time-graph and velocity vs. time graph and vice  versa (STEM_GP12KIN-Ib-16) SPECIFIC LEARNING OUTCOMES

TIME ALLOTMENT 60 minutes

Lesson Outline:  1. Introduction / Review: (5 minutes) Quick review of displacement, average velocity, and instantaneous velocity  2. Instruction / Delivery: (20 minutes)  Average acceleration as the ratio of the change in velocity to the elapsed time  Instantaneous acceleration as the time derivative of velocity  Instantaneous acceleration as the second time derivative of position  Change in velocity as product of average acceleration and time elapsed  Derivation of kinematic equations for 1d-motion under constant acceleration  Change in velocity as an area under the acceleration vs. time curve and as an integral  3. Enrichment: (20 minutes): Inferences from position vs. time, velocity vs. time, and acceleration vs. time curves 4. Evaluation: (15 minutes) Written exercise involving a sinusoidal displacement versus time graph MATERIALS Graphing papers, protractor, ruler

GP1-04-1  GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   RESOURCES University Physics by Young and Freedman (12th edition)  Physics by Resnick, Halliday, and Krane (4th edition)

PROCEDURE MEETING LEARNERS’ Introduction/Review (5 minutes)  1. Do a quick review of the previous lesson on  displacement, average velocity and instantaneous velocity.

Instruction / Delivery (20 minutes)  1. The acceleration of a moving object is a measure of  its change in velocity. Discuss how to calculate the  average acceleration from the ratio of the change in  velocity to the time duration of this change.  !"# = ∆& ∆' = &( − &* '( − '* 2. Recall that the first derivative of the displacement  with respect to time is the instantaneous velocity. Discuss that the instantaneous acceleration is the  first derivative of the velocity with respect to time: ∆& ∆' = 1&1'! = lim ∆.→0

GP1-04-2 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   Figure 1. Average acceleration  Figure 2. Instantaneous  acceleration.  3. Thus, given the displacement as a function of time,  the acceleration can be calculated as a function of time by successive derivations:  ! =#\$#% = ##%#&#% = #'& #%' 4. Given a constant acceleration, the change in velocity  (from an initial velocity) can be calculated from the

GP1-04-3 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   constant average velocity multiplied by the time  interval.  !"# = ∆& ∆' → ∆& = !"#∆' &) − &) = !"#∆' Figure 3. Velocity as area under  the acceleration versus time  curve.  Special case: motion with constant acceleration  Derive the following relations (for constant  acceleration):  Based on the definitions of the average velocity and  average acceleration, we can derive an expression  for the total displacement traveled with known  acceleration and the initial and final velocities:  &"# = ∆+ ∆'→ ∆+ = &"#∆'

GP1-04-4 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   !"# = #%&#' ( Eqn1  )"# = ∆! ∆+ → ∆! = )"#∆+ !( − !( = )"#∆+ Eqn2  ∆. = #%&#' (∆+ Eqn3  ∆+ =!( − !/ )∆+ ∆. =!/ + !( !( − !/ 2 ) ∆. = #''2#%' (" Eqn4 The resulting expression for the total displacement can be re-arranged to derive an expression for the  final velocity, given the initial velocity, acceleration  and the total displacement travelled:  ∆. =!(( − !/( 2) !(( = 2)∆. + !/( !( = 32)∆. + !/( Eqn5 From Eqn2 and Eqn3, the total displacement (from  an initial position to a final position) can be derived  as a function of the total time duration (from an initial  time to a final time) and the constant acceleration:  !/ = )∆+ − !(

GP1-04-5 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   ∆" # \$∆% & '( ) '( 2 ∆% ∆" #12 \$,∆%-( "( & ". # .( \$,∆%-( Eqn6  5. Discuss that with a time-varying acceleration, the  total change in velocity (from an initial velocity) can  be calculated as the area under the acceleration  versus time curve (at a given time duration). Given a  constant acceleration (figure 3), the velocity change  is defined by the rectangular area under the  acceleration vs. time curve subtended by the initial  and final time. Thus, with a continuously time varying  acceleration, the area under the curve is  approximated by the sum of the small rectangular  areas defined by the product of small time intervals  and the local average acceleration. This summation  becomes an integral when the time duration  increments become infinitesimally small.  / !−!# = %&'∆% 01. / 6< # : \$,%-;% ' & '2 # lim ∆6→89\$0∆% 6=01.

Enrichment (20 minutes)

GP1-04-6 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   1. Review the relations between displacement and  velocity, velocity and acceleration in terms of first  derivative in terms of time and area under the curve  within a time interval.  2. Discuss how one can identify whether a velocity is  constant (zero, positive or negative), time varying (slowing down or increasing) using figure 4.  3. Replace the displacement variable with velocity in  figure 4 (figure 5) and discuss what the related  acceleration becomes (constant or time varying).  4. Discuss the inverse: deriving the shape of the  displacement curve based on the velocity versus  time graph; deriving the shape of the velocity curve  based on the acceleration versus time graph.  5. Displacement versus time:  - graph of a line with positive/negative slope ???? positive/negative constant velocity  - graph with monotonically increasing slope ????  increasing velocity  - graph with monotonically decreasing slope ???? decreasing velocity  6. Velocity versus time:  - graph of a line with positive/negative slope ???? positive/negative constant acceleration  - graph with monotonically increasing slope ????  increasing acceleration

GP1-04-7 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line   - graph with monotonically decreasing slope ???? decreasing acceleration  warning: the non-linear parts of the graph were strategically  chosen as sections of a parabola—hence the  corresponding first derivate of these sections is either a  negatively sloping line (for a downward opening parabola)  or a positively sloping line (for an upward opening parabola) Figure 4. Displacement versus time and the corresponding  velocity graphs.

GP1-04-8 GENERAL PHYSICS 1  QUARTER 1  Motion Along a Straight Line    Figure 5. Velocity versus time and the corresponding  acceleration graphs.

Evaluation (15 minutes)  Given a sinusoidal displacement versus time graph  (displacement = A sin(bt); b = 4π/s, A = 2 cm), ask the  class to graph the corresponding velocity versus time and  acceleration versus time graphs. Recall that the velocity is  the first derivative of the displacement with respect to time  and that the acceleration is the first derivative with respect  to time. At which parts of the graph would the velocity or  acceleration become zero or at maximum value (positive or  negative)? Discuss where the equilibrium position would be  based on the motion (as illustrated by the displacement  versus curve graph). What happens to the velocity and  acceleration at the equilibrium position?

GP1-04-9 GENERAL PHYSICS 1  QUARTER 1  TOPIC   TOPIC / LESSON NAME GP1 – 05: Motion with constant acceleration, freely falling bodies CONTENT STANDARDS Uniformly accelerated linear motion  Free-fall motion PERFORMANCE STANDARDS Solve, using experimental and theoretical approaches, multiconcept, rich-context problems  involving measurement, vectors, motions in 1D, 2D, and 3D, Newton’s Laws, work, energy,  center of mass, momentum, impulse, and collisions LEARNING COMPETENCIES 1. Solve for unknown quantities in equations involving one-dimensional uniformly  accelerated motion (STEM_GP12KIN-Ib-17)  2. Use the fact that the magnitude of acceleration due to gravity on the Earth’s surface  is nearly constant and approximately 9.8m/s2 in free-fall problems (STEM_GP12KIN Ib-18) SPECIFIC LEARNING OUTCOMES

TIME ALLOTMENT 60 minutes

Lesson Outline:  1. Introduction / Review: Review of differentiation and integration of polynomials (10 minutes)  2. Motivation: (15 minutes) Mini-experiment on free-frall motion of bodies with different masses  3. Instruction / Delivery/Practice: (25 to 35 minutes)  Derive the velocity and position formulas for one-dimensional uniformly accelerated motion using calculus  Use the data obtained in the mini-experiment and kinematic equations to calculate the local value of the  gravitational acceleration  Solve sample exercises  4. Enrichment: (0 to 10 minutes) Homework or group discussion on : a) Terminal velocity (Homework) or b) Hunter and monkey problem  5. Evaluation: (10 minutes) Problem solving exercise MATERIALS Rubber balls of varying mass (or equivalent objects)  Meter stick (or tape measure), Stop watch RESOURCES University Physics by Young and Freedman (12th edition)  Physics by Resnick, Halliday, and Krane (4th edition)

GP1-05-1  GENERAL PHYSICS 1  QUARTER 1  TOPIC   PROCEDURE MEETING LEARNERS’ Introduction/Review (10 minutes)  1. Give a brief review of differentiation and integration  polynomials.

Motivation (15 minutes)  “Which object will fall faster?”  1. Divide the class into 2 groups and let them device a  simple experiment to test whether the object with  higher mass will fall faster (or whether two objects of  different masses will accelerate differently at free fall).  (3 minutes)  2. The 2 groups organize to perform their designed  experiments. (6 minutes)  3. The representative of each group reports their  observations and results. (6 minutes)  Possible execution:  An object is released from a specific height and the total  time of falling is recorded. This is repeated for another  object with a different mass falling from the same initial  height. Does the heavier object fall faster? The acceleration  is estimated from the calculated average speeds based on  the total time falling at different initial heights. Does this  acceleration equal the acceleration due to gravity?

Instruction / Delivery/Practice (25 minutes)

GP1-05-2 GENERAL PHYSICS 1  QUARTER 1  TOPIC   1. The acceleration (a) can be written as the time  derivative of the velocity (v):  ! =#\$#% & =#!#% & =#'\$ #%' - Since the velocity is the first derivative of the displacement in terms of time, the acceleration is  then the second derivative of the displacement in  terms of time.  - Review the notion of time derivative using the ratio of  the change in the magnitude considered divided by  the corresponding change in time as the change in  time become infinitesimally small. Thus, the time  derivative gives the instantaneous rate of change of  the considered quantity varying in time  Figure. Variable s varies as a

GP1-05-3 GENERAL PHYSICS 1  QUARTER 1  TOPIC   function of time t. As Δt becomes  infinitesimally small, the average  slope Δs/Δt approaches the  instantaneous slope at time to.  The instantaneous slope is the  velocity at to when the variable s is the displacement. The second  derivative of the velocity is the  acceleration, the rate of change  of velocity at a given time.  2. The displacement can then be derived by successive  integration:  !" !# = % , + & !" = & % !#  → " ) "* = %# ,- * " = %# . "* /0 /+ = %# . "* 0 + = 12 %#8 . "*# & !1, = & 3%#4 . "*5 !# 4 →1)1* 0- * 1 =12 %#8 . "*#.1*

GP1-05-4 GENERAL PHYSICS 1  QUARTER 1  TOPIC   Where:  vo = initial velocity  xo = initial position  initial time = 0  Note that the initial velocity and the initial position  contribute to the final position. When the initial time is  not zero, t here refers to the total duration time of the  motion (i.e., the difference between the final and initial  time values).  Note: Primed variables are introduced during integration  because the result is supposed to be substituted by the  integration limits.  3. Based on the expression above calculate the  acceleration due to gravity based on measurements in  the motivation experiment. If the students were not successful in the motivation exercise, perform the  experiment where the total time of falling is measured  for the different masses falling from the same height  (where the initial velocity is then zero, the final distance  is zero, and the initial distance is the height from which  the ball fell).  4. Solve example exercises (applying formulas derived in  the previous lesson)  Different scenarios involving a moving jeepney: a.  running from zero velocity to a final velocity in a given  time or distance; b. one jeepney overtaking another by Tips for the teacher  Do not expect to be able to measure the exact value for the  acceleration due to gravity. Allow the students to discuss  the measured result based on previous lessons in error  analysis and notions of average velocities and  accelerations. Be careful with the use of the positive or  negative sign for velocity or acceleration. For instance, the  acceleration is negative when the corresponding velocity is  slowing down. The choice of coordinates is also a factor.  For instance at free fall (from zero velocity, from an initial  height y0), choosing the vertical axis as y, the right hand  side is negative because the displacement is becoming  smaller (not because the coordinate is negative; in fact, the

GP1-05-5 GENERAL PHYSICS 1  QUARTER 1  TOPIC   increasing its velocity to a final velocity within a given  time or distance.  Scenarios of free fall: a. time required for falling from a  given height; b. time of flight given an initial velocity  (directed horizontally or vertically). coordinate varies from an initial value y0):  ! " !# = " 12 #\$% & = &( − 12 #\$% Enrichment (0 to 10 minutes)  For class group discussions or homework (10 minutes for  group discussions)  1. Terminal velocity (introduce the use of an integration  table; assignment)  2. A hunter on the ground sees a monkey jump at a  certain tree height, from a given horizontal distance.  Ask where the hunter should aim his gun (e.g.,  whether the hunter should anticipate where the  monkey would fall when the bullet reaches the  monkey).

Evaluation (10 minutes)  Problem solving exercise – see Item 4 of  Instruction/Delivery/Practice for suggestions.

GP1-05-6 GENERAL PHYSICS 1  QUARTER 1  TOPIC   TOPIC / LESSON NAME GP1 – 06: Context rich problems involving motion in one-dimension CONTENT STANDARDS 1D Uniform Acceleration Problem PERFORMANCE STANDARDS Solve, using experimental and theoretical approaches, multiconcept, rich-context problems involving measurement, vectors, motions in 1D, 2D, and 3D, Newton’s Laws, work, energy,  center of mass, momentum, impulse, and collisions LEARNING COMPETENCIES 1. Solve problems involving one-dimensional motion with constant acceleration in  contexts such as, but not limited to, the “tailgaiting phenomenon”, pursuit, rocket  launch, and free-fall problems (STEM_GP12KIN-Ib-19) SPECIFIC LEARNING OUTCOMES

TIME ALLOTMENT 60 minutes

Lesson Outline:  1. Introduction / Review/Motivation: (15 minutes)  Reaction time experiment using ruler with discussion  Review of equations for 1D kinematics  2. Instruction / Delivery/Practice: (45 minutes) Assisted group problem solving (Suggested contexts: tail-gaiting  phenomenon and pursuit, rocket launch, free-fall without air resistance) MATERIALS paper, ruler RESOURCES University Physics by Young and Freedman (12th edition)  Physics by Resnick, Halliday, and Krane (4th edition)  http://www.physics.umd.edu/ripe/perg/abp/think/mech/mechki.htm  http://groups.physics.umn.edu/physed/Research/CRP/on-lineArchive/ola.html

PROCEDURE MEETING LEARNERS’ Introduction/Review/Motivation (15 minutes)  1. Ruler drop experiment to measure reaction time.

GP1-06-1  GENERAL PHYSICS 1  QUARTER 1  TOPIC   Ask pairs of students to measure their reaction time. One  volunteer holds the ruler with the thumb and forefinger on  the upper tip. While the lower tip of the ruler is just before  the open hand of the other volunteer.  Figure 1. Ruler drop experiment.  (redraw this figure)  The ruler is dropped from the tip by the first volunteer while  the other tries to catch it. Assuming the ruler falls freely due  to gravity. Determine the time the ruler fell by the  displacement of the ruler at free fall measured from the  lower tip of the ruler to where the second volunteer caught  the ruler. During this experiment, the volunteers should not  look at each other to ensure that the one trying to catch the  ruler reacts only from the moment it sees the ruler falling.  Repeat a few times to get an average. If there are several  pairs who performed the experiment, measure the total  average from all the pairs.  2. Allow the students to discuss what processes occurs  between seeing the ruler fall and the brain telling the hand

GP1-06-2 GENERAL PHYSICS 1  QUARTER 1  TOPIC   to catch the ruler.  For example, the eye first sends signals to the visual cortex  which then notifies the motor cortex that eventually sends a  signal via the spinal cord to the hand to catch the ruler.  Each takes some time to perform.  3. Review previous lessons on motion along a straight line,  speed, velocity, and motion with constant acceleration.  Displacement, given acceleration  Eqn1 ∆" = \$%% − \$'% a, initial and final velocities, v1 2) and v2, respectively.  Eqn2 \$ = )* + \$,Velocity, given acceleration a,  time t, and initial velocity vo.  Eqn3 " = 12 )*% + \$,* + ",Displacement x, given acceleration  a, time t, initial velocity vo, and  initial displacement xo. Eqn4 . = ., − 12 /*%Free fall: vertical displacement y,  from an initial height yo, time t,  and acceleration due to gravity g.

Instruction/Delivery/Practice (45 minutes)  Let the students answer the problems below in groups with  your assistance:

1. Tailgaiting phenomenon and pursuit  Explain that tailgating is when a car follows another car  too closely, narrowing the distance between them. Processes involved for 1a.(Keep these in mind while guiding the students)