# 3.6 Solving Problems Involving Projectile Motion

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1 INTRODUCTION 1-2 Physics and its relation to other fields introduction of physics, its importance and scope 1-5 Units, standards, and the SI System description of the SI System description of base and derived quantities 1-6 Converting units practice of unit conversion 1-7 Order of Magnitude: Rapid Estimating 1-8 Dimensions and Dimensional Analysis Appendix A: Mathematical Review 2. DESCRIBING MOTION: KINEMATICS IN ONE DIMENSION (BIG IDEA 3) 2.1 Reference frames and displacement Description of a frame of reference Definition of displacement 2.2 Average velocity 2.3 Instantaneous Velocity Definition of average and instantaneous velocity 2.4 Acceleration Definition of acceleration and discussion of direction of acceleration 2.5 Motion at constant acceleration Derivation of four kinematic equations when acceleration is constant 2.6 Solving problems 2.7 Falling objects Use the kinematic equations to solve problems involving free fall by using the value of the acceleration due to gravity 2.8 Graphical analysis of motion Graphs of position versus time Graphs of velocity versus time Calculation of shape and area under the curves for various motion graphs 3. KINEMATICS IN TWO DIMENSIONS, VECTORS (BIG IDEA3) 3.1 Vectors and scalars Distinguish between vectors and scalars 3.2 Addition of vectors: graphical methods Addition of two vectors along the same line Addition of two vectors at right angles to one another Parallelogram method and polygon method 3.3 Subtraction of Vectors, and Multiplying of a vector by a Scalar 3.4 Adding vectors by components Component method of vector addition 3.5 Projectile motion Definition of projectile motion and its characteristics Solving problems of projectiles fired horizontally and at an angle

2 3.6 Solving Problems Involving Projectile Motion 4. MOTION AND FORCE: DYNAMICS (BIG IDEAS 1, 2, 3 AND 4) 4.1 Force Definition of force 4.2 Newton s first law of motion Contrast Aristotle s and Galileo s view of motion Statement of Newton s first law of motion Definition of inertia 4.3 Mass Definition of mass and standard units of mass 4.4 Newton s Second Law of Motion Statement and equation of Newton s second law of motion 4.5 Newton s Third Law of Motion Statement of Newton s third law of motion Examples of this law 4.6 Weight The force of gravity and the normal force Calculation of weight using the acceleration due to gravity Discuss the value of a g near the surface of the earth Definition and discussion of the normal force Applications Involving friction, inclines Definition of kinetic friction and its relationship to the normal force between surfaces Definition of static friction Coefficients of static and kinetic friction Normal and frictional forces on an inclined plain 5. CIRCULAR MOTION, GRAVITATION (BIG IDEAS 1, 2, 3 AND 4) 5.1 Kinematics of Uniform Circular Motion Definition of uniform circular motion Derivation of the equation of the centripetal acceleration of an object moving in a circle at constant speed 5.2 Dynamics of Uniform Circular Motion Understand that centripetal force is not some new type of force Understand that centrifugal force does not exist 5.3 A Car Rounding a Curve Driving on curve examples Banking angles calculation 5.4 Nonuniform Circular Motion 5.6 Newton s Law of Universal Gravitation Newton s derivation of his law of universal gravitation Statement of the law of universal gravitation Cavendish experiment and the value of the universal gravitation constant 5.7 Gravity Near the Earth s Surface Derivation of the acceleration due to gravity at the surface of the earth Geophysical applications

3 5.8 Satellites and weightlessness The relationship between the speed and the orbital radius of a satellite Apparent weightlessness in a satellite and in an elevator Kepler s Laws* Statement of Kepler s three laws of planetary motion Derivation of Kepler s third law of planetary motion 6. WORK AND ENERGY (BIG IDEAS 3, 4 AND 5) 6.1 Work Done by a Constant Force Definition of work done by a constant force 6.2 Work Done by a Varying Force Graphical method of estimating the work done by a varying force 6.3 Kinetic Energy and the Work-Energy Theorem Definition of energy as the ability to do work Definition of kinetic energy and the derivation of its equation Statement of the work-energy theorem 6.4 Potential Energy Definition of potential energy and gravitational potential energy Equation for the change in gravitational potential energy General relationship between the change in potential energy and the force producing that change Equation for the change in elastic potential energy 6.5 Conservative and Non conservative Forces Distinguish between conservative and non conservative forces General form of the work-energy theorem 6.6 Mechanical Energy and its Conservation Statement of the law of conservation of energy Power Definition of power 7.LINEAR MOMENTUM (BIG IDEAS 3, 4 AND 5) 7.1 Momentum and its Relation to Force Definition of linear momentum Restatement of Newton s second law of motion in terms of momentum 7.2 Conservation of Momentum Derivation of the conservation of momentum theorem for a one dimensional collision 7.3 Collisions and Impulse Definition of impulse Conservation of Energy and Momentum in collisions Definition of elastic and inelastic collisions and problems involving both types of collisions 7.7 Collisions in Two Dimensions Problem solving for collisions in two dimensions Center of Mass Determination of the center of mass 8. ROTATIONAL MOTION (BIG IDEAS 3, 4 AND 5)

4 8.1 Angular Quantities Definition of angular displacement Definition of angular velocity Definition of angular acceleration 8.2 Constant Angular Acceleration Torque Definition of the lever arm of a force about an axis of rotation Definition of the torque of a given force about an axis of rotation Sign convention for torques 8.5 Rotational Dynamics: Torque and Rotational Inertia 8.6Angular Momentum and Its Conservation 11. VIBRATIONS AND WAVES (BIG IDEAS 3 AND 5) 11.1 Simple Harmonic Motion Definitions of vibrations, periodic motion, equilibrium position, displacement, amplitude, period and frequency Description of the motion of an oscillating spring Definition of simple harmonic motion 11.4 The Simple Pendulum Derivation of the period of a simple pendulum 11.6 Forced Vibrations: Resonance Definition the natural frequency of an object Definition of resonance and resonant frequency Description of examples of resonance 11.7 Wave Motion A wave pulse and a periodic wave are defined A periodic sinusoidal wave is described Equation for wave velocity in terms of its frequency and wavelength 11.8 Types of Waves: Transverse and Longitudinal Definition, characteristics and examples of longitudinal transverse and surface waves 11.9 Energy Transmitted by Waves Describe the relationship between energy of a wave and its amplitude Reflection and Interference of Waves Description of the behavior of waves at a boundary Distinguish between constructive and destructive interference The principle of superposition is stated Standing Waves Definition of standing waves Calculation of the fundamental frequency and overtones 12. SOUND (BIG IDEA 6) 12.1 Characteristics of Sound The speed of sound in air as a function of temperature is given The pitch of a sound is defined as its frequency

5 Ultrasonic and infrasonic sound waves are defined 12.4 Sources of sound The origin of sound in musical instruments is described The resonant frequencies in stringed instruments is described Standing waves are described for a tube open at both ends and for a tube closed at one end Overtones are defined and calculated 12.6 Interference of Sound Waves; Beats the interference of sound waves and the formation of beats are discussed 12.7 Doppler Effect the equations relating frequencies are derived for relative motion between source and observer 16.ELECTRIC CHARGE AND ELECTRIC FIELD (BIG IDEA 1, 2, 3, 4 AND 5) 16.1 Static electricity; Electric Charge and its conservation The origin of the word electricity is described Definition of electrostatics and the nature of an electric charge State the law of electrostatics and the law of conservation of charge 16.2 Electric Charge in the Atom 16.3 Insulators and Conductors Explain the charging an object by contact Definition of conductors and insulators Understand the distribution of charge in a conductor Discuss semiconductors 16.4 Induced Charge; the Electroscope Explain the charging of an object by induction 16.5 Coulomb s Law State Coulomb s law and its equation to calculate the electrostatic force between two charges Define the permittivity of free space 16.7 The Electric Field 16.8 Field Lines The electric field is defined and an expression for it is derived for a single point charge Electric field lines are described as means to depict the electric field 17. ELECTRIC POTENTIAL AND ELECTRIC ENERGY; CAPACITANCE (BIG IDEA 1, 2, 3, 4, 5) Electric Potential and Potential Difference Electric potential is defined as the difference in potential Definition of the volt 17.2 Relation Between Electric Potential and Electric Field The relationship of the potential difference between two points to the uniform electric field existing between the points is given 17.3 Equipotential Lines Equipotential lines and surfaces are defined 17.4 The Electron volt, a Unit of Energy

6 Definition of Electronvolt 17.5 Electric Potential due to Point Charges The potential due to a single point charge is given 17.7 Capacitance 17.8 Dieletrics 17.9 Storage of Electric Energy A capacitor is defined as is its capacitance The equation for the capacitance of a parallel plate capacitor is given The effect of introducing a dielectric into a parallel plate capacitor is discussed An expression for the energy stored in a parallel plate capacitor is derived 18. ELECTRIC CURRENTS (BIG IDEA 1, 2, 3, 4, 5) 18.1 The Electric Battery 18.2 Electric Current The electric current and its unit, the ampere are defined 18.3 Ohm s Law: Resistance and Resistors 18.4 Resistivity Ohm s Law is stated and its equation is given The factors affecting the resistance of a conductor are discussed Electric Power The equation relating electric power to current and voltage is given 19 DC CIRCUITS (BIG IDEA 1, 2, 3, 4, 5) 19.1 EMF and Terminal voltage A source of electromotive force is defined The internal resistance of a battery is defined The equation to calculate the terminal voltage is derived 19.2 Resistors in Series and Parallel Series and parallel circuits are analyzed and calculations of equivalent resistance, current and voltage drop are performed 19.3 Kirchhoff s Laws Kirchhoff s laws to solve complex networks are given 19.5 Circuits containing Capacitors in Series and in Parallel Series and parallel circuits are analyzed and calculations of equivalent capacitance and voltage and charge are performed 19.6 RC Circuits-Resistors and Capacitors in Series

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